Riemann solvers and numerical methods for fluid dynamics: A practical introduction

Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction

Volumn , Issue , 2009, Pages 1-724

  Toro, Eleuterio F ^a  

^a UNIVERSITY OF TRENTO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84889809594     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/b79761     Document Type: Book

References (600)

1. R. Abgrall. How to Prevent Pressure Oscillations in Multicomponent Flow Calculations: A Quasiconservative Approach. J. Comput. Phys., 125: 150-160, 1996.
2. R. Abgrall and M. Mezine. Construction of Second-Order Accurate Monotone and Stable Residual Distribution Schemes for Steady Problems. J. Comput. Phys., 195: 474-507, 2004.
3. C. M. Albone. Report on the AGCFM Working Party on Software Quality Assurance. Technical Report AERO 2105, Royal Aircraft Establishment, Farnborough, UK, 1987.
4. A. Alcrudo and P. García-Navarro. A High Resolution Godunov-Type Scheme in Finite Volumes for the 2D Shallow Water Equations. Int. J. Num. Meth. Fluids, 16: 489-505, 1993.
5. S. R. Allmaras. Contamination of Laminar Boundary Layers by Artificial Dissipation in Navier-Stokes Solutions. In Numerical Methods for Fluid Dynamics, 4, pages 443-449. Oxford University Press, 1993.
6. V. R. Ambati and O. Bokhove. Space-Time Discontinuous Galerkin Discretization of Rotating Shallow Water Equations. J. Comput. Phys., 225(2):1233-1261, 2007.
7. D. A. Anderson, J. C. Tannehill, and R. H. Pletcher. Computational Fluid Mechanics and Heat Transfer. Hemisphere Publishing Corporation, 1984.
8. D. S. Anderson and J. J. Gottlieb. On Random Numbers for the Random Choice Method. Technical Report 258, UTIAS, University of Toronto, Canada, 1987.
9. J. D. Anderson. Hypersonic and High Temperature Gas Dynamics. McGraw-Hill, 1989.
10. J. D. Anderson. Modern Compressible Flow. Mc Graw-Hill, 1990.
11. J. L. Anderson, S. Preiser, and E. L. Rubin. Conservation Form of the Equations of Hydrodynamics in Curvilinear Coordinate Systems. J. Comput. Phys., 2: 279-287, 1968.
12. W. Anderson, J. L. Thomas, and B. van Leer. Comparison of Finite Volume Flux Vector Splittings for the Euler Equations. AIAA Journal, 24: 1453-1460, 1986.
13. W. K. Anderson, J. L. Thomas, and L. Rumsey. Extension and Application of Flux-Vector Splitting to Calculations on Dynamic Meshes. AIAA Journal, 27: 673-674, 1989.
14. N. Andrianov and G. Warnecke. The Riemann Problem for the Baer-Nunziato Two-Phase Flow Model. J. Comput. Phys., 212: 434-464, 2004.
15. T. M. Apostol. Mathematical Analysis. Addison-Wesley Publishing Company, 1974.
16. P. Arminjon and A. St-Cyr. Nessyahu-Tadmor Type Central Finite Volume Methods Without Predictor for 3D Cartesian and Unstructured Tetrahedral Grids. Applied Numerical Mathematics, 46: 135-155, 2003.
17. P. Arminjon, A. St-Cyr, and A. Madrane. New Two- and Three Dimensional Non-Oscillatory Central Finite Volume Methods on Staggered Cartesian Grids. Applied Numerical Mathematics, 40: 367-390, 2002.
18. P. Arminjon and R. Touma. Central Finite Volume Methods with Constrained Transport Divergence Treatment for Ideal MHD. J. Comput. Phys., 204: 737-759, 2005.
19. M. Arora and P. L. Roe. On Postshock Oscillations Due to Shock Capturing Schemes in Unsteady Flows. J. Comput. Phys., 130: 25-40, 1997.
20. E. H. Atta and J. Vadyak. A Grid Overlapping Scheme for Flowfield Computations About Multicomponent Configurations. AIAA Journal, 21(9):1271-1277, 1983.
21. M. R. Baer and J. W. Nunziato. A Two-Phase Mixture Theory for the Deflagration-to-Detonation Transition (DDT) in Reactive Granular Materials. J. Multiphase Flow, 12: 861-889, 1986.
22. M. J. Baines and M. E. Hubbard. Multi-dimensional Upwinding with Grid Adaptation. In Numerical Methods for Wave Propagation. Toro, E. F. and Clarke, J. F. (Editors), pages 33-54. Kluwer Academic Publishers, 1998.
23. M. J. Baines and P. K. Sweby. A Flux Limiter Based on Fromm's Scheme. Technical Report 9/84, Department of Mathematics, University of Reading, UK, 1984.
24. G. J. Ball and R. A. East. Shock and Blast Attenuation by Aqueous Foam Barriers: Influences of Barrier Geometry. J. Shock Waves, 9(1):37-47, 1999.
25. D. Balsara and C. W. Shu. Monotonicity Preserving Weighted Essentially Nonoscillatory Schemes with Increasingly High Order of Accuracy. J. Comput. Phys., 160: 405-452, 2000.
26. D Balsara and D. Spicer. A Staggered Mesh Algorithm Using High Order Godunov Fluxes to Ensure Solenoidal Magnetic Fields in Magnetohydrodynamic Simulations. J. Comput. Phys., 149: 270-292, 1999.
27. D. Balsara and D. Spicer. Maintaining Pressure Positivity in Magneto-hydrodynamic Simulations. J. Comput. Phys., 149: 133-148, 1999.
28. D. S. Balsara, T. Rumpf, M. Dumbser, and C. D. Munz. Efficient, High Accuracy ADER-WENO Schemes for Hydrodynamics and Divergence-Free Magnetohydrodynamics. J. Comput. Phys., 2008 (Submitted).
29. A. A. Barmin, A. G. Kulikovskii, and N. V. Pogorelov. Shock-Capturing Approach and Nonevolutionary Solutions in Magnetohydrodynamics. J. Comput. Phys., 126: 77-90, 1996.
30. F. Bassi, A. Crivellini, D. A. Di Pietro, and S. S. Rebay. An Artificial Compressibility Flux for the Discontinuous Galerkin Solution of the Incompressible Navier-Stokes Equations. J. Comput. Phys., 218: 794-815, 2006.
31. F. Bassi and S. S. Rebay. High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations. J. Comput. Phys., 131: 267-279, 1997.
32. P. Batten, N. Clarke, C. Lambert, and D. Causon. On the Choice of Wave Speeds for the HLLC Riemann Solver. SIAM J. Sci. and Stat. Comp., 18: 1553-1570, 1997.
33. P. Batten, M. A. Leschziner, and U. C. Goldberg. Average-State Jacobians and Implicit Methods for Compressible Viscous and Turbulent Flows Flows. J. Comput. Phys., 137: 38-78, 1997.
34. A. Bayliss and E. Turkel. Radiation-Boundary Conditions for Wave-Like Equations. Comm. Pure and Appl. Maths., 33: 708-725, 1980.
35. E. Becker. Gas Dynamics. Academic Press, 1968.
36. M. Ben-Artzi. Application of the Generalised Riemann Problem Method to 1-D Compressible Flows with Interfaces. J. Comput. Phys., 65: 170-178, 1986.
37. M. Ben-Artzi and J. Falcovitz. A Second Order Godunov-Type Scheme for Compressible Fluid Dynamics. J. Comput. Phys., 55: 1-32, 1984.
38. M. Ben-Artzi and J. Falcovitz. A High Resolution Upwind Scheme for Quasi 1-D Flows. In Numerical Methods for the Euler Equations of Fluid Dynamics, pages 66-83. INRIA, SIAM, 1985.
39. M. Ben-Artzi and J. Falcovitz. Generalized Riemann Problems in Computational Fluid Dynamics. Cambridge University Press, 2003.
40. M. Ben-Artzi and J. Li. Hyperbolic Balance Laws: Riemann Invariants and Hyperbolic Balance Laws. Numerische Mathematik, 106: 69-425, 2007.
41. M. Ben-Artzi, J. Li, and G. Warnecke. A Direct Eulerian GRP Scheme for Compressible Fluid Flows. J. Comput. Phys., 218(19-43), 2006.
42. G. Ben-Dor. Shock Wave Reflection Phenomena. Springer-Verlag, 1992.
43. J. A. Benek, J. L. Steger, and F. C. Dougherty. A Flexible Grid Embedding Technique with Application to the Euler Equations. AIAA Paper 83-1944, 1983.
44. F. Benkhaldoun and A. Chalabi. Characteristic Based Scheme for Conservation Laws with Source Terms. Technical Report 95.15, Centre National de la Recherche Scientifique, Université Paul Sabatier, UFR-MIG, 118 route de Narbone, 31062, Toulouse Cedex, France, 1995.
45. M. J. Berger. Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations. PhD thesis, Dept. of Computer Science, Stanford University, California, 1982.
46. M. J. Berger and P. Colella. Local Adaptive Mesh Refinement for Shock Hydrodynamics. J. Comput. Phys., 82: 64-84, 1989.
47. M. J. Berger and R. J. LeVeque. Stable Boundary Conditions for Cartesian Grid Calculations. Technical Report ICASE 90-37, NASA Langley Research Center, USA, 1990.
48. M. J. Berger and J. Oliger. Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations. J. Comput. Phys., 53: 484-512, 1984.
49. A. C. C. Berkenbosch, E. F. Kaasschieter, and J. H. M. ten Thije Boonkkamp. The Numerical Computation of One-dimensional Detonation Waves. Technical Report RANA 94-21, Eindhoven University of Technology, Department of Mathematics and Computer Science, The Netherlands, 1994.
50. L. Bermúdez, A. Dervieux, J. A. Desideri, and M. E. Vázquez. Upwind Schemes for the Two-Dimensional Shallow Water Equations with Variable Depth Using Unstructured Meshes. Technical Report 2738, INRIA, Rocquencourt, 78153 Le Chesnay, France, 1995.
51. L. Bermúdez and M. E. Vázquez. Upwind Methods for Hyperbolic Conservation Laws with Source Terms. Computers and Fluids, 23: 1049-1071, 1994.
52. H. Bershader and R. Hanson (Editors). Shock Waves and Shock Tubes (Proc. 15th Int. Symp. on Shock Waves and Shock Tubes, Berkeley, California, USA 1985). Stanford University Press, 1986.
53. C. Berthon, P. Charrier, and B. Dubroca. An HLLC Scheme to Solve The M1 Model of Radiative Transfer in Two Space Dimensions. Journal of Scientific Computing, 31(3):347-389, 2007.
54. C. Berthon, F. Coquel, J. M. Hérard, and M. Uhlmann. An Approximate Solution of the Riemann Problem for a Realisable Second-Moment Turbulent Closure. J. Shock Waves, 11(2):245-269, 2002.
55. M. Berzins, P. M. Dew, and R. M. Fuzerland. Developing Software for Time-Dependent Problems Using the Method of Lines and Differential Algebraic Integrators. Applied Numerical Mathematics, 5: 375-397, 1989.
56. M. Berzins and J. M. Ware. Solving Convection and Convection Reaction Problems using M. O. L. Applied Numerical Mathematics, 20: 83-89, 1996.
57. F. Bianco, G. Puppo, and G. Russo. High Order Central Schemes for Hyperbolic Systems of Conservation Laws. SIAM J. Scientific Computing, 21: 294-322, 1999.
58. S. J. Billett. Numerical Aspects of Convection Diffusion Problems. MSc. Thesis, College of Aeronautics, Cranfield Institute of Technology, UK, 1991.
59. S. J. Billett. A Class of Upwind Methods for Conservation Laws. Ph. D thesis, College of Aeronautics, Cranfield University, UK, 1994.
60. S. J. Billett and E. F. Toro. Restoring Monotonicity of Slowly-Moving Shocks Computed with Godunov-Type Schemes. CoA Report 9207, Cranfield Institute of Technology, UK, 1992.
61. S. J. Billett and E. F. Toro. Implementing a Three-Dimensional Finite Volume WAF-Type Scheme for the Euler Equations. In Proc. Third ECCOMAS Computational Fluid Dynamics Conference, 9-13 September 1996, Paris, France, pages 732-738. Wiley, 1996.
62. S. J. Billett and E. F. Toro. On the Accuracy and Stability of Explicit Schemes for Multi-dimensional Linear Homogeneous Advection Equations. J. Comp. Phys., 131: 247-250, 1997.
63. S. J. Billett and E. F. Toro. WAF-Type Schemes for Multi-dimensional Hyperbolic Conservation Laws. J. Comp. Phys., 130: 1-24, 1997.
64. S. J. Billett and E. F. Toro. UnsplitWAF-Type Schemes for Three Dimensional Hyperbolic Conservation Laws. In Numerical Methods for Wave Propagation. Toro, E. F. and Clarke, J. F. (Editors), pages 75-124. Kluwer Academic Publishers, 1998.
65. S. J. Billett and E. F. Toro. TVB Limiter Functions for Multi-dimensional Schemes. In Proc. 6th Intern. Symposium on Computational Fluid Dynamics, Lake Tahoe, Nevada, USA, pages 117-122, September 4-8, 1995.
66. E. P. Boden. An Adaptive Gridding Technique for Conservation Laws on Complex Domains. PhD thesis, Department of Aerospace Science, Cranfield University, UK, 1997.
67. E. P. Boden and E. F. Toro. A Combined Chimera-AMR Technique for Hyperbolic PDEs. In Proc. Fifth Annual Conference of the CFD Society of Canada, pages 5.13-5.18. University of Victoria, Canada, 1997.
68. G. Bodo, S. Masaglia, A. Mignone, and P. Rossi (Editors). Jets from Young Stars III. Numerical MHD and Instabilities. Lecture Notes in Physics 754. Springer, 2008.
69. D. L. Book, J. P. Boris, and K. Hain. Flux Corrected Transport II: Generalizations of the Method. J. Comput. Phys., 18: 248-283, 1975.
70. J. P. Boris and D. L. Book. Flux-Corrected Transport. I. SHASTA, A Fluid Transport Algorithm that Works. J. Comput. Phys., 11: 38-69, 1973.
