Relaxation of energy and approximate riemann solvers for general pressure laws in fluid dynamics

SIAM Journal on Numerical Analysis

Volumn 35, Issue 6, 1998, Pages 2223-2249

  Coquel, Frédéric ^a   Perthame, Benoît ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

Entropy; Fluid dynamics; Real pressure laws; Relaxation of hyperbolic systems; Riemann solvers

Indexed keywords

EID: 0001130290     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142997318528     Document Type: Article

References (20)

1. [CLL] G.-Q. CHEN, C.D. LEVERMORE, AND T.P. LIU, Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math., 48 (1995), pp. 787-830.
2. [CP] F. COQUEL AND B. PERTHAME, work in progress.
3. [CrP] F. CORON AND B. PERTHAME, Numerical passage from kinetic to fluid equations, SIAM J. Numer. Anal., 28 (1991), pp. 26-42.
4. [GR] E. GODLEWSKI AND P.-A. RAVIART, Numerical Approximation of Hyperbolic Systems of Conservation Laws. Appl. Math. Sci. 118, Springer-Verlag, New York, 1996.
5. [GG] 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 (1988), pp. 437-458.
6. [H] A. HARTEN, On the symmetric form of systems of conservation laws with entropy, J. Comput., Phys., 49 (1983), pp. 151-164.
7. [HL] A. HARTEN AND P.D. LAX, A random choice finite difference scheme for hyperbolic conservation laws, SIAM J. Numer. Anal., 18 (1981), pp. 289-315.
8. [HLV] A. HARTEN, P.D. LAX, AND B. VAN LEER, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Rev., 25 (1983), pp. 35-61.
9. [I] A. IN, Numerical evaluation of an energy relaxation method for inviscid real fluids, SIAM J. Sci. Comput., to appear.
10. [JX] S. JlN AND Z. XIN, The relaxation schemes for systems of conservation laws in arbitrary space dimension, Comm. Pure. Appl. Math., 48 (1995), pp. 235-276.
11. [KT] M. KATSOULAKIS AND A.E. TZAVARAS, Contractive relaxation systems and the scalar multidimensional conservation law, Comm. Partial Differential Equations, to appear.
12. [La] B. LARROUTUROU, How to preserve the mass fraction positivity when computing multi-component flows, J. Comput. Phys., 95 (1991), pp. 59-84.
13. [L] T.P. LIU, Hyperbolic conservation laws with relaxation, Comm. Math. Phys., 108 (1987), pp. 153-175.
14. [N] R. NATALINI, Convergence to equilibrium for the relaxation approximations of conservation laws, Comm. Pure Appl. Math., 49 (1996), pp. 1-30.
15. [OS] S. OSHER AND F. SOLOMON, Upwind schemes for hyperbolic systems of conservation laws, Math. Comp., 38 (1982), pp. 339-374.
16. [R] P.L. ROE, Approximate Riemann solvers, parameter vectors and difference schemes, J. Comput. Phys., 43 (1981), pp. 357-372.
17. [S] I. SULICIU,On the Thermodynamics of Rate-type Fluids and Phase Transitions. I. Rate-type Fluids, preprint.
18. [T] E. TADMOR, A minimum entropy principle in the gas dynamics equations, Appl. Numer. Math., 2 (1986), pp. 211-219.
19. [VK] W. VINCENTI AND C. KRUGER, Introduction to Physical Gas Dynamics, Wiley, New York, 1965.
20. [W] J. WHITHAM, Linear and Nonlinear Waves, Wiley, New York, 1974.