Multidimensional Tests of a Finite-Volume Solver for MHD With a Real-Gas Equation of State

This article considers two algorithms of a finite-volume solver for the MHD equations with a real-gas equation of state (EOS). Both algorithms use a multistate form of the Harten-Lax-Van Leer approximate Riemann solver as formulated for MHD discontinuities. This solver is modified to use the generalized sound speed from the real-gas EOS. Two methods are tested: EOS evaluation at cell centers and flux interfaces where the former is more computationally efficient. A battery of 1-D and 2-D tests is employed: convergence of 1-D and 2-D linearized waves, shock tube Riemann problems, a 2-D nonlinear circularly polarized Alfvén wave, and a 2-D magneto-Rayleigh-Taylor instability test. The cell-centered-EOS-evaluation algorithm produces unresolvable thermodynamic inconsistencies in the intermediate states leading to spurious solutions while the flux-interface EOS evaluation algorithm robustly produces the correct solution. The linearized wave tests show that this inconsistency is associated with the magnetosonic waves and the magneto-Rayleigh-Taylor instability test demonstrates simulation results, where the spurious solution leads to an unphysical simulation.