The MoT-ICE: A new high-resolution wave-propagation algorithm for multidimensional systems of conservation laws based on fey's method of transport

Journal of Computational Physics

Volumn 164, Issue 2, 2000, Pages 283-334

  Noelle, Sebastian ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

Fey's Method of Tranport; Interface centered evolution; Multidimensional flux vector splitting; Systems of conservation laws

Indexed keywords

ICE; PHYSICAL PROPERTIES; WAVE PROPAGATION;

FEY METHOD OF TRANPORT; FLUX VECTOR SPLITTING; HIGH RESOLUTION; INTERFACE-CENTERED EVOLUTION; MULTIDIMENSIONAL FLUX VECTOR; MULTIDIMENSIONAL FLUX-VECTOR SPLITTING; NEW HIGH; SECOND ORDERS; SYSTEMS OF CONSERVATION LAWS; WAVE PROPAGATION ALGORITHM;

FINITE DIFFERENCE METHOD;

EID: 0000783988     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2000.6598     Document Type: Article

References (48)

1. Billet S., Toro E. On WAF-type schemes for multidimensional hyperbolic conservation laws. J. Comput. Phys. 130:1997;1.
2. Cockburn B., Coquel F., LeFloch P. Convergence of the finite volume method for multidimensional conservation laws. SIAM J. Nurner. Anal. 32:1995;687.
3. Colella P. Multidimensional upwind methods for hyperbolic conservation laws. J. Comput. Phys. 87:1990;171.
4. Crandall M., Majda A. Monotone difference approximations for scalar conservation laws. Math. Comput. 34:1980;1.
5. Deconinck H., Paillère H., Struijs R., Roe P. Multidimensional upwind schemes based on fluctuation-splitting for systems of conservation laws. Comput. Mech. 11:1993;323.
6. Deshpande S. A Second Order Accurate, Kinetic-Theory Based, Method for Inviscid Compressible Flows. 1986.
7. Fey M. Ein echt mehrdimensionales Verfahren zur Lösung der Eulergleichungen. 1993.
8. Fey M. Multidimensional upwinding. I. The method of transport for solving the Euler equations. J. Comput. Phys. 143:1998;159.
9. Fey M. Multidimensional upwinding. II. Decomposition of the Euler equations into advection equations. J. Comput. Phys. 143:1998;181.
10. M. Fey, and, R. Jeltsch, A simplified multidimensional Euler scheme, in, Proceedings of the First European Fluid Dynamics Conference, Brussels, Sept. 7-11, 1992, edited by, Ch. Hirsch, Elsevier, Amsterdam, 1992.
11. Fey M., Jeltsch R., Maurer J., Morel A.-T. The Method of Transport for Non-Linear Systems of Hyperbolic Conservation Laws in Several Space Dimensions. 1997.
12. 2-Stability of the Method of Transport for the 2-d Wave Equation, Research Report, Seminar for Applied Mathematics, ETH Zürich, 1998.
13. Godunov S. Finite difference methods for numerical computation of discontinuous solutions of the equations of fluid dynamics. Math. Sb. 47:1959;271.
14. Harten A., Lax P. A random choice finite difference scheme for hyperbolic conservation laws. SIAM J. Numer. Anal. 18:1981;289.
15. Hirsch C. Numerical Computation of Internal and External Flows. 2:1990.
16. Jiang G.-S., Shu C.-W. Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126:1996;202.
17. Kröner D., Noelle S., Rokyta M. Convergence of higher order upwind finite volume schemes on unstructured grids for scalar conservation laws in several space dimensions. Numer. Math. 71:1995;527.
18. Langseth J.-O., LeVeque R. A Wave Propagation Method for Three-Dimensional Hyperbolic Problems. 1995.
19. LeVeque R. A large timestep generalization of Godunov's method for conservation laws. SIAM J. Numer. Anal. 22:1985;1051.
20. R. LeVeque, CLAWPACK software, http://www.amath.washington.edu/rjl/clawpack.htlm .
21. LeVeque R. J. Wave propagation algorithms for multidimensional hyperbolic systems. J. Comput. Phys. 131:1997;327.
22. R. J. LeVeque, and, R. Walder, Grid alignment effects and rotated methods for computing complex flows in astrophysics, in, Proceedings of the Ninth GAMM Conference on Numerical Methods in Fluid Mechanics, edited by, J. B. Vos, A. Rizsi, and I. L. Rhyming, Notes Numer. Fluid Mech. 35, 376, 1992.
