Numerical comparison of Riemann solvers for astrophysical hydrodynamics

Journal of Computational Physics

Volumn 227, Issue 1, 2007, Pages 12-35

  Klingenberg, Christian ^a   Schmidt, Wolfram ^a   Waagan, Knut ^b  

^a UNIVERSITY OF WÜRZBURG   (Germany)

^b UNIVERSITY OF OSLO   (Norway)

Author keywords

Compressible turbulence; Euler equations; Godunov methods; Riemann solvers

Indexed keywords

ASTROPHYSICS; CODES (SYMBOLS); COMPUTATIONAL FLUID DYNAMICS; NUMERICAL METHODS; TURBULENCE;

APPROXIMATE RIEMANN SOLVER; ASTROPHYSICAL FLUID DYNAMICS; ASTROPHYSICAL HYDRODYNAMICS; COMPRESSIBLE TURBULENCE; EULER'S EQUATION; GODUNOV METHOD; NUMERICAL COMPARISON; RIEMANN SOLVER; STATE-OF-THE-ART ALGORITHMS; TURBULENCE SIMULATION;

SHOCK TUBES;

EID: 35348862409     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.07.034     Document Type: Article

References (21)

1. Bouchut F. Entropy satisfying flux vector splittings and kinetic BGK models. Numer. Math. 94 4 (2003) 623-672
2. Bouchut F. Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources. Frontiers in Mathematics (2004), Birkhäuser Verlag, Basel
3. Colella P., and Glaz H.M. Efficient solution algorithms for the Riemann problem for real gases. J. Comput. Phys. 59 (1985) 264-289
4. Colella P., and Woodward P.R. The piecewise parabolic method (PPM) for gas-dynamical simulations. J. Comput. Phys. 54 (1984) 174-201
5. Coquel F., and LeFloch P.G. A second order entropy satisfying scheme for systems of conservation laws (Un schéma entropique du second ordre pour les systèmes de lois de conservation). C.R. Acad. Sci., Paris, Sér. I 320 10 (1995) 1263-1268
6. Dobler W., Haugen N.E.L., Yousef T.A., and Brandenburg A. Bottleneck effect in three-dimensional turbulence simulations. Phys. Rev. E 68 (2003) 026304
7. Frisch U. Turbulence (1995), Cambridge University Press, Cambridge
8. B.A. Fryxell, E. Müller, W.D. Arnett, Hydrodynamics and nuclear burning, MPA preprint, 449, 1989.
9. Harten A., Lax P.D., and Leer B.v. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 25 (1983) 35-61
10. Hillebrandt W., Reinecke M., Schmidt W., Röpke F.K., Travaglio C., and Niemeyer J.C. Simulations of turbulent thermonuclear burning in type ia supernovae. In: Gerald W. (Ed). Analysis and Numerics for Conservation Laws (2005), Springer, Berlin 363-384
11. Pedelty J.A., and Woodward Paul R. Numerical simulations of the nonlinear kink modes in linearly stable supersonic slip surfaces. J. Fluid Mech. 225 (1991) 101-120
12. Reinecke M., Hillebrandt W., and Niemeyer J.C. Thermonuclear explosions of chandrasekhar-mass c + o white dwarfs. Astron. Astrophys. 347 (1999) 739-747
13. Reinecke M., Hillebrandt W., and Niemeyer J.C. Three-dimensional simulations of type ia supernovae. Astron. Astrophys. 391 (2002) 1167-1172
14. Roe P.L. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43 (1981) 357-372
15. Schmidt W., and Niemeyer J.C. Thermonuclear supernova simulations with stochastic ignition. Astron. Astrophys. 446 (2006) 627-633
16. Wolfram Schmidt, Turbulent thermonuclear combustion in degenerate stars, Ph.D. Thesis, 2004.
17. Wolfram Schmidt, Christoph Federrath, A parameter study of forced supersonic turbulence in large eddy simulations, in press.
18. Schmidt W., Hillebrandt W., and Niemeyer J.C. Numerical dissipation and the bottleneck effect in simulations of compressible isotropic turbulence models. Comp. Fluids 35 (2006) 353-371
19. Sytine I.V., Porter D.H., Woodward P.R., Hodson S.W., and Winkler K.-H. Convergence tests for the piecewise parabolic method and Navier-Stokes solutions for homogeneous compressible turbulence. J. Comput. Phys. 158 2 (2000) 225-238
20. Toro E.F., Spruce M., and Speares W. Restoration of the contact surface in the HLL-Riemann solver. Shock Waves 4 1 (1994) 25-34
21. Toro E.F. Riemann Solvers and Numerical Methods for Fluid Dynamics. second ed. (1999), Springer-Verlag, Berlin (a practical introduction)