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

Abstract

This work 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 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 at flux interfaces where the former is more computationally efficient. A battery of 1D and 2D tests are employed: convergence of 1D and 2D linearized waves, shock tube Riemann problems, a 2D nonlinear circularly polarized Alfvén wave, and a 2D 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 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.

Cross-Code verification and sensitivity analysis to effectively model the electrothermal instability

“…[10] For these fluxes, USim utilizes the Harten-Lax-van Leer-Discontinuities (HLLD) approximate Riemann solver given by Miyoshi and Kusano [11] (5-wave) modified to incorporate the changes to the waves introduced by the real-gas EOS. [12] Additionally, USim utilizes hyperbolic divergence cleaning as given by Dedner et al [13]. For hyperbolic temporal integration, USim uses a 2 nd order Runge-Kutta time integration scheme with variable time step.…”