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.

中文翻译：

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具有真实气体状态方程的 MHD 有限体积求解器的多维测试

本文考虑使用真实气体状态方程 (EOS) 求解 MHD 方程的两种有限体积求解器算法。两种算法都使用 Harten-Lax-Van Leer 近似黎曼求解器的多态形式，如为 MHD 不连续性制定的。该求解器经过修改以使用来自真实气体 EOS 的广义声速。测试了两种方法：单元中心的 EOS 评估和通量接口，前者计算效率更高。使用了一系列一维和二维测试：一维和二维线性波的收敛、激波管黎曼问题、二维非线性圆极化阿尔文波和二维磁瑞利–泰勒不稳定性测试。以单元为中心的 EOS 评估算法在中间状态中产生无法解决的热力学不一致，从而导致虚假解，而通量界面 EOS 评估算法稳健地产生正确的解。线性化波测试表明这种不一致与磁声波有关，而磁-瑞利-泰勒不稳定性测试证明了仿真结果，其中虚假解导致非物理仿真。