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An HLLC-Type Approximate Riemann Solver for Ideal Magnetohydrodynamics



Katharine F. Gurski


This paper presents a new solver based on the HLLC (Harten-Lax-van Leer-contact wave) approximate nonlinear Riemann solver for gas dynamics for the ideal magnetohydrodynamics (MHD) equations written in conservation form. It is shown how this solver also can be considered a modification of Linde's Adequate solver. This approximation method is intended to be less diffusive for all problems containing contact waves than the HLL solver. Compared to exact nonlinear solvers and Roe's solver, this new solver is computationally inexpensive. In addition, the method will exactly resolve isolated shocks and contacts. The method also is guaranteed to preserve positive density and pressure although in a few cases positivity may require changing the wavespeeds of the Riemann fan for the underlying HLL method. While the method is intended for a three-dimensional MHD problem, the simulation results concentrate on one-dimensional test cases.
Journal of Computational Physics


contact discontinuity, magnetohydrodynamics, MHD, nonlinear, positivity, Riemann solver


Gurski, K. (2001), An HLLC-Type Approximate Riemann Solver for Ideal Magnetohydrodynamics, Journal of Computational Physics (Accessed April 18, 2024)
Created January 2, 2001, Updated June 2, 2021