A robust shock-capturing scheme based on rotated Riemann solvers

Computers and Fluids

Volumn 32, Issue 10, 2003, Pages 1379-1403

  Ren, Yu Xin ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

Carbuncle phenomenon; Flux difference splitting; Hyperbolic conservation laws; Numerical simulation; Shock capturing; Shock instability

Indexed keywords

APPROXIMATION THEORY; FINITE VOLUME METHOD; ROBUSTNESS (CONTROL SYSTEMS); VECTORS;

SHOCK INSTABILITY;

SHOCK TESTING;

FINITE VOLUME TECHNIQUE; FLUID DYNAMICS; MATHEMATICAL MODELING; SHOCK WAVE;

EID: 0038266921     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7930(02)00114-7     Document Type: Article

References (31)

1. Billet S. Toro E. On WAF-type schemes for multidimensional hyperbolic conservation laws J. Comput. Phys. 130 1997 1-24
2. Colella P. Multidimensional upwind methods for hyperbolic conservation laws J. Comput. Phys. 87 1990 171-200
3. Davis S. A rotationally biased upwind difference scheme for the Euler equations J. Comput. Phys. 56 1984 65-92
4. Deconinck H. Paillere H. Struijs R. Roe P. Multidimensional upwind schemes based on fluctuation-splitting for systems of conservation laws Comput. Mech. 11 1993 323-340
5. Edwards J.R. A low-diffusion flux-splitting scheme for Navier-Stokes calculations Comput. Fluids 26 1997 635-659
6. Fey M. Multidimensional upwinding. I. The method of transport for solving the Euler equations J. Comput. Phys. 143 1998 159-180
7. Godunov S. Finite difference methods for numerical computation of discontinuous solutions of the equations of fluid dynamics Math. Sb. 47 1959 271-290
8. Harten A. Engquist B. Osher S. Chakravarthy S.R. Uniformly high-order accurate essentially nonoscillatory scheme, III J. Comput. Phys. 71 1987 231-303
9. Harten A. Hyman J.M. Self adjusting grid methods for one-dimensional hyperbolic conservation laws J. Comput. Phys. 50 1983 235-269
10. Harten A. Lax P. A random choice finite difference scheme for hyperbolic conservation laws SIAM J. Numer. Anal. 18 1981 289-315
11. Huynh H.T. Accurate upwind methods for the Euler equations SIAM J. Numer. Anal. 32 1995 1565-1619
12. LeVeque R.J. Walder R. Grid alignment effects and rotated methods for computing complex flows in astrophysics Vos J.B. Rizsi A. Rhyming I.L. Proceedings of the Ninth GAMM Conference on Numerical Methods in Fluid Mechanics Notes on Numerical Fluid Mechanics vol. 35 1992 376 Vieweg Verlag Braunschweig
13. LeVeque R.J. Wave propagation algorithms for multidimensional hyperbolic systems J. Comput. Phys. 131 1997 327-353
14. Levy D.W. Powell K.G. Van Leer B. Use of a rotated Riemann Solver for the two-dimensional Euler equations J. Comput. Phys. 106 1993 201-214
15. Liou M.-S. Mass flux schemes and connection to shock instability J. Comput. Phys. 160 2000 623-648
16. Noelle S. Hyperbolic systems of conservation laws, the Weyl equation, and multidimensional upwinding J. Comput. Phys. 115 1994 22-26
17. Osher S. Solomon F. Upwind difference schemes for hyperbolic systems of conservation laws Math. Comput. 38 1982 339-374
18. Pandolfi M. D'Ambrosio D. Numerical instabilities in upwind methods: analysis and cures for the "carbuncle" phenomenon J. Comput. Phys. 166 2001 271-301
19. Quirk J. A contribution to the Great Riemann Solver Debate Int. J. Numer. Meth. Fluid Dyn. 18 1994 555-574
20. Roe P. Approximate Riemann solvers, parameter vectors, and difference schemes J. Comput. Phys. 43 1981 357-372
21. Roe P. Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics J. Comput. Phys. 63 1986 458-476
22. Rumsey C. Van Leer B. Roe P. A multidimensional flux function with applications to the Euler and Navier-Stokes equations J. Comput. Phys. 105 1993 306-323
23. Sanders R. Morano E. Druguet M. Multidimensional dissipation for upwind schemes: stability and applications to gas dynamics J. Comput. Phys. 145 1998 511-537
24. Shu C.-W. Osher S.J. Efficient implementation of essentially non-oscillatory shock capturing schemes J. Comput. Phys. 77 1988 439-471
25. Steger J.L. Warming R.F. Flux vector splitting of the inviscid gas-dynamic equations with applications to finite difference methods J. Comput. Phys. 40 1981 263-293
26. Toro E. Riemann solvers and numerical methods for fluid dynamics 1999 Springer-Verlag New York
27. Van Leer B. Towards the ultimate conservative difference scheme V J. Comput. Phys. 32 1979 101-136
28. Van Leer B. Flux-vector splitting for the Euler equations. Technical Report 82-30, ICASE, 1982
29. Wada Y. Liou M.-S. An accurate and robust flux splitting scheme for shock and contact discontinuities SIAM J. Sci. Comput. 18 1997 633-657
30. Woodward P. Colella P. Numerical simulations of two-dimensional fluid flow with strong shocks J. Comput. Phys. 54 1984 115-173
31. Xu K. Li Z. Dissipative mechanism in Godunov-type schemes Int. J. Numer. Meth. Fluids. 37 2001 1-22