71. J. P. Boris and D. L. Book. Flux-Corrected Transport III: Minimal-Error FCT Algorithms. J. Comput. Phys., 20: 397-431, 1976.
72. J. P. Boris and E. S. Oran. Numerical Simulation of Reactive Flow. Elsevier, Amsterdam-New York, 1987.
73. A. G. L. Borthwick, M. Fujihara, and B. D. Rogers. Godunov Solutions of Shallow Water Equations on Curvilinear and Quadtree Grids. In Godunov Methods: Theory and Applications. Edited Review, E. F. Toro (Editor), pages 141-148. Kluwer Academic/Plenum Publishers, 2001.
74. F. Bouchut. Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation laws and Well-Balanced Schemes. Birkhäuser, 2004.
75. F. Bouchut, C. Klingenberg, and K. Waagan. A Multiwave Approximate Riemann Solver for Ideal MHD Based on Relaxation I - Theoretical Framework. Numer. Math., 108(1):7-42, 2007.
76. A. Bourgeade, P. Le Floch, and Raviart P. A. An Asymptotic Expansion for the Solution of the Generalized Riemann Problem. Part 2: Application to the Euler Equations of Gas Dynamics. Ann. Inst. Henri Poincaré. Analyse non Lineáre, 6(6):437-480, 1989.
77. A. Bourlioux and A. J. Majda. Theoretical and Numerical Structure for Unstable Two-Dimensional Detonations. Combustion and Flame, 90: 211-229, 1992.
78. A. Bourlioux, A. J. Majda, and V. Roytburd. Theoretical and Numerical Structure for Unstable One-Dimensional Detonations. SIAM J. Appl. Math., 51: 303-343, 1991.
79. C. E. Brennen. Fundamentals of Multiphase Flow. Cambridge University Press, 2005.
80. M. Brio and C. C. Wu. An Upwind Differencing Scheme for the Equations of Ideal Magnetohydrodynamics. J. Comput. Phys., 75: 400-422, 1988.
81. M. Brown. Differential Equations and their Applications. Springer-Verlag, 1975.
82. R. E. Brown. Numerical Solution of the 2D Unsteady Navier-Stokes Equations Using Viscous-Convective Operator Splitting. MSc. Thesis, Department of Aerospace Science, Cranfield University, UK, 1990.
83. R. Brun and L. Z. Dumitrescu (Editors). Shock Waves @ Marseille (Proc. 19th Int. Symp. on Shock Waves, Marseille, France, 1993), Four Volumes. Springer-Verlag, 1995.
84. M. Cáceres. Development of a Third-Order Accurate Scheme of the MUSCL Type for the Time-Dependent One-Dimensional Euler Equations. MSc. Thesis, Department of Aerospace Science, Cranfield University, UK, 1993.
85. A. Canestrelli, A. Siviglia, M. Dumbser, and E. F. Toro. Well-Balanced High-Order Centred Schemes for Non-Conservative Hyperbolic Systems. Application to Shallow Water with Fixed and Mobile Bed. (Submitted), 2008.
86. G. Capdeville. Towards a Compact High-Order Method for Non-linear Hyperbolic Systems, II. The Hermite-HLLC Scheme. J. Comput. Phys., 227(22):9428-9462, 2008.
87. Carasso, Raviart, and Serre. Proc. First International Conference on Hyperbolic Problems. Springer, 1986.
88. J. Casper and H. L. Atkins. A Finite Volume High-Order ENO Scheme for Two-Dimensional Hyperbolic Systems. J. Comput. Phys., 106: 62-76, 1993.
89. C. E. Castro. High-Order ADER FV/DG Numerical Methods for Hyperbolic Equations. PhD thesis, Department of Civil and Environmental Engineering, University of Trento, Italy, 2007.
90. C. E. Castro and E. F. Toro. A Riemann Solver and Upwind Methods for a Two-Phase Flow Model in Non-Conservative Form. Int. J. for Numer. Meth. in Fluids, 60: 275-307, 2006.
91. C. E. Castro and E. F. Toro. Solvers for the High-Order Riemann Problem for Hyperbolic Balance Laws. J. Comput. Phys., 227: 2481-2513, 2008.
92. M. J. Castro, J. M. Gallardo, J. A. López, and C. Parés. Well-Balanced High Order Extensions of Godunov's Method for Semilinear Balance Laws. SIAM Journal of Numerical Analysis, 46: 1012-1039, 2008.
93. M. J. Castro, P. G. LeFloch, M. L. Muñoz-Ruiz, and C. Parés. Why Many Theories of Shock Waves are Necessary: Convergence Error in Formally Path-Consistent Schemes. J. Comput. Phys., 227: 8107-8129, 2008.
94. M. J. Castro, A. Pardo, C. Parés, and E. F. Toro. On Some FastWell-Balanced First Order Solvers for Nonconservative Systems. Mathematics of Computation, 2008 (submitted).
95. V. Casulli and E. F Toro. Preliminary Results on a Semi-Lagrangian Version of the WAF Method. Technical Report 9018, College of Aeronautics, Cranfield Institute of Technology, UK, 1990.
96. A. Chakraborty and E. F. Toro. Development of an Approximate Riemann Solver for the Steady Supersonic Euler Equations. The Aeronautical Journal, 98: 325-339, 1994.
97. S. R. Chakravarthy, D. A. Anderson, and M. D. Salas. The Split-Coefficient Matrix Method for Hyperbolic Systems of Gas Dynamics Equations. AIAA Paper 80-0268, AIAA 19th Aerospace Science Meeting, 1980.
98. A. Chalabi. Stable Upwind Schemes for Conservation Laws with Source Term. IMA J. Numer. Anal., 12: 217-241, 1992.
99. A. Chalabi. On Convergence of Numerical Schemes for Hyperbolic Conservation Laws with Stiff Source Terms. Technical Report 95.22, Centre National de la Recherche Scientifique, Université Paul Sabatier, UFR-MIG, 118 route de Narbone, 31062, Toulouse Cedex, France, 1995.
100. A. Chalabi. An Error Bound for the Polygonal Approximation of Hyperbolic Conservation Laws with Source Terms. Computers and Mathematics with Applications, 32: 59-63, 1996.
101. A. Chalabi. On Convergence of Numerical Schemes for Hyperbolic Conservation Laws with Stiff Source Terms. Math. of Comput., 66: 527-545, 1997.
102. C. H. Chang and M. S. Liou. A Robust and Accurate Approach to Computing CompressibleMultiphase Flow: Stratified Flow Model and AUSM+ up Scheme. J. Comput. Phys., 225: 840-873, 2007.
103. G. Q. Chen and E. F. Toro. Centred Schemes for Non-Linear Hyperbolic Equations. Journal of Hyperbolic Differential Equations, 1(1):531-566, 2004.
104. D. N. Cheney. Upwinding Convective and Viscous Terms via a Modified GRP Approach. MSc. Thesis, Department of Aerospace Science, Cranfield University, UK, 1994.
105. G. Chesshire and W. D. Henshaw. Composite Overlapping Meshes for the Solution of Partial Differential Equations. J. Comput. Phys., 90: 1-64, 1990.
106. G. Chesshire and W. D. Henshaw. A Scheme for Conservative Interpolation on Overlapping Grids. SIAM J. Sci. Stat., 15(4):819-845, 1994.
107. B. L. Chessor, Jr. Evaluation of Computed Steady and Unsteady Quasi-One-Dimensional Viscous/Inviscid Interacting Internal Flow Fields Through Comparison with Two-Dimensional Navier-Stokes Solutions. MSc. Thesis, 1992, Mississippi State University, USA, 1992.
108. T. Chiang and Hoffmann K. K. AIAA 20th Fluid Dynamics, Plasma Dynamics and Lasers Conference, Buffalo, New York, June 12-14, USA, 1989, Paper AIAA 89-1855, 1989.
109. A. J. Chorin. A Numerical Method for Solving Viscous Flow Problems. J. Comput. Phys., 2: 12-26, 1967.
110. A. J. Chorin. Random Choice Solutions of Hyperbolic Systems. J. Comput. Phys., 22: 517-533, 1976.
111. A. J. Chorin. Random Choice Methods with Applications to Reacting Gas Flow. J. Comput. Phys., 25: 253-272, 1977.
112. A. J. Chorin and J. E. Marsden. A Mathematical Introduction to Fluid Mechanics. Springer-Verlag, 1993.
113. C. S. Chu and C. W. Shu. High Order Residual Distribution Conservative Finite Difference WENO Schemes for Convection-Diffusion Steady State Problems on Non-Smooth Meshes. J. Comput. Phys., 224: 992-1020, 2007.
114. D. K. Clarke, M. D. Salas, and H. A. Hassan. Euler Calculations for Multielement Airfoils Using Cartesian Grids. AIAA J., 24: 353-, 1987.
115. J. F. Clarke. Compressible Flow Produced by Distributed Sources of Mass: An Exact Solution. Technical Report CoA Report 8710, College of Aeronautics, Cranfield Institute of Technology, Cranfield, UK, 1987.
116. J. F. Clarke. Chemical Reactions in High Speed Flows. Phil. Trans. Roy. Soc. London, A 335: 161-199, 1989.
117. J. F. Clarke. Fast Flames, Waves and Detonations. Prog. Energy Comb. Sci., 15: 241-271, 1989.
118. J. F. Clarke, S. Karni, J. J. Quirk, L. G. Simmons, P. L. Roe, and E. F. Toro. Numerical Computation of Two-Dimensional, Unsteady Detonation Waves in High Energy Solids. J. Comput. Phys., 106: 215-233, 1993.
119. J. F. Clarke and M. McChesney. Dynamics of Relaxing Gases. Butterworths, 1976.
120. J. F. Clarke and E. F. Toro. Gas Flows Generated by Solid-Propellant Burning. In R. Glowinski, B. Larrouturou, and R. Teman, editors, Proc. Intern. Confer. on Numerical Simulation of Combustion Phenomena, number 241 in Lecture Notes in Physics, pages 192-205, INRIA, Sophia Antipolis, France, May 21-24 1985.
121. B. Cockburn, S. Hou, and C. W. Shu. The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws IV: the Multi-dimensional Case. Mathematics of Computation, 54: 545-581, 1990.
122. B. Cockburn, G. E. Karniadakis, and C. W. Shu. Discontinuous Galerkin Methods. Lecture Notes in Computational Science and Engineering. Springer, 2000.
123. B. Cockburn, S. Y. Li, and C. W. Shu. TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws III: One Dimensional Systems. J. Comput. Phys., 84: 90-113, 1989.
124. B. Cockburn and C. Shu. Nonlinearly Stable Compact Schemes for Shock Calculations. SIAM J. Numer. Anal., 31: 607-627, 1994.
125. B. Cockburn and C. W. Shu. TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework. Mathematics of Computation, 52: 411-435, 1989.
126. B. Cockburn and C. W. Shu. The Runge-Kutta Local Projection P1-Discontinuous Galerkin Finite Element Method for Scalar Conservation Laws. Mathematical Modelling and Numerical Analysis, 25: 337-361, 1991.
127. B. Cockburn and C. W. Shu. The Local Discontinuous Galerkin Method for Time-Dependent Convection Diffusion Systems. SIAM Journal on Numerical Analysis, 35: 2440-2463, 1998.
128. B. Cockburn and C. W. Shu. The Runge-Kutta Discontinuous Galerkin Method for Conservation Laws V: Multi-dimensional Systems. J. Comput. Phys., 141: 199-224, 1998.
129. B. Cockburn and C. W. Shu. Runge-Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems. Journal of Scientific Computing, 16: 173-261, 2001.
130. E. Coddington and N. Levinson. Theory of Ordinary Differential Equations. McGraw-Hill, New York, 1955.
131. P. Colella. An Analysis of the Effect of Operator Splitting and of the Sampling Procedure on the Accuracy of Glimm's Method. PhD thesis, Department of Mathematics, University of California, USA, 1978.
132. P. Colella. Glimm's Method for Gas Dynamics. SIAM J. Sci. Stat. Comput., 3(1):76-110, 1982.
133. P. Colella. A Direct Eulerian MUSCL Scheme for Gas Dynamics. SIAM J. Sci. Stat. Comput., 6: 104-117, 1985.
134. P. Colella. Multi-dimensional Upwind Methods for Hyperbolic Conservation Laws. J. Comput. Phys., 87: 171-200, 1990.
135. P. Colella and H. H. Glaz. Efficient Solution Algorithms for the Riemann Problem for Real Gases. J. Comput. Phys., 59: 264-289, 1985.
136. P. Colella, A. Majda, and V. Roytburd. Theoretical and Numerical Structure for Reacting Shock Waves. SIAM J. Sci. Stat. Comput., 7: 1059-1080, 1986.
137. P. Colella and P. R. Woodward. The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulation. J. Comput. Phys., 54: 174-201, 1984.
138. P. Concus and W. Proskurowski. Numerical Solution of a Nonlinear Hyperbolic Equation by the Random Choice Method. J. Comput. Phys., 30: 153-166, 1979.
139. S. D. Conte and C. de Boor. Elementary Numerical Analyis. McGraw-Hill Kogakusha Ltd., 1980.
140. J. M. Corberán and M. Ll. Gascón. TVD Schemes for the Calculation of Flow in Pipes of Variable Cross-Section. Mathl. Comput. Modelling, 21: 85-92, 1995.
141. J. Corner. Theory of the Interior Ballistics of Guns. Wiley, 1950.
142. J. Cortes, A. Debussche, and I. Toumi. A Density Perturbation Method to Study the Eigenstructure of Two-Phase Flow Equation Systems. J. Comput. Phys., 147: 1-22, 1998.
143. R. Courant and K. O. Friedrichs. Supersonic Flow and Shock Waves. Springer-Verlag, 1985.
144. R. Courant, E. Isaacson, and M. Rees. On the Solution of Nonlinear Hyperbolic Differential Equations by Finite Differences. Comm. Pure. Appl. Math., 5: 243-255, 1952.
145. M. G. Crandall and A. Majda. Monotone Difference Approximations for Scalar Conservation Laws. Mathematics of Computations, 34: 1-34, 1980.
