Numerical comparison of the method of transport to a standard scheme

Computers and Fluids

Volumn 34, Issue 4-5 SPEC.ISS., 2005, Pages 541-560

  Kröger, Tim ^a   Noelle, Sebastian ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ENERGY DISSIPATION; KINETIC THEORY; NUMERICAL METHODS; VECTORS;

MULTIDIMENSIONAL FLUX VECTOR; MULTIDIMENSIONAL INSTABILITIES; RIEMANN SOLVER;

COMPUTATIONAL FLUID DYNAMICS;

MATHEMATICAL METHOD;

EID: 11144289534     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compfluid.2003.12.002     Document Type: Article

References (24)

1. Bultelle M. Grassin M. Serre D. Unstable Godunov discrete profiles for steady shock waves SIAM J. Numer. Anal. 35 6 1998 2272-2297
2. Einfeldt B. On Godunov-type methods for gas dynamics SIAM J. Numer. Anal. 25 2 1988 294-318
3. Engquist B. Osher S. One-sided difference approximations for nonlinear conservation laws Math. Comput. 36 154 1981 321-351
4. Fey M. Ein echt mehrdimensionales Verfahren zur Lösung der Eulergleichungen. Dissertation, Zürich, 1993
5. Fey M. Multidimensional upwinding. I. The method of transport for solving the Euler equations J. Comput. Phys. 143 1998 159-180
6. Fey M. Multidimensional upwinding. II. Decomposition of the Euler equations into advection equations J. Comput. Phys. 143 1998 181-199
7. Godunov S.K. A difference scheme for numerical computation of discontinuous solutions of equations of fluid dynamics Math. Sb. 47 1959 271-306
8. Harten A. Lax P.D. van Leer B. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws SIAM Rev. 25 1 1983 35-61
9. Kröger T. Multidimensional systems of hyperbolic conservation laws, numerical schemes, and characteristic theory. Connections, differences and numerical comparison. Dissertation, RWTH Aachen, Germany, 2004
10. 2AN, IGPM Preprint no. 228, RWTH Aachen, Germany, submitted for publication
11. Noelle S. The MoT-ICE: A new high-resolution wave-propagation algorithm for multidimensional systems of conservation laws based on Fey's method of transport J. Comput. Phys. 164 2 2000 283-334
12. Osher S. Solomon F. Upwind difference schemes for hyperbolic systems of conservation laws Math. Comput. 38 158 1982 339-374
13. Pandolfi M. D'Ambrosio D. Numerical instabilities in upwind methods: analysis and cures for the 'carbuncle' phenomenon J. Comput. Phys. 166 2 2001 271-301
14. Quirk J.J. A contribution of the great Riemann solver debate Int. J. Numer. Meth. Fluids 18 1994 555-574
15. Roe P.L. Approximate Riemann solvers, parameter vectors, and difference schemes J. Comput. Phys. 43 2 1981 357-372
16. Roe P.L. Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics J. Comput. Phys. 63 1986 458-476
17. Schmid P.J. Henningson D.S. Stability and transition in shear flows 2001 Springer New York
18. Shu C.-W. Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes, II J. Comput. Phys. 83 1 1989 32-78
19. Sweby P.K. High resolution schemes using flux limiters for hyperbolic conservation laws SIAM J. Numer. Anal. 21 2 1984 995-1011
20. von Törne C. MOTICE - Adaptive, parallel numerical solution of hyperbolic conservation laws. Dissertation, Bonner Mathematische Schriften, No. 334, 2000
21. Toro E.F. Riemann solvers and numerical methods for fluid dynamics. A practical introduction 2nd ed 1999 Springer Berlin
22. Toro E.F. Spruce M. Speares W. Restoration of the contact surface in the HLL-Riemann solver Shock Waves 4 1994 25-34
23. Zimmermann S. The method of transport for the Euler equations written as a kinetic scheme Int. Ser. Numer. Math. 141 2001 999-1008
24. Zimmermann S. Properties of the method of transport for the Euler equations. Dissertation, Zürich, 2001