High-order central schemes for hyperbolic systems of conservation laws

SIAM Journal of Scientific Computing

Volumn 21, Issue 1, 1999, Pages 294-322

  Bianco, Franca ^a   Puppo, Gabriella ^a   Russo, Giovanni ^b  

^a POLITECNICO DI TORINO   (Italy)

^b UNIVERSITY OF L'AQUILA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATION THEORY; INTEGRAL EQUATIONS; INTEGRATION; LINEAR SYSTEMS; PROBLEM SOLVING; VECTORS;

CONSERVATION LAWS; ESSENTIALLY NONOSCILLATORY RECONSTRUCTION; HIGH ORDER CENTRAL SCHEMES; HYPERBOLIC SYSTEMS; NATURAL CONTINUOUS EXTENSION; NUMBER OF EXTREMA DECREASING;

RUNGE KUTTA METHODS;

EID: 0033296324     PISSN: 10648275     EISSN: None     Source Type: None    
DOI: 10.1137/S1064827597324998     Document Type: Article

References (20)

1. A. M. ANILE, V. ROMANO, AND G. RUSSO, Hydrodynamical models for semiconductors based on extended thermodynamics, VLSI Design, 8 (1998), pp. 521-525.
2. F. BIANCO, G. PUPPO, AND G. RUSSO, Proceedings of the High Order Central Schemes for Hyperbolic Systems of Conservation Laws Conference, HYP-98 Seventh International Conference on Hyperbolic Problems, Theory, Numerics, Applications, ETH Zürich, Switzerland, 1998.
3. A. HARTEN, B. ENGQUIST, S. OSHER, AND S. CHAKRAVARTHY, Uniformly high order accurate essentially non-oscillatory schemes III, J. Comput. Phys., 71 (1987), pp. 231-303.
4. G. S. JIANG AND E. TADMOR, Non-Oscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws, CAM Report 96-36, UCLA, Los Angeles, CA, 1996.
5. P. D. LAX, Weak solutions of non-linear hyperbolic equations and their numerical computation, Comm. Pure Appl. Math., 7 (1954), pp. 159-193.
6. R. J. LEVEQUE, Numerical Methods for Conservation Laws, Lectures in Mathematics, Birkhäuser-Verlag, Basel, Switzerland, 1992.
7. D. LEVY, G. PUPPO, AND G. RUSSO, Central WENO Schemes for Hyperbolic Systems of Conservation Laws, Ecole Normale Superieure report LMENS-98-17; Math. Model. Numer. Anal., to appear.
8. D. LEVY, G. PUPPO, AND G. RUSSO, Central WENO Schemes for Hyperbolic Systems of Conservation Laws, Ecole Normale Superieure report LMENS-98-17; Math. Model. Numer. Anal., to appear.
9. D. LEVY, G. PUPPO, AND G. RUSSO, Central WENO Schemes for 2D Hyperbolic Systems of Conservation Laws, in Proceedings of ICOSAHOM 98, D. Gottlieb, ed., Herzliya, Israel, 1998.
10. D. LEVY AND E. TADMOR, Non-oscillatory central differencing for the Incompressible 2-D Euler Equations, CAM Report 96-37, UCLA, Los Angeles, CA, 1996.
11. X. D. LIU AND E. TADMOR, Third order non-oscillatory central scheme for hyperbolic conservation laws, Numer. Math., 79 (1998), pp. 397-425.
12. H. NESSYAHU AND E. TADMOR, Non-oscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys., 87 (1990), pp. 408-448.
13. A. M. ROGERSON AND E. MEIBURG, A numerical study of the convergence properties of ENO schemes, J. Sci. Comput., 5 (1990), pp. 151-167.
14. V. ROMANO AND G. RUSSO, Numerical solution for hydrodynamical models of semiconductors, Math. Models Methods Appl. Sci., submitted.
15. R. SANDERS AND A. WEISER, High Resolution Staggered Mesh Approach for Nonlinear Hyperbolic Systems of Conservation Laws, J. Comput. Phys., 101 (1992), pp. 314-329.
16. C. W. SHU, Numerical experiments on the accuracy of ENO and modified ENO schemes, J. Sci. Comput., 5 (1990), pp. 127-149.
17. C. W. SHU AND S. OSHER, Efficient Implementation of Essentially Non-Oscillatory Shock-Capturing Schemes, II, J. Comput. Phys., 83 (1989), pp. 32-78.
18. G. SOD, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, J. Comput. Phys., 22 (1978), pp. 1-31.
19. P. WOODWARD AND P. COLELLA, The numerical simulation of two-dimensional fluid flow with strong shocks, J. Comput. Phys., 54 (1984), pp. 115-173.
20. M. ZENNARO, Natural Continuous Extensions of Runge-Kutta Methods, Math. Comp. 46 (1986), pp. 119-133.