146. W. Dai and P. R. Woodward. An Approximate Riemann Solver for Ideal Magnetohydrodynamics. J. Comput. Phys., 111: 354-372, 1994.
147. W. Dai and P. R. Woodward. Extension of the Piecewise Parabolic Method to Multi-dimensional Ideal Magnetohydrodynamics. J. Comput. Phys., 115: 485-, 1994.
148. G. Dal Maso, P. G. LeFloch, and F. Murat. Definition and Weak Stability of Nonconservative Products. J. Math. Pure Appl., 74: 483-548, 1995.
149. S. F. Davis. TVD Finite Difference Schemes and Artificial Viscosity. Technical Report ICASE 84-20, NASA Langley Research Center, Hampton, USA, 1984.
150. S. F. Davis. Simplified Second-Order Godunov-Type Methods. SIAM J. Sci. Stat. Comput., 9: 445-473, 1988.
151. A. S. Dawes. Natural Coordinates and High Speeed Flows. A Numerical Method for Reactive Gases. PhD thesis, College of Aeronautics, Cranfield Institute of Technology, UK, 1992.
152. H. Deconinck, K. G. Powell, P. L. Roe, and R. Struijs. Multi-dimensional Schemes for Scalar Advection. AIAA, 91(1532), 1991.
153. H. Deconinck, P. L. Roe, and R. Struijs. Multi-dimensional Generalisation of Roe's Flux Difference Splitter for the Euler Equations. Computers and Fluids, 22: 215-222, 1993.
154. A. Dedner, F. Kemm, D. Kröner, C. D. Munz, T. Schnitzer, and M. Wesenberg. Hyperbolic Divergence Cleaning for the MHD Equations. J. Comput. Phys., 175: 645-673, 2002.
155. L. Del Zanna, N. Bucciantini, and P. Londrillo. An Efficient Shock-Capturing Central Scheme for Multi-dimensional Relativistic Flows II. Magnetohydrodynamics. Astronomy and Astrophysics, 400: 397-413, 2003.
156. V. Deledicque and M. V. Papalexandris. An Exact Riemann Solver for Compressible Two-Phase Flow Models Containing Nononservative Products. J. Comput. Phys., 222: 217-245, 2007.
157. T. DeNeff and G. Moretti. Shock Fitting for Everyone. Computers and Fluids, 8: 327-334, 1980.
158. J. M. Dewey. Mach Reflection Research-Paradox and Progress. In Shock Waves (Proc. 18th Int. Symp. on Shock Waves, Sendai, Japan, 1991. Takayama, Editor), Vol. I, pages 113-120. Springer-Verlag, 1992.
159. J. Dobes and H. Deconinck. Second Order Blended Multi-dimensional Upwind Residual Distribution Scheme for Steady and Unsteady Computations. Journal of Computational and Applied Mathematics, 215: 378-389, 2008.
160. D. A. Drew and R. Gulliver. Particulate Flows: Processing and Rheology. Springer, 1997.
161. D. A. Drew, J. E. Marsden, and L. Sirovich. Theory of Multicomponent Fluids. Springer, 1998.
162. D. Drikakis. A Characteristic-Based Method for Incompressible Flow. Int. J. Numer. Meth. Fluids, 19: 667-685, 1994.
163. D. Drikakis. A Parallel Multiblock Characteristic-Based Method for Three-Dimensional Incompressible Flows. Advances in Engineering Software, 26: 111-119, 1996.
164. D. Drikakis, O. P. Iliev, and D. P. Vassileva. A Nonlinear Multigrid Method for the Three-Dimensional Incompressible Navier-Stokes Equations. J. Comput. Phys., 146: 301-321, 1998.
165. D. Drikakis and W. Rider. High-Resolution Methods for Incompressible and Low-Speed Flows. Springer, 2005.
166. D. Drikakis and S. Tsangaris. On the Solution of the Compressible Navier-Stokes Equations Using Improved Flux Vector Splitting Methods. Appl. Math. Modelling, 17: 282-297, 1993.
167. F. Dubois and G. Mehlman. A Non-Parameterized Entropy Fix for Roe's Method. AIAA Journal, 31(1):199-200, 1993.
168. J. K. Dukowicz. A General, Non-Iterative Riemann Solver for Godunov's Method. J. Comput. Phys., 61: 119-137, 1985.
169. M. Dumbser. Arbitrary High Order Schemes for the Solution of Hyperbolic Conservation Laws in Complex Domains. PhD thesis, PhD thesis, Institut für Aero-un Gasdynamik, Universität Stuttgart, Germany, 2005.
170. M. Dumbser. Building Blocks for Arbitrary High Order Discontinuous Galerkin Schemes. Journal of Scientific Computing, 27: 215-230, 2006.
171. M. Dumbser, D. Balsara, E. F. Toro, and C. D. Munz. A Unified Framework for the Construction of One-Step Finite-Volume and Discontinuous Galerkin Schemes. J. Comput. Phys., 227: 8209-8253, 2008.
172. M. Dumbser, M. J. Castro, C. Parés, and E. F. Toro. ADER Schemes on Unstructured Meshes for Nonconservative Hyperbolic Systems: Applications to Geophysical Flows. Computers and Fluids, 2008 (submitted).
173. M. Dumbser, C. Enaux, and E. F. Toro. Finite Volume Schemes of Very High Order of Accuracy for Stiff Hyperbolic Balance Laws. J. Comput. Phys., 227(8):3971-4001, 2008.
174. M. Dumbser, A. Hidalgo, M. J. Castro, C. Parés, and E. F. Toro. FORCE Schemes on Unstructured Meshes II: Nonconservative Hyperbolic Systems. Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK. Preprint NI09053-NPA, December 2008. Submitted to J. Comput. Phys., 2008.
175. M. Dumbser and M. Käser. Arbitrary High Order Non-Oscillatory Finite Volume Schemes on Unstructured Meshes for Linear Hyperbolic Systems. J. Comput. Phys., 221(2):693-723, 2007.
176. M. Dumbser, M. Käser, V. A. Titarev, and E. F. Toro. Quadrature-Free Non-Oscillatory Finite Volume Schemes on Unstructured Meshes for Nonlinear Hyperbolic Systems. J. Comput. Phys., 226(8):204-243, 2007.
177. M. Dumbser, M. Käser, and E. F. Toro. An Arbitrary High Order Discontinuous Galerkin Method for ElasticWaves on Unstructured Meshes V: Local Time Stepping and p-Adaptivity. Geophysical Journal International, 171: 695-717, 2007.
178. M. Dumbser and C. D. Munz. ADER Discontinuous Galerkin Schemes for Aeroacoustics. Comptes Rendus Mécanique, 333: 683-687, 2005.
179. P. Dutt. A Riemann Solver Based on a Global Existence Proof for the Riemann Problem. Technical Report ICASE 86-3, NASA Langley Research Center, USA, 1986.
180. D. H. Edwards, G. O. Thomas, and T. L. Williams. Initiation of Detonation by Steady Planar Incident Shock Waves. Combustion and Flame, 43: 187-198, 1981.
181. B. Einfeldt. On Godunov-Type Methods for Gas Dynamics. SIAM J. Numer. Anal., 25(2):294-318, 1988.
182. B. Einfeldt, C. D. Munz, P. L. Roe, and B. Sjögreen. On Godunov-Type Methods near Low Densities. J. Comput. Phys., 92: 273-295, 1991.
183. P. Embid and M. Baer. Mathematical Analysis of a Two-Phase Continuum Mixture Theory. Continuum Mech. Thermodyn., 4: 279-312, 1992.
184. B. Engquist and B. Gustafsson. Proc. Third International Conference on Hyperbolic Problems, Vol. I and II. Chartwell-Bratt, 1991.
185. B. Engquist and S. Osher. One Sided Difference Approximations for Nonlinear Conservation Laws. Math. Comp., 36(154):321-351, 1981.
186. L. C. Evans. Partial Differential Equations. American Mathematical Society, 2002.
187. S. A. E. G. Falle and S. S. Komissarov. An Upwind Numerical Scheme for Relativistic Hydrodynamics with a General Equation of State. Monthly Notices of the Royal Astronomical Society, 278: 586-602, 1996.
188. S. A. E. G. Falle and S. S. Komissarov. A Multi-dimensional Upwind Scheme for Magnetohydrodynamics. Monthly Notices of the Royal Astronomical Society, 297: 265-277, 1997.
189. M. Feistauer, J. Felcman, and I. Straskraba. Mathematical and Computational Methods for Compressible Flow. Oxford University Press, 2003.
190. M. Fey, R. Jeltsch, and S Müller. The Influence of a Source Term, an Example: Chemically Reacting Hypersonic Flow. Technical Report 92-06, SAM, Eidgenössische Technische Hochschule (ETH), Zürich, Switzerland, 1992.
191. W. Fickett and W. Davis. Detonation. University of California Press, 1979.
192. C. A. J. Fletcher. Computational Techniques for Fluid Dynamics, Vols. I and II. Springer-Verlag, 1988.
193. L. Fraccarollo and E. F. Toro. A Shock-Capturing Method for Two Dimensional Dam-Break Problems. Proceedings of the Fifth International Symposium in Computational Fluid Dynamics, Sendai, Japan, 1993.
194. L. Fraccarollo and E. F. Toro. Experimental and Numerical Assessment of the Shallow Water Model for Two-Dimensional Dam-Break Type problems. Journal of Hydraulic Research, 33: 843-864, 1995.
195. J. E. Fromm. A Method for Reducing Dispersion in Convective Difference Schemes. J. Comput. Phys., 3: 176-189, 1968.
196. M. Gallardo, C. Parés, and M. J. Castro. On a Well-Balanced High-Order Finite Volume Scheme for Shallow Water Equations with Topography and Dry Areas. J. Comput. Phys., 227: 574-601, 2007.
197. P. García-Navarro, M. E. Hubbard, and A. Priestley. Genuinely Multi-dimensional Upwinding for the 2D Shallow Water Equations. J. Comput. Phys., 121: 79-93, 1995.
198. P. H. Gaskell and A. K. C. Lau. Curvature Compensated Convective Transport: SMART, a New Boundedness Preserving Transport Algorithm. Int. J. Numer. Meth. Fluids, 8: 617-641, 1988.
199. S. L. Gavrilyuk, N. Favrie, and R. Saurel. Modelling Wave Dynamics of Compressible Elastic Materials. J. Comput. Phys., 227(5):2941-2969, 2007.
200. C. W. Gear. Numerical Initial-Value Problems in Ordinary Differential Equations. Prentice-Hall, Englewood Cliffs, NJ, 1971.
201. B. E. Gelfand, S. M. Frolov, and M. A. Nettleton. Gaseous Detonations-A Selective Review. Prog. Energy Comb. Sci., 17: 327-371, 1991.
202. B. Giacomazzo and L. Rezzolla. The Exact Solution of the Riemann Problem in Relativistic Magnetohydrodynamics. Journal of Fluid Mechanics, 562: 223-259, 2006.
203. D. Gidaspow. Multiphase Flow and Fluidization. Academic Press, 1994.
204. R. B. Gilbert and R. A. Strehlow. Theory of Detonation Initiation Behind Reflected Shock Waves. AIAA Journal, 4: 1777-1783, 1966.
205. M. B. Giles. Non-Reflecting Boundary Conditions for Euler Equation Calculations. AIAA J., 28: 2050-2058, 1990.
206. L. Giraud and G. Manzini. Parallel Implementations of 2D Explicit Euler Solvers. J. Comput. Phys., 123: 111-118, 1996.
207. P. Glaister. Difference Schemes for the Shallow Water Equations. Technical Report 9/87, Department of Mathematics, University of Reading, England, 1987.
208. P. Glaister. An Approximate Linearised Riemann Solver for the Euler Equations of Gas Dynamics. J. Comput. Phys., 74: 382-408, 1988.
209. P. Glaister. An Approximate Linearised Riemann Solver for the Three-Dimensional Euler Equations for Real Gases Using Operator Splitting. J. Comput. Phys., 77: 361-383, 1988.
210. H. M. Glaz, P. Colella, I. I. Glass, and R. L. Deschambault. A Detailed Numerical, Graphical and Experimental Study of Oblique Shock Wave Reflections. Technical Report 285, Institute for Aerospace Science, University of Toronto (UTIAS), 1985.
211. H. M. Glaz, P. Colella, I. I. Glass, and R. L. Deschambault. A Numerical Study of Oblique Shock-Wave Reflections with Experimental Comparisons. Proc. Roy. Soc. London, A 398: 117-140, 1985.
212. J. Glimm. Solution in the Large for Nonlinear Hyperbolic Systems of Equations. Comm. Pure. Appl. Math., 18: 697-715, 1965.
213. J. Glimm, M. J. Graham, J. W Grove, and B. J. Plohr. Proc. Fifth International Conference on Hyperbolic Problems. World Scientific, 1996.
214. J. Glimm, G. Marshall, and B. Plohr. A Generalized Riemann Problem for Quasi-One-Dimensional Gas Flows. Advances in Applied Mathematics, 5: 1-30, 1984.
215. E. Godlewski and P. A. Raviart. Numerical Approximation of Hyperbolic Systems of Conservation Laws. Applied Mathematical Sciences, Vol. 118, Springer-Verlag, New York, 1996.
216. S. K. Godunov. A Finite Difference Method for the Computation of Discontinuous Solutions of the Equations of Fluid Dynamics. Mat. Sb., 47: 357-393, 1959.
217. S. K. Godunov, A. V. Zabrodin, and G. P. Prokopov. -. J. Comp. Math. Phys. USSR 1(1962), pages 1187-, 1962.
218. J. B. Goodman and R. J. LeVeque. On the Accuracy of Stable Schemes for 2D Scalar Conservation Laws. Math. Comp., 45(21):15-21, 1985.
219. L. Gosse. A Well-Balanced Flux-Vector Splitting Scheme Designed for Hyperbolic Systems of Conservation Laws with Source Terms. Computers and Mathematics with Applications, 39: 135-159, 2000.
