An HLLC-type approximate Riemann solver for ideal magnetohydrodynamics

SIAM Journal on Scientific Computing

Volumn 25, Issue 6, 2004, Pages 2165-2187

  Gurski, K F ^a  

^a GEORGE WASHINGTON UNIVERSITY   (United States)

Author keywords

Magnetohydrodynamics; Positivity; Riemann solver

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; GAS DYNAMICS; MAGNETIC FLUX; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PROBLEM SOLVING; VELOCITY;

HLLC METHOD; MAGNETOHYDRODYNAMICS (MHD); POSITIVITY; RIEMAN SOLVER;

NONLINEAR SYSTEMS;

EID: 10244232990     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827502407962     Document Type: Article

References (22)

1. D. S. BALSARA, Total variation diminishing scheme for adiabatic and isothermal magnetohydrodynamics, Astrophys, J. Supplement Series, 116 (1998), pp. 144-153.
2. P. BATTEN, N. CLARKE, C. LAMBERT, AND D. M. CAUSON, On the choice of wavespeeds for the HLLC Riemann solver, SIAM J. Sci. Comput., 18 (1997), pp. 1553-1570.
3. M. BRIO AND C. Wu, An upwind differencing scheme for the equations of ideal magnetohydrodynamics, J. Comput. Phys., 75 (1988), pp. 400-422.
4. P. CARGO AND G. GALLICE, Roe matrices for ideal MHD and systematic construction of Roe matrices for systems of conservation laws, J. Comput. Phys., 136 (1997), pp. 446-466.
5. S. F. DAVIS, Simplified second-order Godunov-type methods, SIAM J. Sci. Statist. Comput., 9 (1988), pp. 445-473.
6. B. EINFELDT, On Godunov-type methods for gas dynamics, SIAM J. Numer. Anal., 25 (1988), pp. 294-318.
7. B. EINFELDT, C. D. MÜNZ, P. L. ROE, AND B. SJÖGREEN, On Godunov-type methods near low densities, J. Comput. Phys., 92 (1991), pp. 273-295.
8. K. O. FRIEDRICHS AND H. KRANZER, Notes on Magneto-hydrodynamics, VII. Nonlinear Wave Motion, Tech. Report NYO-6486-VII, Courant Institute of Mathematical Sciences, Magneto-Fluid Dynamics Division, New York University, New York, 1958.
9. S. K. GODUNOV, A difference method for the numerical calculation of discontinuous solutions of hydrodynamic equations, Mat. Sb., 47 (1959).
10. T. I. GOMBOSI, D. L. DEZEEUW, R. M. HÄBERLIN, AND K. G. POWELL, Three-dimensional multiscale MHD model of cometary plasma environments, J. Geophys. Res., 101 (1996), pp. 15233-15253.
11. 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.
12. P. JANHUNEN, A positive conservative method for magnetohydrodynamics based on HLL and Roe methods, J. Comput. Phys., 160 (2000), pp. 649-661.
13. T. J. LINDE, A Three-Dimensional Adaptive Multifluid MHD Model of the Heliosphere, Ph.D. Dissertation, University of Michigan, Ann Arbor, MI, 1998.
14. T. J. LINDE, T. I. GOMBOSI, P. L. ROE, K. G. POWELL, AND D. L. DEZEEUW, The heliosphere in magnetized local interstellar medium: Results of a 3D MHD simulation, J. Geophys. Res., 103 (1998), pp. 1889-1904.
15. K. G. POWELL, An Approximate Riemann Solver for Magnetohydrodynamics (That Works in More than One Dimension), Tech. Report 94-24, ICASE, NASA Langley Research Center, Hampton, VA, 1994.
16. K. G. POWELL, P. L. ROE, T. J. LINDE, T. I. GOMBOSI, AND D. L. DEZEEUW, 7 solutionadaptive upwind scheme for ideal magnetohydrodynamics, J. Comput. Phys., 154 (1999), pp. 284-309.
17. P. L. ROE, Approximate Riemann solvers, parameter vectors and difference schemes, J. Comput. Phys., 43 (1981), pp. 357-372.
18. D. RYU AND T. W. JONES, Numerical magnetohydrodynamics in astrophysics: Algorithm and tests for one-dimensional flow, Astrophys. J., 442 (1995), pp. 228-258.
19. T. TANAKA, Finite volume TVD scheme on an unstructured grid system for three-dimensional MHD simulations of inhomogeneous systems including strong background potential field, J. Comput. Phys., 111 (1994), pp. 381-389.
20. E. F. TORO, Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer-Verlag, Berlin, 1999.
21. E. F. TORO, M. SPRUCE, AND W. SPEARES, Restoration of the contact surface in the HLLRiemann solver, Shock Waves, 4 (1994), pp. 25-34.
22. A. L. ZACHARY AND P. COLELLA, A higher-order Godunov method for the equations of ideal magnetohydrodynamics, J. Comput. Phys., 99 (1992), pp. 341-347.