23. Liu X.-D., Osher S., Chan T. Weighted essentially nonoscillatory schemes. J. Comput. Phys. 115:1994;200.
24. Lukacova-Medvidova M., Morton K., Warnecke G. Evolution Galerkin Methods for Hyperbolic Systems in Two Space Dimensions. 1997.
25. J. Maurer, A genuinely multi-dimensional scheme for mixed hyperbolic-parabolic systems, in, Proceedings of the 7th International Conference on Hyperbolic Problems, Zürich, 1998, edited by, M. Fey and R. Jeltsch, Birkhäuser Basel, 1999, p, 713.
26. Morel A.-T. A Genuinely Multidimensional High-Resolution Scheme for the Shallow-Water. 1997.
27. Noelle S. Hyperbolic systems of conservation laws, the Weyl equation, and multidimensional upwinding. J. Comput. Phys. 115:1994;22.
28. Noelle S. Convergence of higher order finite volume schemes on irregular grids. Adv. Comput. Math. 3:1995;197.
29. Noelle S. A note on entropy inequalities and error estimates for higher order accurate finite volume schemes on irregular families of grids. Math. Comput. 65:1996;1155.
30. S. Noelle, The MoT-ICE: A new high-resolution wave-propagation algorithm based on Fey's Method of Transport, invited plenary lecture, in, Proceedings of the Second International Symposium on Finite Volumes for Complex Applications - Problems and Perspectives, Duisburg, Germany (July 1999), p, 95.
31. Ostkamp S. Multidimensional characteristic Galerkin schemes and evolution operators for hyperbolic systems. Math. Meth. Appl. Sci. 20:1997;1111.
32. Pandolfi M., D'Ambrosio D. Numerical instabilities in upwind methods: Analysis and cures for the "carbuncle" phenomenon. 1999.
33. Perthame B. Second order Boltzmann schemes for compressible Euler equations in one and two variables. SIAM J. Numer. Anal. 29:1992;1.
34. Quirk J. A contribution to the Great Riemann Solver Debate. Int. J. Numer. Meth. Fluid Dyn. 18:1994;555.
35. Roe P. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43:1981;357.
36. Roe P. Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics. J. Comput. Phys. 63:1986;458.
37. Roe P. Discontinuous solutions to hyperbolic systems under operator splitting. Numer. Meth. Part. Diff. Eq. 7:1991;207.
38. Roe P. Sonic flux formulae. SIAM J. Sci. Stat. Comput. 13:1992;611.
39. Sanders R., Prendergast K. The possible relation of the 3-kiloparsec arm to explosions in the galactic nucleus. Astrophys. J. 188:1974;489.
40. Steger J., Warming R. Flux vector splitting of the inviscid gas-dynamic equations with applications to finite difference methods. J. Comput. Phys. 40:1981;263.
41. Szepessy A. Convergence of a shock capturing streamline diffusion finite element method for a scalar conservation law in two space dimensions. Math. Comput. 53:1989;527.
42. Van Leer B. Towards the ultimate conservative difference scheme V. J. Comput. Phys. 32:1979;101.
43. Van Leer B. Flux vector splitting for the Euler equations. Proceedings of the 8th International Conference on Numerical Methods in Fluid Dynamics. 1982.
44. Van Leer B. Progress in Multi-Dimensional Upwinding. 1992.
45. R. Vilsmeier, F. Benkhallldoun, and, D. Hänel, (editors), Proceedings of the Second International Symposium on Finite Volumes for Complex Applications - Problems and Perspectives, Duisburg, Germany, July 1999, Hermes, Paris, 1999.
46. M. Westdickenberg, and, S. Noelle, A new convergence proof for finite volume schemes using the kinetic formulation of conservation laws. Accepted for publication.
47. Xu K. Gas Evoution Dynamics in Godunov-Type Schemes and Analysis of Numerical Shock Instability. 1999.
48. S. Zimmermann, The method of transport written as a kinetic scheme, in, Proceedings of the 7th International Conference on Hyperbolic Functions, Zürich, 1998, edited by, M. Fey and R. Jeltsch, Birkhäuser, Basel, 1999, p, 999.