220. J. J. Gottlieb. Staggered and Non-Staggered Grids with Variable Node Spacing and Local Timestepping for Random Choice Method. J. Comput. Phys., 78: 160-177, 1988.
221. J. J. Gottlieb and C. P. T. Groth. Assessment of Riemann Solvers for Unsteady One-Dimensional Inviscid Flows of Perfect Gases. J. Comput. Phys., 78: 437-458, 1988.
222. S. Gottlieb and C. W. Shu. Total Variation Diminishing Runge-Kutta Schemes. Technical Report ICASE 96-50, NASA Langley Research Center, Hampton, USA, 1996.
223. G. Grassner, F. Lörcher, and C. D. Munz. A Contribution to the Construction of Diffusion Fluxes for Finite Volume and Discontinuous Galerkin Schemes. J. Comput. Phys., 224: 1049-1063, 2007.
224. J. M. Greenberg and A. Y. LeRoux. A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations. SIAM J. Numerical Analysis, 33: 1-16, 1996.
225. J. M. Greenberg, A. Y. LeRoux, R. Baraille, and A Noussair. Analysis and Approximation of Conservation Laws with Source Terms. SIAM J. Numerical Analysis, 34: 1980-2007, 1997.
226. D. F. Griffiths, A. M. Stuart, and H. C. Yee. Numerical Wave Propagation in an Advection Equation with a Nonlinear Source Term. SIAM J. Numer. Anal., 29: 1244-1260, 1992.
227. H. Grönig (Editor). Shock Tubes and Waves (Proc. 16th Int. Symp. on Shock Tubes and Waves, Aachen Germany 1987). VCH Verlagsgessellschaft mbH, 1988.
228. V. Guinot. Godunov-Type Schemes. An Introduction for Engineers. Elsevier, 2003.
229. K. F. Gurski. An HLLC-Type Approximate Riemann Solver for Ideal Magnetohydrodynamics. SIAM J. Sci. Comput., 25(6):2165-2187, 2004.
230. B. Haasdonk, D. Kröner, and C. Rhode. Convergence of a Staggered Lax-Friedrichs Scheme on Unstructured Grids in 2D. Numerische Mathematik, 88: 459-484, 2001.
231. R. Haberman. Mathematical Models. SIAM, 1998.
232. J. M. Hammersley and D. C. Handscombe. Monte Carlo Methods. Chapman and Hall, 1964.
233. D. Hänel. On the Numerical Solution of the Navier-Stokes Equations for Compressible Flow. VKI Lecture Series 1989-04 on Computational Fluid Dynamics, 1989.
234. D. Hänel and S. D. Sharma. Simulation of Hydrodynamical Free-Surface Flow. In Proc. Third ECCOMAS Computational Fluid Dynamics Conference, 9-13 September 1996, Paris, France, pages 1019-1024. Wiley, 1996.
235. E. Harabetian. A Convergent Series Expansion for Hyperbolic Systems of Conservation Laws. Trans Amer. Math. Soc., 294: 383-424, 1986.
236. R. Harris, Z. J. Wang, and Y. Liu. Efficient Quadrature-Free High-Order Spectral Volume Method on Unstructured Grids: Theory and 2D. J. Comput. Phys., 227(3):1620-1642, 2008.
237. A. Harten. High Resolution Schemes for Hyperbolic Conservation Laws. J. Comput. Phys., 49: 357-393, 1983.
238. A. Harten. On a Class of High Resolution Total Variation Stable Finite Difference Schemes. SIAM J. Numer. Anal., 21(1):1-23, 1984.
239. A. Harten. Preliminary Results on the Extension of ENO Schemes to Two-Dimensional Problems. In International Conference on Non-Linear Hyperbolic Problems, pages 23-51. Springer-Verlag, Berlin, 1987.
240. A. Harten. ENO Schemes with Subcell Resolution. J. Comput. Phys., 83: 148-184, 1989.
241. A. Harten, B. Engquist, S. Osher, and S. R. Chakravarthy. Uniformly High Order Accuracy Essentially Non-oscillatory Schemes III. J. Comput. Phys., 71: 231-303, 1987.
242. A. Harten and J. M. Hyman. Self Adjusting Grid Methods for One-Dimensional Hyperbolic Conservation Laws. J. Comput. Phys., 50: 235-269, 1983.
243. A. Harten, P. D. Lax, and B. van Leer. On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws. SIAM Review, 25(1):35-61, 1983.
244. A. Harten and S. Osher. Uniformly High-Order Accurate Nonoscillatory Schemes I. SIAM J. Numer. Anal., 24(2):279-309, 1987.
245. W. Heilig and H. Reichenbach. High Speed Interferometric Study of Unstationary Shok Wave Processes. Technical report, Fraunhofer Institut für Kurzzeitdynamik, Ernst-Mach-Institut, Freiburg im Breisgau, Germany, 1982.
246. P. W. Hemker and S. P. Spekreijse. Multiple Grid and Osher's Scheme for the Efficient Solution of the Steady Euler Equations. Applied Numerical Mathematics, 2: 475-493, 1986.
247. J. S. Hesthaven and T. Warburton. Nodal Discontinuous Galerkin Methods: Algorithms, Analysis and Applications. Springer, 2008.
248. F. B. Hildebrand. Introduction to Numerical Analysis. Tata McGraw-Hill Publishing Co. Limited, New Delhi, 1974.
249. R. Hillier. Numerical Modelling of Shock Wave Diffraction. In Shock Waves @ Marseille, Vol. 4 (Brun and Dumitrescu, Editors), pages 17-26. Springer-Verlag, 1995.
250. C. Hirsch. Numerical Computation of Internal and External Flows, Vol. I: Fundamentals of Numerical Discretization. Wiley, 1988.
251. C. Hirsch. Numerical Computation of Internal and External Flows, Vol. II: Computational Methods for Inviscid and Viscous Flows. Wiley, 1990.
252. K. A. Hoffmann. Computational Fluid Dynamics for Engineers. Engineering Education Systems, Austin, Texas, USA, 1989.
253. M. Holt. Numerical Methods in Fluid Dynamics. Springer-Verlag, 1984.
254. V. Honkkila and P. Janhunen. HLLC Solver for Ideal Relativistic MHD. J. Comput. Phys., 203(1):344-357, 2007.
255. H. Honma and I. I. Glass. Random Choice Solutions forWeak Spherical Shock-Wave Transitions of N-Waves in Air with Vibrational Excitation. Technical Report 253, UTIAS, University of Toronto, Canada, 1983.
256. H. Honma, M. Wada, and K. Inomata. Random Choice Solutions for Two-Dimensional and Axi-Symetric Supersonic Flows. Technical Report S. P. Number 2, The Institute of Space and Astronautical Science, 1984.
257. L. Hörmander. Lectures on Nonlinear Hyperbolic Differential Equations, Mathématiques et Applications 26. Springer-Verlag, 1997.
258. T. Y. Hou and LeFloch P. Why Non-Conservative Schemes Converge to the Wrong Solutions: Error Analysis. Math. of Comput., 62: 497-530, 1994.
259. E. L. Ince and I. N. Sneddon. The Solution of Ordinary Differential Equations. Longman Scientific and Technical, 1987.
260. M. Ishii and T. Hibiki. Thermo-fluid Dynamics of Two-Phase Flow. Springer, 2006.
261. M. J. Ivings, D. M. Causon, and E. F. Toro. On Hybrid High-Resolution Upwind Methods for Multicomponent Flows. ZAMM, 77, Issue 9: 645-668, 1997.
262. M. J. Ivings, D. M. Causon, and E. F. Toro. On Riemann Solvers for Compressible Liquids. Technical Report 97-4, Department of Mathematics and Physics, Manchester Metropolitan University, UK, 1997.
263. M. J. Ivings, D. M. Causon, and E. F. Toro. On Riemann Solvers for Compressible Liquids. Int. J. Numer. Meth. Fluids, 28: 395-418, 1998.
264. R. Jackson. The Dynamics of Fluidized Particles. Cambridge University Press, 2000.
265. A. Jameson and P. D. Lax. Conditions for the Construction of Multi-Point Total Variation Diminishing Difference Schemes. Technical Report MAE 1650, Department of Mechanical and Aerospace Engineering, University of Princeton, USA, 1984.
266. A. Jameson, W. Schmidt, and E. Turkel. Numerical Solution of the Euler Equations by Finite Volume Methods using Runge-Kutta Stepping Schemes. Technical Report 81-1259, AIAA, 1981.
267. A. Jeffrey. Quasilinear Hyperbolic Systems and Waves. Pitman, 1976.
268. G. S. Jiang and C. W. Shu. Efficient Implementation of Weighted ENO Schemes. J. Comp. Phys., 126: 202-228, 1996.
269. G. S. Jiang and E. Tadmor. Non-oscillatory Central Schemes for Multi-dimensional Hyperbolic Conservation Laws. SIAM Journal of Scientific Computing, 19(6):1892-1917, 1998.
270. F. John. Partial Differential Equations. Springer-Verlag, 1982.
271. L. W. Johnson and R. D. Riess. Numerical Analysis. Addison-Wesley Publishing Company, 1982.
272. P. Jorgenson and E. Turkel. Central-Difference TVD and TVB Schemes for Time-Dependent and Steady State Problems. Technical Report ICOMP-91-27; AIAA-92-0053, NASA Lewis Research Center, Cleveland, Ohio, USA, 1992.
273. D. Kahaner, C. Moler, and S. Nash. Numerical Methods and Software. Prentice Hall, Englewood Cliffs, New Jersey, 1989.
274. K. Kailasanath, E. S. Oran, J. P. Boris, and T. R. Young. Determination of the Detonation Cell Size and the Role of Transverse Waves in Two-Dimensional Detonations. Combustion and Flame, 61: 199-209, 1985.
275. S. Karni. Accelerated Convergence to Steady State by Gradual Far-Field Damping. AIAA J., 30: 1220-1228, 1992.
276. S. Karni. Multicomponent Flow Calculations Using a Consistent Primitive Algorithm. J. Comput. Phys., 112(1):31-43, 1994.
277. S. Karni. Hybrid Multifluid Algorithms. Technical Report 95-001, Courant Mathematics and Computing Laboratory, 1995.
278. S. Karni and S. Čanić. Computations of Slowly Moving Shocks. J. Comput. Phys., 136: 132-139, 1997.
279. M. Käser. Adaptive Methods for the Numerical Simulation of Transport Processes. PhD thesis, Institute of Numerical Mathematics and Scientific Computing, University of Munich, Germany, 2003.
280. M. Käser. ADER Schemes for the Solution of Conservation Laws on Adaptive Triangulations. Mathematical Methods and Modelling in Hydrocarbon Exploration and Production. Springer-Verlag (to appear), 2004.
281. M. Käser and A. Iske. Adaptive ADER Schemes for the Solution of Scalar Non-Linear Hyperbolic Problems. J. Comput. Phys.,-:-, 2005.
282. K. S. Kim and J. Ballmann. Numerische Simulation Mechanischer Wellen in Geschichteten Elastischen Körpern. Z. Angew. Math. Mech., 70: 204-206, 1990.
283. C. Klingenberg, W. Schmidt, and K. Waagan. Numerical Comparison of Riemann Solvers for Astrophysical Hydrodynamics. J. Comput. Phys., 227(1):12-35, 2007.
284. L. Knut-Andreas and S. Noelle. An Improved Quadrature Rule for the Flux Computation in Staggered Central Difference Schemes in Multidimensions. J. Scientific Computing, 18(1):69-81, 2003.
285. V. P. Kolgan. Application of the Principle of Minimum Derivatives to the Construction of Difference Schemes for Computing Discontinuous Solutions of Gas Dynamics (in Russian). Uch. Zap. TsaGI, Russia, 3(6):68-77, 1972.
286. V. P. Kolgan. Finite Difference Schemes for the Computation of Three-dimensional Solutions of Gas Dynamics and Calculation of the Flow over a Body under an Angle of Attack (in Russian). Technical Report Vol. 6, No 2, pp 1-6, Uchenye Zapiski) TsaGI (Scientific Notes of the Central Institute of Aerodynamics, Russia), 1975.
287. V. P. Kolgan. Finite Difference Schemes for the Computation of Two-dimensional Discontinuous Solutions of Non-stationary Gas Dynamics (in Russian). Technical Report Vol. 6, No 1, pp 9-14, Uchenye Zapiski) TsaGI (Scientific Notes of the Central Institute of Aerodynamics, Russia), 1975.
288. B. Koren and S. P. Spekreijse. Multigrid and Defect Correction for the Efficient Solution of the Steady Euler Equations. In Notes on Numerical Fluid Mechanics, Vol. 17, pages 87-100. Vieweg, 1987.
289. D. Kröner. Numerical Schemes for Conservation Laws. Wiley Teubner, 1997.
290. A. G. Kulikovskii, N. V. Pogorelov, and A. Y. Semenov. Mathematical Aspects of Numerical Solution of Hyperbolic Systems. Chapman and Hall, 2001.
291. A. Kurganov and G. Petrova. A Third-Order Semi-Discrete Genuinely Multi-dimensional Central Scheme for Hyperbolic Conservation Laws and Related Problems. Numerische Mathematik, 88(3):683-729, 2001.
292. A. Lafon and H. C. Yee. Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations, Part III. The Effects of Nonlinear Source Terms in Reaction-Convection Equations. Intern. J. Computational Fluid Dynamics, 6: 1-36, 1996.
293. A. Lafon and H. C. Yee. Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations, Part IV. Stability vs. Methods of Discretizing Nonlinear Source Terms in Reaction-Convection Equations. Intern. J. Computational Fluid Dynamics, 6: 89-123, 1996.
294. J. D. Lambert. Computational Methods in Ordinary Differential Equations. John Wiley and Sons, 1973.
295. L. D. Landau and E. M. Lifshitz. Fluid Mechanics. Pergamon Press, 1982.
296. C. B. Laney. Computational Gasdynamics. Cambridge University Press, 1998.
297. P. D. Lax. Weak Solutions of Nonlinear Hyperbolic Equations and Their Numerical Computation. Comm. Pure. Appl. Math., VII: 159-193, 1954.
298. P. D. Lax. The Formation and Decay of Shock Waves. American Mathematical Monthly, 79: 227-241, 1972.
299. P. D. Lax. Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves. Society for Industrial and Applied Mathematics, Philadelphia, 1990.
300. P. D. Lax and B. Wendroff. Systems of Conservation Laws. Comm. Pure Appl. Math., 13: 217-237, 1960.
301. P. D. Lax and B. Wendroff. Difference Schemes for Hyperbolic Equations with High Order Accuracy. Comm. Pure Appl. Math., XVII: 381-393, 1964.
302. P. Le Floch and P. A. Raviart. An Asymptotic Expansion for the Solution of the Generalized Riemann Problem. Part 1: General Theory. Ann. Inst. Henri Poincaré. Analyse non Lineáre, 5(2):179-207, 1988.
303. P. Le Floch and L. Tatsien. A Global Asymptotic Expansion for the Solution of the Generalized Riemann Problem. Ann. Inst. Henri Poincaré. Analyse non Lineáre, 3: 321-340, 1991.
304. L. Lehner. Numerical Relativity: a Review. Class. Quantum Grav., 18: R25-R86, 2001.
305. B. P. Leonard. Simple High-Accuracy Resolution Program for Convective Modelling of Discontinuities. Int. J. Numer. Methods in Fluids, 8: 1291-1318, 1988.
306. R. J. LeVeque. Numerical Methods for Conservation Laws. Birkhäuser Verlag, 1992.
307. R. J. LeVeque. Simplified Multi-dimensional Flux Limiter Methods. In M. J. Baines and K. W. Morton, editors, Numerical Methods in Fluid Dynamics 4: Proceedings of the 1992 International Conference on Numerical Methods in Fluids, pages 173-189, Reading, 1993.
308. R. J. LeVeque. Balancing Source Terms and Flux Gradients in High-Resolution Godunov Methods. J. Comput. Phys., 146: 346-365, 1998.
309. R. J. LeVeque. Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, 2002.
310. R. J. LeVeque, D. Mihalas, E. A. Dorfi, and E. Müller. Computational Methods for Astrophysical Flow. Springer-Verlag, 1998.
311. R. J. LeVeque and K. M. Shyue. Two-Dimensional Front Tracking Based on High Resolution Wave Propagation Methods. J. Comput. Phys., 123: 354-368, 1996.
312. R. J. LeVeque and H. C. Yee. A Study of Numerical Methods for Hyperbolic Conservation Laws with Stiff Source Terms. J. Comput. Phys., 86: 187-210, 1990.
313. D. W. Levy, G. Puppo, and G. Russo. Central WENO Schemes for Hyperbolic Systems of Conservation Laws. Mathematical Models and Numerical Analysis, 33: 547-571, 1999.
314. D. W. Levy, G. Puppo, and G. Russo. A Fourth Order Central WENO Scheme for Multi-dimensional Systems of Hyperbolic Conservation Laws. SIAM J. Scientific Computing, 24: 480-506, 2002.
315. K. M. Li and M. Holt. Numerical Solutions to Water Waves Generated by Shallow Underwater Explosions. Phys. Fluids, 24: 816-824, 1981.
316. S. Li. An HLLC Riemann Solver for Magneto-Hydrodynamics. J. Comput. Phys., 203(1):344-357, 2005.
317. NAG Library. NAG Library Routines, Mark 18, Routines D03PWF and D03PXF, 1996.
318. X. Lin and J. Ballmann. A Riemann Solver and a Second-Order Godunov Method for Elastic-Plastic Wave Propagation in Solids. Int. J. Impact Engng., 13(3):463-478, 1993.
319. X. Lin and Ballmann J. J. Archive of Applied Mechanics, 63: 261-282, 1993.
320. X. Lin and Ballmann J. J. Archive of Applied Mechanics, 63: 283-295, 1993.
321. X. Lin and Ballmann J. J. Engineering Fracture and Mechanics, 44(5):735-739, 1993.
322. T. J. Linde. A Three-Dimensional Adaptive Multifluid MHD Model for the Heliosphere. PhD thesis, Aerospace Engineering, University of Michigan, USA, 1998.
323. T. J. Linde, T. I. Gombosi, P. L. Roe, K. G. Powell, and D. L. DeZeeuw. The Heliosphere in Magnetized Local Interstellar Medium: Results of a 3D MHD Simulation. J. Geophys. Res., 103(A2):1989-1904, 1998.
324. W. B. Lindquist. Current Progress in Hyperbolic Systems: Riemann Problems and Computations. American Mathematical Society, 1989.
325. M. S. Liou. Recent Progress and Applications of AUSM+. In Sixteenth International Conference on Numerical Methods in Fluid Dynamics, Lecture Notes in Physics 515, pages 302-307. Springer-Verlag, 1998.
326. M. S. Liou and C. J. Steffen. A New Flux Splitting Scheme. J. Comput. Phys., 107: 23-39, 1993.
327. R. Liska and B. Wendroff. Composite Schemes for Conservation Laws. SIAM J. Numerical Analysis, 35(6):2250-2271, 1998.
328. X. D. Liu and P. D. Lax. Positive Schemes for Solving Multi-Dimensional Hyperbolic Conservation Laws. Technical Report 95-003, Courant Mathematics and Computing Laboratory, New York University, USA, 1995.
329. X. D. Liu and T. Osher, S. Chan. Weighted Essentially Non-oscillatory Schemes. J. Comput. Phys., 115: 200-212, 1994.
330. C. Y. Loh, M. S. Liou, and W. H. Hui. An Investigation of Random Choice Method for Three Dimensional Steady Supersonic Flow. In First Asian Computational Fluid Dynamics Conference, pages 963-971. The Hong Kong University of Science and Technology, 1995.
331. J. Lorenz and H. J. Schroll. Stiff Well-Posedness for Hyperbolic Systems with Large Relaxation Terms. Technical Report 125, Institut für Geometrie un Praktische Mathematik, RWTH Aachen, Germany, 1996.
332. H. Luo, J. D. Baum, and R. Löhner. A Hermite WENO-Based Limiter for Discontinuous Galerkin Method on Unstructured Grids. J. Comput. Phys., 225(1):686-713, 2007.
333. A. Majda and S. Osher. Numerical Viscosity and Entropy Condition. Comm. Pure and Applied Mathematics, 32: 797-838, 1979.
334. J. C. Mandal and S. M. Desphande. Kinetic Flux Vector Splitting for the Euler Equations. Computers and Fluids, 23: 447-, 1994.
335. M. J. Maron and R. J. Lopez. Numerical Analysis. Wadsworth, 1991.
336. A. Marquina, J. M. Martí, J. M. Ibañez, Miralles J. A., and R. Donat. Ultrarelativistic Hydrodynamics: High-Resolution Shock-Capturing Methods. Astron. Astrophys., 258: 566-, 1992.
337. E. Marshall and R. Méndez. Computational Aspects of the Random Choice Method for Shallow Water Equations. J. Comput. Phys., 39: 1.21, 1981.
338. G. Marshall and B. Plohr. A Random Choice Method for Two. Dimensional Steady Supersonic Shock Wave Diffraction Problems. J. Comput. Phys., 56: 410.427, 1984.
339. J. M. Martí, J. M. Ibañez, and J. A. Miralles. Numerical Relativistic Hydrodynamics: Local Characteristic Approach. Phys. Rev., 43: 3794., 1991.
340. J. M. Martí and E. Müller. The Analytical Solution of the Riemann Problem for Relativistic Hydrodynamics. Journal of Fluid Mechanics, 258: 317.333, 1994.
341. J. M. Martí, E. Müller, J. A. Font, J. M. Iba.nez, and A. Marquina. Morphology and Dynamics of Relativistic Jets. Technical Report MPA 895, Max. Planck. Institut für Astrophysik, Garching, Germany, 1995.
342. Y. P. Marx. A Practical Implementation of Turbulence Models for the Computation of Three. Dimensional Separated Flows. Int. J. Numer. Meth. Fluids, 13: 775.796, 1991.
343. Y. P. Marx. Evaluation of the Artificial Compressibility Method for the Solution of the Incompressible Navier. Stokes Equations. In Notes on Numerical Fluid Mechanics, Vol. 35, pages 201. 210. Vieweg, 1991.
344. Y. P. Marx. Time Integration Schemes for the Unsteady Incompressible Navier. Stokes Equations. J. Comput. Phys., 112: 182.209, 1994.
345. J. H. Mathews. Numerical Methods. Prentice. Hall International, Inc., 1987.
346. C. Y. McNeil. Efficient Upwind Algorithms for Solution of the Euler and Navier. Stokes Equations. PhD thesis, Department of Aerospace Science, Cranfield University, UK, 1995.
347. R. Menikoff and B. J. Plohr. The Riemann Problem for Fluid Flow of Real Materials. Reviews of Modern Physics, 61: 75.130, 1989.
348. I. S. Men'shov. Increasing the Order of Approximation of Godunov's Scheme Using the Generalized Riemann Problem. USSR Comput. Math. Phys., 30(5):54.65, 1990.
349. A. Mignone and G. Bodo. An HLLC Riemann Solver for Relativistic Flows. Monthly Notices of the Royal Astronomical Society, 368(3):1040.1054, 2006.
350. A. R. Mitchell and D. F. Griffiths. The Finite Difference Method in Partial Differential Equations. John Wiley and Sons, 1980.
351. G. Moretti. The Λ-scheme. Computers and Fluids, 7: 191.205, 1979.
352. G. Moretti. Computation of Flows with Strong Shocks. Ann. Rev. Fluid Mech., 19: 313.337, 1987.
353. G. Moretti and G. Bleich. A Time. Dependent Computational Method for Blunt. Body Flows. AIAA J., 4: 2136.2141, 1966.
354. S. Müller and A. Voss. The Riemann Problem for the Euler Equations with Nonconvex and Nonsmooth Equation of State: Construction of Wave Curves. SIAM Journal on Scientific Computing, 28(2):651.681, 2006.
355. S. T. Munkejord, S. Evje, and T. Flatten. A Multi. Stage Centred Scheme Approach Applied to a Drift Flux Two. Phase Flow Model. Int. J. Numer. Meth. Fluids, 52: 679.705, 2006.
356. C. D. Munz. A Tracking Method for Gas Flow into Vacuum Based on the Vacuum Riemann Problem. Mathematical Methods in Applied Sciences, 17: 597-612, 1994.
357. C. D. Munz, R. Schneider, and O. Gerlinger. The Numerical Approximation of a Free Gas. Vacuum Interface. In Numerical Methods for the Navier. Stokes Equations, pages 181-190. Vieweg-Verlag, 1994.
358. S. Navarro-Martinez and O. R. Tutty. Numerical Simulation of Görtler Vortices in Hypersonic Compression Ramps. Computers and Fluids, 34(2):225-247, 2005.
359. A. Nemec and M. J. Aftosmis. Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method. J. Comput. Phys., 227(4):2724-2742, 2008.
360. H. Nessyahu and E. Tadmor. Non-Oscillatory Central Differencing for Hyperbolic Conservation Laws. J. Comput. Phys., 87: 408-463, 1990.
361. N. Nikiforakis and J. F. Clarke. Quasi-Steady Structures in the Two Dimensional Initiation of Detonations. Proc. Roy. Soc. Lond. A, 452: 2023-2042, 1996.
362. H. Olivier and H. Grönig. The Random Choice Method Applied to Two-Dimensional Shock Focusing and Diffraction. J. Comput. Phys., 63: 85-106, 1986.
363. A. K. Oppenheim and R. I. Soloukhin. Experiments in Gas Dynamics of Explosions. Annual Review of Fluid Mechanics, 5: 31-58, 1973.
364. E. Oran and J. P. Boris. Numerical Simulation of Reactive Flow. Cambridge University Press, 2001.
365. E. S. Oran and J. P. Boris. Detailed Modelling of Combustion Systems. Prog. Energy. Comb. Sci., 7: 1-72, 1981.
366. E. S. Oran and J. P. Boris. Numerical Simulation of Reactive Flow. Elsevier, New York, 1987.
367. S. Osher. Riemann Solvers, the Entropy Condition and Difference Approximations. SIAM J. Numer. Anal., 21(2):217-235, 1984.
368. S. Osher and S. Chakravarthy. Upwind Schemes and Boundary Conditions with Applications to Euler Equations in General Geometries. J. Comput. Phys., 50: 447-481, 1983.
369. S. Osher and S. Chakravarthy. High Resolution Schemes and the Entropy Condition. SIAM J. Numer. Anal., 21(5):955-984, 1984.
370. S. Osher and F. Solomon. Upwind Difference Schemes for Hyperbolic Conservation Laws. Math. Comp., 38, 158: 339-374, 1982.
371. Liu T. P. and J. A. Smoller. On the Vacuum State for the Isentropic Gas Dynamics Equations. Advances in Applied Mathematics, 1: 345-359, 1980.
372. M. Pandolfi. Computation of Steady Supersonic Flows by a Flux-Difference Splitting Method. Computers and Fluids, 10: 37-46, 1985.
373. C. Parés. Numerical Methods for Nonconservative Hyperbolic Systems: a Theoretical Framework. SIAM Journal on Numerical Analysis, 44: 300-321, 2006.
374. M. Pelanti, F. Bouchut, and A. Mangeney. A Roe-Type Scheme for Two-Phase Shallow Granular Flows over Variable Topography. Mathematical Modelling and Numerical Analysis, 42: 851-885, 2008.
375. R. B. Pember. Numerical Methods for Hyperbolic Conservation Laws with Stiff Relaxation I: Spurious Solutions. SIAM J. Appl. Math., 53: 1293-1330, 1993.
376. R. B. Pember. Numerical Methods for Hyperbolic Conservation Laws with Stiff Relaxation II: Higher-Order Godunov Methods. SIAM J. Sci. Comput., 14: 824-859, 1993.
377. L. L. Pennisi. Elements of Complex Analysis. Holt, Rinehart and Winston, 1963.
378. B. Perthame. Boltzmann Type Schemes for Gas Dynamics and the Entropy Property. SIAM J. Numer. Anal., 27: 1405-1421, 1990.
379. B. Perthame. Second-Order Boltzman Schemes for Compressible Euler Equations in one and two Space Dimensions. SIAM J. Numer. Anal., 29: 1992, 1992.
380. L. Pesch and J. J. W. van der Vegt. A Discontinuous Galerkin Finite Element Discretization of the Euler Equations for Compressible and Incompressible Fluids. J. Comput. Phys., 227(11):5426-5446, 2008.
381. I. G. Petrovskii. Partial Differential Equations. London Cliffe Books Ltd., 1967.
382. J. Pike. Riemann Solvers for Perfect and Near-Perfect Gases. AIAA Journal, 31(10):1801-1808, 1993.
383. B. Pitman and L. Le. A Two-Fluid Model for Avalanche and Debris Flows. Phil. Trans. R. Soc. A, 363: 1573-1601, 2005.
384. B. J. Plohr and D. H. Sharp. Riemann Problems and their Application to Ultra-Relativistic Heavy Ion Collisions. In The VIII International Conference on Mathematical Physics (Mebkhout and Sénéor, editors), pages 708-713. World Scientific Pub. Co., Singapore, 1987.
385. K. H. Prendergast and K. Xu. Numerical Hydrodynamics from Gas-Kinetic Theory. J. Comput. Phys., 109: 53-66, 1993.
386. A. Prosperetti and G. Tryggvason. Fundamentals of Multiphase Flow. Cambridge University Press, 2007.
387. D. I. Pullin. Direct Simulation Methods for Compressible Inviscid Ideal Gas Flow. J. Comput. Phys., 34: 231-244, 1980.
388. N. Qin. A Comparative Study of Two Upwind Schemes as Applied to Navier-Stokes Solutions for Resolving Boundary Layers in Hypersonic Viscous Flow. Technical Report GU Aero Report 9120, Department of Aerospace Engineering, University of Glasgow, UK, 1992.
389. N. Qin and G. W. Foster. Study of Flow Interactions due to a Supersonic Lateral Jet Using High Resolution Navier-Stokes Solutions. In AIAA-95-2151 Paper, 27th AIAA Fluid Dynamics Conference, June 1995, San Diego, USA, 1995.
390. N. Qin and A. Redlich. Massively Separated Flows due to Transverse Sonic Jet in Hypersonic Laminar Stream. In AIAA-96-1934 Paper, 27th AIAA Fluid Dynamics Conference, June 1996, New Orleans, USA, 1996.
391. N. Qin and B. E. Richards. Sparse Quasi-Newton Method for High Resolution Schemes. In Notes on Numerical Fluid Mechanics, Vol. 20, pages 310-317. Vieweg, 1988.
392. N. Qin and B. E. Richards. Sparse Quasi-Newton Method for Navier-Stokes Solution. In Notes on Numerical Fluid Mechanics, Vol. 29, pages 474-483. Vieweg, 1990.
393. N. Qin, K. W. Scriba, and B. E. Richards. Shock-Shock, Shock-Vortex Interaction and Aerodynamic Heating In Hypersonic Corner Flow. The Aeronautical Journal, pages 152-160, 1991.
394. N. Qin, X. Xu, and B. E. Richards. Newton-Like Methods for Fast High Resolution Simulation of Hypersonic Viscous Flows. Computing Systems in Engineering, 3: 429-435, 1992.
395. J. Qiu, B. C. Khoo, and C. W. Shu. A Numerical Study for the Performance of the Runge-Kutta Discontinuous Galerkin Method Based on Different Numerical Fluxes. J. Comput. Phys., 212(2):540-565, 2006.
396. L. Quartapelle, L. Castelletti, A. Guardone, and G. Quaranta. Solution of the Riemann Problem of Classical Gasdynamics. J. Comput. Phys., 190: 118-140, 2003.
397. J. J. Quirk. An Adaptive Grid Algorithm for Computational Shock Hydrodynamics. PhD Thesis, College of Aeronautics, Cranfield Institute of Technology, UK, 1991.
398. J. J. Quirk. An Alternative to Unstructured Grids for Computing Gas Dynamic Flows Around Arbitrarily Complex Two Dimensional Bodies. Computers and Fluids, 23(1):125-142, 1994.
399. S. Rhebergen, O. Bokhove, and J. J. W. van der Vegt. Discontinuous Galerkin Finite Element Methods for Hyperbolic Nonconservative Partial Differential Equations. J. Comput. Phys., 227: 1887-1922, 2008.
400. R. D. Richtmyer and K. W. Morton. Difference Methods for Initial Value Problems. Interscience-Wiley, New York, 1967.
401. N. H. Risebro and A. Tveito. Front Tracking Applied to Nonstrictly Hyperbolic Systems of Conservation Laws. SIAM J. Sci. Stat. Comput., 12: 1401-1419, 1991.
402. A. Rizzi. Numerical Implementation of Solid-Body Boundary Conditions for the Euler Equations. ZAMM, 58: 301-304, 1978.
403. P. J. Roache. Computational Fluid Dynamics. Hermosa Publishers, 1982.
404. T. W. Roberts. The Behavior of Flux Difference Splitting Schemes near Slowly Moving Shock Waves. J. Comput. Phys., 90: 141-160, 1990.
405. P. L. Roe. Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes. J. Comput. Phys., 43: 357-372, 1981.
406. P. L. Roe. Numerical Algorithms for the Linear Wave Equation. Technical Report 81047, Royal Aircraft Establishment, Bedford, UK, 1981.
407. P. L. Roe. Some Contributions to the Modelling of Discontinuous Flows. In Proceedings of the SIAM/AMS Seminar, San Diego, 1983.
408. P. L. Roe. Generalized Formulation of TVD Lax-Wendroff Schemes. Technical Report ICASE 84-53, NASA Langley Research Center, Hampton, USA, 1984.
409. P. L. Roe. Discrete Models for the Numerical Analysis of Time-Dependent Multi-dimensional Gas Dynamics. J. Comput. Phys., 63: 458-476, 1986.
410. P. L. Roe. Upwind Differencing Schemes for Hyperbolic Conservation Laws with Source Terms. In Proc. First International Conference on Hyperbolic Problems, Carasso, Raviart and Serre (Editors), pages 41-51. Springer, 1986.
411. P. L. Roe. Remote Boundary Conditions for Unsteady Multi-dimensional Aerodynamic Computations. Computers and Fluids, 17: 221-231, 1989.
412. P. L. Roe. Sonic Flux Formulae. SIAM J. Sci. Stat. Comput., 13(2):611-630, 1992.
413. P. L. Roe. The Harten Memorial Lecture-New Applications of Upwinding. In Numerical Methods for Wave Propagation. Toro, E. F. and Clarke, J. F. (Editors), pages 1-31. Kluwer Academic Publishers, 1998.
414. P. L. Roe and J. Pike. Efficient Construction and Utilisation of Approximate Riemann Solutions. In Computing Methods in Applied Science and Engineering. North-Holland, 1984.
415. E. Romenski, E. D. Resnyanski, and E. F. Toro. Conservative Hyperbolic Formulation for Compressible Two-Phase Flow with Different Phase Pressures and Temperatures. Quarterly of Applied Mathematics, 65: 259-279, 2007.
416. V. V. Rusanov. Calculation of Interaction of Non-Steady Shock Waves with Obstacles. J. Comput. Math. Phys. USSR, 1: 267-279, 1961.
417. G. Russo, E. F. Toro, and V. A. Titarev. ADER-Runge-Kutta Schemes for Conservation Laws in One Space Dimension. In Hyperbolic Problems: Theory, Numerics and Applications. Benzone-Gavage S. and Serre D. (Editors), Vol. 1, pages 929-936. Springer, 2008.
418. A. V. Safranov. Difference Method for Gasdynamical Equations Based on the Jump Conditions (in Russian). Mathematical Modelling, 20: 76-84, 2008.
419. L. Sainsaulieu. Finite Volume Approximation of Two Phase-Fluid Flows Based on an Approximate Roe-Type Riemann Solver. J. Comput. Phys., 121: 1-28, 1995.
420. T. Saito and I. I. Glass. Application of Random Choice to Problems in Shock and Detonation Wave Dynamics. Technical Report UTIAS 240, Institute for Aerospace Studies, University of Toronto, 1979.
421. D. A. Sánchez. Ordinary Differential Equations and Stability Theory. Dover Publications, Inc., 1968.
422. R. H. Sanders and K. H. Prendergast. On the Origin the Three Kiloparsec Arm. Astrophys. J., 188: 489-500, 1974.
423. A. Sangan. An HLLC Scheme for Ten-Moments Approximation Coupled with Magnetic Field. Internat. J. Comput. Science and Math., 2(1/2):73-109, 2008.
424. R. Saurel and R. Abgrall. A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows. J. Comput. Phys., 150: 425-467, 1999.
425. R. Saurel, E. Daniel, and J. C. Loraud. Two-Phase Flows: Second Order Schemes and Boundary Conditions. AIAA Journal, 32(6):1214-1221, 1994.
426. R. Saurel, A. Forestier, D. Veyret, and J.-C. Loraud. A Finite Volume Scheme for Two-Phase Compressible Flows. Int. J. Numer. Meth. Fluids, 18: 803-819, 1994.
427. R. Saurel, M. Larini, and J. C. Loraud. Exact and Approximate Riemann Solvers for Real Gases. J. Comput. Phys., 112: 126-137, 1994.
428. M. Schleicher. Ein Einfaches und Effizientes Verfahren zur Loesung des Riemann-Problems. Z. Flugwiss. Weltraumforsch., 17: 265-269, 1993.
429. V. Schneider, U. Katscher, D. H. Rischke, B. Waldhauser, J. A. Maruhn, and C. D. Munz. New Algorithms for Ultra-Relativistic Numerical Hydrodynamics. J. Comput. Phys., 105: 92-, 1993.
430. H. J. Schroll and A. Tveito. A System of Conservation Laws with a Relaxation Term. Technical Report 103, Institut für Geometrie un Praktische Mathematik, RWTH Aachen, Germany, 1994.
431. H. J. Schroll, A. Tveito, and R. Winther. An Error Bound for a Finite Difference Scheme Applied to a Stiff System of Conservation Laws. Technical Report 1994-3, Department of Informatics, University of Oslo, Norway, 1994.
432. H. J. Schroll and R. Winther. Finite Difference Schemes for Scalar Conservation Laws with Source Terms. Technical Report 107, Institut für Geometrie un Praktische Mathematik, RWTH Aachen, Germany, 1994.
433. T. Schwartzkopff. Finite-Volumen Verfahren Hoher Ordnung und Heterogene Gebietszerlegung für die Numerische Aeroakustik. PhD thesis, Institut für Aeroun Gasdynamik, Universität Stuttgart, Germany, 2005.
434. T. Schwartzkopff, M. Dumbser, and C. D. Munz. Fast High Order ADER Schemes for Linear Hyperbolic Equations. J. Comput. Phys., 197: 532-539, 2004.
435. T. Schwartzkopff, C. D. Munz, and E. F. Toro. ADER: High-Order Approach for Linear Hyperbolic Systems in 2D. J. Scientific Computing, 17: 231-240, 2002.
436. D. W. Schwendeman, C. W. Wahle, and A. K. Kapila. The Riemann Problem and a High-Resolution Godunov Method for a Model of Compressible Two-Phase Flow. J. Comput. Phys., 212: 490-526, 2006.
437. F. W. Sears and G. L. Salinger. Thermodynamics, Kinetic Theory and Statistical Thermodynamics. Addison-Wesley, 1986.
438. C. C. L. Sells.. Technical Report RAE TR 80065, Royal Aircraft Establishment, Bedford, UK, 1980.
439. L. F. Shampine. Numerical Solution of Ordinary Differential Equations. Chapman and Hall, London and New York, 1994.
440. J. S. Shang. A Fractional-Step Method for Solving 3D, Time-Domain Maxwell Equations. J. Comput. Phys., 118: 109-119, 1995.
441. Z. C. Shi and J. J. Gottlieb. Random Choice Method for Two Dimensional Planar and Axisymmetric Steady Supersonic Flows. Technical Report 297, UTIAS, University of Toronto, Canada, 1985.
442. C. Shu and S. Osher. Efficient Implementation of Essentially Non-oscillatory Shock-Capturing Schemes II. J. Comput. Phys., 83: 32-78, 1989.
443. C. W. Shu. TVB Boundary Treatment for Numerical Solutions of Conservation Laws. Math. Comp., 49(179):123-134, 1987.
444. C. W. Shu. TVB Uniformly High-Order Schemes for Conservation Laws. Math. Comput., 49(179):105-121, 1987.
445. C. W. Shu and S. Osher. Efficient Implementation of Essentially Non-oscillatory Shock-Capturing Schemes. J. Comput. Phys., 77: 439-471, 1988.
446. G. Singh. A Numerical Study of the Evolution of Piston Driven Detonation. PhD thesis, Department of Arospace Science, Cranfield University, UK, 1990.
447. G. Singh and J. F. Clarke. Transient Phenomena in the Initiation of a Mechanically Driven Plane Detonation. Proc. Roy. Soc. London A, 438: 23-46, 1992.
448. G. D. Smith. Numerical Solution of Partial Differential Equations. Clarendon Press, Oxford, 1978.
449. J. Smoller. Shock Waves and Reaction-Diffusion Equations. Springer-Verlag, 1994.
450. G. A. Sod. A Numerical Study of a Converging Cylindrical Shock. J. Fluid Mechanics, 83: 785-794, 1977.
451. G. A. Sod. A Survey of Several Finite Difference Methods for Systems of Nonlinear Hyperbolic Conservation Laws. J. Comput. Phys., 27: 1-31, 1978.
452. G. A. Sod. Numerical Methods in Fluid Dynamics. Cambridge University Press, 1985.
453. G. A. Sod. A Random Choice Method for the Stefan Problem. Computers Math. Applic., 19: 1-9, 1990.
454. W. Speares. A Finite Volume Approach to the Weighted Average Flux Method. MSc thesis, College of Aeronautics, Cranfield Institute of Technology, UK, 1991.
455. W. Speares and E. F. Toro. A High-Resolution Algorithm for Time-Dependent Shock Dominated Problems with Adaptive Mesh Refinement. Z. Flugwiss. Weltraumforsch. (Journal of Flight Sciences and Space Research), 19: 267-281, 1995.
456. S. P. Spekreijse. Multigrid Solution of Monotone Second-Order Discretizations of Hyperbolic Conservation Laws. Math. Comp., 49(179):135-155, 1987.
457. S. P. Spekreijse. Multigrid Solution of the Steady Euler Equations. PhD thesis, Centre for Mathematics and Computer Science, Amsterdam, The Netherlands, 1988.
458. H. Städtke. Gasdynamic Aspects of Two-Phase Flow. Wiley-VCH, Berlin, 2006.
459. H. Städtke, G. Franchello, B. Worth, U. Graf, P. Romstedt, A. Kumbaro, J. García-Cascales, H. Pailliere, H. Deconinck, M. Ricchiuto, B. Smith, F. De Cachard, E. F. Toro, E. Romenski, and S. Mimouni. Advanced Three-Dimensional Two-Phase Flow Simulation Tools for Application to Reactor Safety (ASTAR). Nuclear Engineering and Design, 235: 379-400, 2005.
460. J. L. Steger, F. C. Dougherty, and J. A. Benek. A Chimera Grid Scheme. In Advances in Grid Generation, ASME FED, Vol. 5, 1983.
461. J. L. Steger and R. F. Warming. Flux Vector Splitting of the Inviscid Gasdynamic Equations with Applications to Finite Difference Methods. J. Comput. Phys., 40: 263-293, 1981.
462. H. B. Stewart and B. Wendroff. Two-Phase Flow: Models and Methods. J. Comput. Phys., 56: 363-409, 1984.
463. J. J. Stoker. Water Waves. The Mathematical Theory with Applications. John Wiley and Sons, 1992.
464. G. Strang. On the Construction and Comparison of Difference Schemes. SIAM J. Numer. Anal., 5(3):506-517, 1968.
465. R. C. Swanson and E. Turkel. On Central-Difference and Upwind Methods. Technical Report ICASE 90-44, NASA Langley Research Center, Hampton, Virginia, USA, 1990.
466. B. K. Swartz and B. Wendroff. AZTEC: A Front Tracking Code Based on Godunov's Method. Applied Numerical Mathematics, 2: 385-397, 1986.
467. P. K. Sweby. Shock Capturing Schemes. PhD thesis, Department of Mathematics, University of Reading, UK, 1982.
468. P. K. Sweby. High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws. SIAM J. Numer. Anal., 21: 995-1011, 1984.
469. P. K. Sweby. TVD Schemes for Inhomogeneous Conservation Laws. In Notes on Numerical Fluid Mechanics, Vol. 24, Non-Linear Hyperbolic Equations-Theory, Computation Methods and Applications, pages 599-607. Vieweg, 1989.
470. P. K. Sweby and M. J. Baines. On Convergence of Roe's Scheme for the General Non-linear Wave Equation. J. Comput. Phys., 56(1):135-148, 1984.
471. E. Tadmor. Convenient Total Variation Diminishing Conditions for Non-Linear Difference Schemes. SIAM J. Numer. Anal., 25: 1002-1014, 1988.
472. M. Takahiro and K. Kanya. A Multi-State HLL Approximate Riemann Solver for Ideal Magnetohydrodynamics. J. Comput. Phys., 208(1):315-344, 2005.
473. Y. Takakura and E. F. Toro. Arbitrarily Accurate Non-Oscillatory Schemes for a Non-Linear Conservation Law. J. Computational Fluid Dynamics, 11: 7-18, 2002.
474. Y. Takano. An Application of the Random Choice Method to a Reactive Gas with Many Chemical Species. J. Comput. Phys., 67: 173-187, 1986.
475. K. Takayama. Optical Flow Visualization of Shock Wave Phenomena (Paul Vieille Memorial Lecture). In Shock Waves @ Marseille, Vol. 4 (Brun and Dumitrescu, Editors), pages 7-16. Springer-Verlag, 1995.
476. K. Takayama (Editor). Shock Waves (Proc. 18th Int. Symp. on Shock Waves, Sendai, Japan, 1991), Two Volumes. Springer-Verlag, 1992.
477. S. Taki and T. Fujiwara. Numerical Analysis of Two-Dimensional Nonsteady Detonations. AIAA Journal, 16: 73-77, 1978.
478. C. K. W. Tam and J. C. Webb. Dispersion-Relation-Preserving Finite Difference Schemes for Computational Acoustics. J. Comput. Phys., 107: 262-281, 1993.
479. P. Tamamidis, G. Zhang, and D. N. Assanis. Comparison of Pressure-Based and Artificial Compressibility Methods for Solving 3D Steady Incompressible Viscous Flows. J. Comput. Phys., 124(1):1-13, 1996.
480. T. Tanaka. Finite Volume TVD Scheme on an Unstructured Grid System for Three-Dimensional MHD Simulation of Inhomogeneous Systems Including Strong Background Potential Fields. J. Comput. Phys., 111: 381-, 1994.
481. L. Tatsien and Y. Wenci. Boundary-Value Problems for Quasi-Linear Hyperbolic Systems. Duke University Mathematics Series, 1985.
482. J. W. Thomas. Numerical Partial Differential Equations, Texts in Applied Mathematics 22. Springer-Verlag, 1998.
483. J. F. Thompson, F. C. Thames, and C. W. Mastin. Automatic Numerical Grid Generation of Body-Fitted Curvilinear Coordinate System for Field Containing any Number of Arbitrary Two-Dimensional Bodies. J. Comput. Phys., 15: 299-319, 1974.
484. J. F. Thompson, J. F. Warsi, and C. W. Mastin. Grid Generation: Foundations and Applications. North-Holland, 1982.
485. J. F. (Editor) Thompson. Numerical Grid Generation. North-Holland, 1982.
486. K. W. Thompson. The Special Relativistic Shock Tube. J. Fluid Mechanics, 171: 365-, 1986.
487. K. W. Thompson. Time Dependent Boundary Conditions for Hyperbolic Systems. J. Comput. Phys., 68: 1-24, 1987.
488. V. A. Titarev. Derivative Riemann Problem and ADER Schemes. PhD thesis, Department of Mathematics, University of Trento, Italy, 2005.
489. V. A. Titarev, E. Romenski, and E. F. Toro. MUSTA-Type Upwind Fluxes for Non-Linear Elasticity. Int. J. Numer. Meth. Engineering, 73: 897-926, 2008.
490. V. A. Titarev and E. F. Toro. ADER: Arbitrary High Order Godunov Approach. J. Scientific Computing, 17: 609-618, 2002.
491. V. A. Titarev and E. F. Toro. Finite Volume WENO Schemes for Three-Dimensional Conservation Laws. J. Comput. Phys., 201(1):238-260, 2004.
492. V. A. Titarev and E. F. Toro. ADER Schemes for Three-Dimensional Hyperbolic Systems. J. Comput. Phys., 204: 715-736, 2005.
493. V. A. Titarev and E. F. Toro. MUSTA Schemes for Multi-Dimensional Hyperbolic Systems: Analysis and Improvements. Int. J. Numer. Meth. Fluids, 49: 117-147, 2005.
494. E. F. Toro. Multi-Stage Predictor-Corrector Fluxes for Hyperbolic Equations. Technical Report NI03037-NPA, Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK, 17th June, 2003.
495. E. F. Toro. A New Numerical Technique for Quasi-Linear Hyperbolic Systems of Conservation Laws. Technical Report CoA-8608, College of Aeronautics, Cranfield Institute of Technology, UK, 1986.
496. E. F. Toro. A Fast Riemann Solver with Constant Covolume Applied to the Random Choice Method. Int. J. Numer. Meth. Fluids, 9: 1145-1164, 1989.
497. E. F. Toro. A Weighted Average Flux Method for Hyperbolic Conservation Laws. Proc. Roy. Soc. London, A423: 401-418, 1989.
498. E. F. Toro. Random Choice Based Hybrid Schemes for one and Two-Dimensional Gas Dynamics. In Non-linear Hyperbolic Equations - Theory, Computation Methods and Applications. Notes on Numerical Fluid Mechanics, pages 630-639. Vieweg, Braunschweig, 1989.
499. E. F. Toro. Riemann-Problem Based Techniques for Computing Reactive Two-Phase Flows. In Dervieux and Larrouturrou, editors, Proc. Third. Intern. Confer. on Numerical Combustion, number 351 in Lecture Notes in Physics, pages 472-481, Antibes, France, May 1989.
500. E. F. Toro. A Linearised Riemann Solver for the Time-Dependent Euler Equations of Gas Dynamics. Proc. Roy. Soc. London, A434: 683-693, 1991.
501. E. F Toro. Some Aspects of Shock Capturing Methods for Gas Dynamics. Technical Report COA-9112, College of Aeronautics, Cranfield Institute of Technology, UK, 1991.
502. E. F. Toro. Riemann Problems and the WAF Method for Solving Two-Dimensional Shallow Water Equations. Phil. Trans. Roy. Soc. London Series A: Physical Sciences and Engineering, A338: 43-68, 1992.
503. E. F. Toro. The Weighted Average Flux Method Applied to the Euler Equations. Phil. Trans. Roy. Soc. London Series A: Physical Sciences and Engineering, A341: 499-530, 1992.
504. E. F. Toro. The Weighted Average Flux Method Applied to the Time-Dependent Euler Equations. Phil. Trans. Roy. Soc. London, A341: 499-530, 1992.
505. E. F. Toro. Viscous Flux Limiters. In J. B. Vos, A. Rizzi, and I. L. Ryhming, editors, Notes on Numerical Fluid Dynamics, Vol. 35, pages 592-600. Vieweg, 1992.
506. E. F. Toro. Defects of Conservative Approaches and Adaptive Primitive-Conservative Schemes for Computing Solutions to Hyperbolic Conservation Laws. Technical Report MMU 9401, Department of Mathematics and Physics, Manchester Metropolitan University, UK, 1994.
507. E. F. Toro. Direct Riemann Solvers for the Time-Dependent Euler Equations. Shock Waves, 5: 75-80, 1995.
508. E. F. Toro. MUSCL-Type Primitive Variable Schemes. Technical Report MMU-9501, Department of Mathematics and Physics, Manchester Metropolitan University, UK, 1995.
509. E. F. Toro. On Adaptive Primitive-Conservative Schemes for Conservation Laws. In M. M. Hafez, editor, Sixth International Symposium on Computational Fluid Dynamics: A Collection of Technical Papers, volume 3, pages 1288-1293, Lake Tahoe, Nevada, USA, September 4-8, 1995.
510. E. F Toro. Some IVPs for Which Conservative Methods Fail Miserably. In M. M. Hafez, editor, Sixth International Symposium on Computational Fluid Dynamics: A Collection of Technical Papers, volume 3, pages 1294-1299, Lake Tahoe, Nevada, USA, September 4-8, 1995.
511. E. F. Toro. On Glimm-Related Schemes for Conservation Laws. Technical Report MMU-9602, Department of Mathematics and Physics, Manchester Metropolitan University, UK, 1996.
512. E. F. Toro. Exact and Approximate Riemann Solvers for the Artificial Compressibility Equations. Technical Report 97-02, Department of Mathematics and Physics, Manchester Metropolitan University, UK, 1997.
513. E. F. Toro. On Two Glimm-Related Schemes for Hyperbolic Conservation Laws. In Proc. Fifth Annual Conference of the CFD Society of Canada, pages 3.49-3.54. University of Victoria, Canada, 1997.
514. E. F. Toro. Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer-Verlag, 1997.
515. E. F. Toro. Primitive, Conservative and Adaptive Schemes for Hyperbolic Conservation Laws. In Numerical Methods for Wave Propagation. Toro, E. F. and Clarke (Editors), J. F., pages 323-385. Kluwer Academic Publishers, 1998.
516. E. F. Toro. NUMERICA: A Library of Source Codes for Teaching, Research and Applications. Numeritek Ltd., www.numeritek.com, 1999.
517. E. F. Toro. Riemann Solvers and Numerical Methods for Fluid Dynamics, Second Edition. Springer-Verlag, 1999.
518. E. F. Toro. Shock-Capturing Methods for Free-Surface Shallow Flows. Wiley and Sons Ltd., 2001.
519. E. F. Toro. A Multi-Stage Numerical Flux. Appl. Numer. Math., 56: 1464-1479, 2006.
520. E. F. Toro. Riemann Solvers with Evolved Initial Conditions. Int. J. Numer. Meth. in Fluids, 52: 433-453, 2006.
521. E. F Toro and Titarev V. V. J. Comput. Phys., 212(1):150-165, 2006.
522. E. F Toro and Titarev V. V. J. Comput. Phys., 216: 403-429, 2006.
523. E. F. Toro, S. J. Billet, and E. P. Boden. Advanced Modelling Techniques for Propulsion Systems. In Proceedings of Conference on Energetic Materials and Propulsion Technology, Salsbury, Australia, April 18-19, 1996, pages-.-, 1996.
524. E. F. Toro and S. J. Billett. Centred TVD Schemes for Hyperbolic Conservation Laws. Technical Report MMU-9603, Department of Mathematics and Physics, Manchester Metropolitan University, UK, 1996.
525. E. F. Toro and S. J. Billett. A Unified Riemann-Problem Based Extension of the Warming-Beam and Lax-Wendroff Schemes. IMA J. Numer. Anal., 17: 61-102, 1997.
526. E. F. Toro and S. J. Billett. Centred TVD Schemes for Hyperbolic Conservation Laws. IMA J. Numerical Analysis, 20: 47-79, 2000.
527. E. F. Toro and R. E. Brown. The WAF Method and Splitting Procedures for Viscous, Shocked Flows. In Proceedings of the 18th International Symposium on Shock Waves, Tohoku University, Sendai, Japan (K. Takayama, Editor), pages 1119-1126. Springer-Verlag, 1992.
528. E. F. Toro and C. E. Castro. The Derivative Riemann Problem for the Baer-Nunziato Equations. In Hyperbolic Problems: Theory, Numerics and Applications. Vol. 1. Benzoni-Gavage and Serre (editors), pages 1045-1052. Springer, 2008.
529. E. F. Toro and C. E. Castro. The Derivative Riemann Problem for the Baer-Nunziato Equations. In Hyperbolic Problems: Theory, Numerics and Applications HYPE2006, Vol. 1. S. Benzoni-Gavage and D. Serre (Editors), pages 1045-1052. Springer, 2008.
530. E. F. Toro and A. Chakraborty. Development of an Approximate Riemann Solver for the Steady Supersonic Euler Equations. The Aeronautical Journal, 98: 325-339, 1994.
531. E. F. Toro and C. C. Chou. A Linearised Riemann Solver for the Steady Supersonic Euler Equations. Int. J. Numer. Meth. Fluids, 16: 173-186, 1993.
532. E. F. Toro and P. García-Navarro. Godunov-Type Methods for Free-Surface Shallow Flows: A Review. J. Hydraulic Research, 45(6):736-751, 2007.
533. E. F. Toro and A. Hidalgo. ADER Finite Volume Schemes for Diffusion-Reaction Equations. Applied Numerical Mathematics, 59: 73-100, 2009.
534. E. F. Toro, A. Hidalgo, and M. Dumbser. FORCE Schemes on Unstructured Meshes I: Conservative Hyperbolic Systems. Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK. Preprint NI09005-NPA, September 2008. Submitted to J. Comput. Phys., 2008.
535. E. F. Toro, R. C. Millington, and L. A. M. Nejad. Towards Very High-Order Godunov Schemes. In Godunov Methods: Theory and Applications. Edited Review, E. F. Toro (Editor), pages 905-937. Kluwer Academic/Plenum Publishers, 2001.
536. E. F. Toro, M. Olim, and K. Takayama. Unusual Increase in Tsunami Wave Amplitude at the Okushiri Island: Mach Reflection of Shallow Water Waves. In Proceedings of the 22nd International Symposium on Shock Waves, Vol. II. Ball, Hillier and Roberts (Editors), pages 1207-1212. University of Southampton, UK, 1999.
537. E. F. Toro and P. L. Roe. A Hybridised High-Order Random Choice Method for Quasi-Linear Hyperbolic Systems. In Grönig, editor, Proc. 16th Intern. Symp. on Shock Tubes and Waves, pages 701-708, Aachen, Germany, July 1987.
538. E. F. Toro and P. L. Roe. A Hybrid Scheme for the Euler Equations Using the Random Choice and Roe's Methods. In Numerical Methods for Fluid Dynamics III. The Institute of Mathematics and its Applications Conference Series, New Series No. 17, Morton and Baines (Editors), pages 391-402. Oxford University Press, New York, 1988.
539. E. F. Toro, M. Spruce, and W. Speares. Restoration of the Contact Surface in the HLL-Riemann Solver. Technical Report CoA-9204, Department of Aerospace Science, Collegue of Aeronautics, Cranfield Institute of Technology, UK, 1992.
540. E. F. Toro, M. Spruce, and W. Speares. Restoration of the Contact Surface in the HLL-Riemann Solver. Shock Waves, 4: 25-34, 1994.
541. E. F. Toro and V. A. Titarev. Solution of the Generalised Riemann Problem for Advection-Reaction Equations. Proc. Roy. Soc. London A, 458: 271-281, 2002.
542. E. F. Toro and V. A. Titarev. ADER Schemes for Scalar Hyperbolic Conservation Laws with Source Terms in Three Space Dimensions. J. Comput. Phys., 202(1):196-215, 2005.
543. E. F. Toro (Editor). Godunov Methods: Theory and Applications. Edited Review. Kluwer Academic/Plenum Publishers, 2001.
544. I. Toumi. A Weak Formulation of Roe's Approximate Riemann Solver. J. Comput. Phys., 102: 360-373, 1992.
545. I. Toumi. An Upwind Numerical Method for Two-Fluid Two-Phase Flow Models. Nuclear Science and Engineering, 123: 147-168, 1996.
546. I. Toumi and D. Caruge. An Implicit Second-Order Numerical Method for Three-Dimensional Two-Phase Flow Calculations. Nuclear Science and Engineering, 130: 1-13, 1998.
547. I. Toumi and A. Kumbaro. An Approximate Linearized Riemann Solver for a Two-Fluid Model. J. Comput. Phys., 124: 286-300, 1996.
548. E. Turkel and A. Arnone. Pseudo-Compressibility Methods for the Incompressible Flow Equations. Technical Report ICASE 93-66, NASA Langley Research Center, USA, 1993.
549. A. Tveito and R. Winther. Introduction to Partial Differential Equations. Springer-Verlag, 1998.
550. G. D. van Albada, B. van Leer, and W. W. Roberts. A Comparative Study of Computational Methods in Cosmic Gas Dynamics. Astron. Astrophysics, 108: 76-84, 1982.
551. J. J. W. van der Vegt and H. van der Ven. Space-Time Discontinuous Galerkin Finite Element Method with Dynamic Grid Motion for Inviscid Compressible Flows: General Formulation. J. Comput. Phys., 182(2):546-585, 2002.
552. B. van Leer. Towards the Ultimate Conservative Difference Scheme I. The Quest for Monotonicity. Lecture Notes in Physics, 18: 163-168, 1973.
553. B. van Leer. Towards the Ultimate Conservative Difference Scheme II. Monotonicity and Conservation Combined in a Second Order Scheme. J. Comput. Phys., 14: 361-370, 1974.
554. B. van Leer. MUSCL, A New Approach to Numerical Gas Dynamics. In Computing in Plasma Physics and Astrophysics, Max-Planck-Institut für Plasma Physik, Garchung, Germany, April 1976.
555. B. van Leer. Towards the Ultimate Conservative Difference Scheme III. Upstream-Centered Finite Difference Schemes for Ideal Compressible Flow. J. Comput. Phys., 23: 263-275, 1977.
556. B. van Leer. Towards the Ultimate Conservative Difference Scheme IV. A New Approach to Numerical Convection. J. Comput. Phys., 23: 276-299, 1977.
557. B. van Leer. Towards the Ultimate Conservative Difference Scheme V. A Second Order Sequel to Godunov's Method. J. Comput. Phys., 32: 101-136, 1979.
558. B. van Leer. Flux-Vector Splitting for the Euler Equations. Technical Report ICASE 82-30, NASA Langley Research Center, USA, 1982.
559. B. van Leer. Flux Vector Splitting for the Euler Equations. In Proceedings of the 8th International Conference on Numerical Methods in Fluid Dynamics, pages 507-512. Springer-Verlag, 1982.
560. B. van Leer. On the Relation Between the Upwind-Differencing Schemes of Godunov, Enguist-Osher and Roe. SIAM J. Sci. Stat. Comput., 5(1):1-20, 1985.
561. B. van Leer. Progress in Multi-Dimensional Upwind Differencing. Technical Report CR-189708/ICASE 92-43, NASA, Sept. 1992.
562. B. van Leer. Upwind and High-Resolution Methods for Compressible Flow: from Donor Cell to Residual Distrubution Schemes. Review Article. Commun. Comput. Phys., 1(2):192-206, 2006.
563. B. van Leer, J. L. Thomas, and P. L. Roe. A comparison of numerical flux formulas for the euler and navier-stokes equations. AIAA 8th Computational Fluid Dynamics Conference, June 9-11, 1987, Honolulu, Hawaii. Paper AIAA-87-1104-CP, 1987.
564. M. H. P. M van Puten. A Numerical Implementation of MHD in Divergence Form. J. Comput. Phys., 105: 339-353, 1993.
565. M. O. Varner, W. R. Martindale, W. J. Phares, and J. C. Adams. Large Perturbation Flow Field Analysis and Simulation for Supersonic Inlets. Technical Report NASA CR-174676, NASA, USA, 1984.
566. M. E. Vázquez-Cendón. Estudio de Esquemas Descentrados para su Aplicación a las Leyes de Conservación Hiperbólicas con Términos de Fuente. PhDthesis, Departamento de Matemáticas Aplicadas, Universidad de Santiago de Compostela, España, 1994.
567. M. E. Vázquez-Cendón. Improved Treatment of Source Terms in Upwind Schemes for the Shallow Water Equations in Channels with Irregular Geometry. J. Comput. Phys., 148: 497-526, 1999.
568. M. Vinokur. An Analysis of Finite-Difference and Finite-Volume Formulations of Conservation Laws. J. Comput. Phys., 81: 1-52, 1989.
569. A. I. Volpert. The Space BV and Quaslinear Equations. Math. USSR Sbornik, 73: 225-267, 1967.
570. L. Wang and D. J. Mavriplis. Implicit Solution of the Unsteady Euler Equations for High-Order Accurate Discontinuous Galerkin Discretizations. J. Comput. Phys., 225(2):1994-2015, 2007.
571. S. Y. Wang, P. B. Buttler, and H. Krier. Non-Ideal Equations of State for Combusting and Detonating Explosives. Prog. Energy Combust. Sci., 11: 311-331, 1985.
572. R. F. Warming and R. W. Beam. Upwind Second Order Difference Schemes with Applications in Aerodynamic Flows. AIAA Journal, 24: 1241-1249, 1976.
573. Z. U. A. Warsi. Fluid Dynamics: Theoretical and Computational Approaches. CRC Press Inc., 1992.
574. G. Watson, D. H. Peregrine, and E. F. Toro. Numerical Solution of the Shallow Water Equations on a Beach Using the Weighted Average Flux Method. In Computational Fluid Dynamics 1992, Vol. 1, pages 495-502. Elsevier, 1992.
575. N. P. Weatherill. Numerical Grid Generation. Lecture series 1990-06, von Karman Institute for Fluid Dynamics, 1990.
576. N. P. Weatherill. An Upwind Kinetic Flux Vector Splitting Method on General Mesh Topologies. Intern. J. Numer. Meth. Engineering, 37: 623-643, 1994.
577. E. Weinan and C. W. Shu. A Numerical Resolution Study of High-Order Essentially Non-Oscillatory Schemes Applied to Incompressible Flow. Technical Report ICASE 92-39, NASA Langley Research Center, USA, 1992.
578. B. V. Wells, M. J. Baines, and P. Glaister. Generation of Arbitrary Lagrangian-Eulerian (ALE) Velocities, Based on Monitor Functions, for the Solution of Compressible Fluid Equations. Int. J. Numer. Methods in Fluids, 47: 1375-1381, 2005.
579. P. Wesseling. Principles of Computational Fluid Dynamics. Springer, 2001.
580. G. B. Whitam. Linear and Non-linear Waves. John Wiley and Sons, 1974.
581. F. A. Williams. Combustion Theory. Benjamin Cummings Publishing Company, Inc Merlo Park, California, 1985.
582. P. Woodward and P. Colella. The Numerical Simulation of Two-Dimensional Fluid Flow with Strong Shocks. J. Comput. Phys., 54: 115-173, 1984.
583. K. Xu. Gas Kinetic Schemes for Unsteady Compressible Flow Simulations. VKI Fluid Dynamics Lecture Series, 1998-3, 1998.
584. K. Xu, L. Martinelli, and A. Jameson. Gas-Kinetic Finite Volume Methods, Flux-Vector Splitting and Artificial Diffusion. J. Comput. Phys., 120: 48-65, 1995.
585. K. Xu and K. H. Prendergast. Numerical Navier-Stokes Solutions from Gas-Kinetic Theory. J. Comput. Phys., 114: 9-17, 1994.
586. N. N. Yanenko. The Method of Fractional Steps. Springer-Verlag, New York, 1971.
587. G. Yang, D. M. Causon, D. M. Ingram, R. Saunders, and P. Batten. A Cartesian Cut Cell Method for Compressible Flows Part A: Static Body Problems. Aeronautical Journal, 101: 47-56, 1997.
588. G. Yang, D. M. Causon, D. M. Ingram, R. Saunders, and P. Batten. A Cartesian Cut Cell Method for Compressible Flows Part B: Moving Body Problems. Aeronautical Journal, 101: 57-65, 1997.
589. J. Y. Yang, M. H. Chen, I. N. Tsai, and J. W. Chang. A Kinetic Beam Scheme for Relativistic Gas Dynamics. J. Comput. Phys., 136: 19-40, 1997.
590. H. C. Yee. Construction of Explicit and Implicit Symmetric TVD Schemes and their Applications. J. Comput. Phys., 68: 151-179, 1987.
591. H. C. Yee. A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods. Von Karman Institute of Fluid Dynamics, Lecture Series 1989-04, 1989.
592. H. C. Yee and P. K. Sweby. Non-Linear Dynamics and Numerical Uncertainties in CFD. Technical Report TM 110398, NASA Ames Research Center, Moffett Field, USA, 1996.
593. H. C. Yee, R. F. Warming, and A. Harten. Implicit Total Variation Diminishing (TVD) Schemes for Steady State Problems. J. Comput. Phys., 57: 327-360, 1985.
594. E. C. Zachmanoglou and D. W. Thoe. Introduction to Partial Differential Equations. Dover Publications, Inc. New York, 1986.
595. S. T. Zalesak. Fully Multi-dimensional Flux-Corrected Transport Algorithms for Fluids. J. Comput. Phys., 31: 335-362, 1979.
596. D. D. Zeeuw and K. G. Powell. An Adaptively Refined Cartesian Mesh Solver for the Euler Equations. J. Comput. Phys., 104: 56-68, 1993.
597. Y. B. Zeldovich and Y. P. Raizer. Physics of Shock Waves and High Temperature Hydrodynamic Phenomena. Academic Press, 1966.
598. G-C. Zha and E. Bilgen. Numerical Solution of Euler Equations by a New Flux Vector Splitting Scheme. Int. J. Numer. Meth. Fluids, 17: 115-144, 1993.
599. T. Zhang and Y. Zheng. Conjecture on the Structure of Solutions of the Riemann Problem for Two Dimensional Gas Dynamics. SIAM J. Math. Anal., 21(3):593-630, 1990.
600. H. W. Zheng, C. Shu, and Chew Y. T. An Object-Oriented and Quadrilateral-Mesh Based Solution Adaptive Algorithm for Compressible Multi-Fluid Flows. J. Comput. Phys., 227(14):6895-6921, 2008.