将慢磁声波模式加入HLL型多态近似黎曼解

中文摘要 AI 辅助

理想磁流体动力学（MHD）的多态HLL型近似黎曼解通常假设黎曼扇内的介质不可压缩，因此慢磁声波模式无法包含在其近似状态的时空波构型中。我们提出了一种设计多态HLL型近似解的新策略，允许黎曼扇内的介质可压缩。特别地，对于MHD黎曼问题的完整七波构型，我们首先估计慢磁声波速度和慢模式之间的纵向流动速度，然后遵循守恒定律以及穿过快波、阿尔芬波和慢波的Rankine-Hugoniot跳跃关系，计算黎曼扇内的所有中间状态。此外，我们讨论了当某些波模式退化时的解，确保完备波构型与退化波构型之间的适定性和平滑过渡。使用有限体积（FV）求解器的数值模拟表明，所提出的近似黎曼解比经典HLLD格式扩散性更小，尤其对于慢模式波。例如，在一个具有强纵向磁场的1D测试案例中，新格式比经典HLLD格式少一个数量级的网格单元即可分辨所有波模式。

英文摘要

Multi-state HLL-type approximate Riemann solutions of ideal magnetohydrodynamics (MHD) typically assume that the medium within the Riemann fan is incompressible, and thus the slow magnetoacoustic mode cannot be included in their space-time wave configurations for the approximated states. We propose a new strategy to design multi-state HLL-type approximate solutions, allowing for the medium within the Riemann fan to be compressible. In particular, for the complete seven-wave configuration of the MHD Riemann problem, we first estimate the slow magnetoacoustic speeds and a longitudinal flow speed between the slow modes, and then follow the conservation laws and Rankine-Hugoniot jump relations across the fast, Alfvén, and slow waves, to calculate all the intermediate states within the Riemann fan. Moreover, we discuss the solutions when certain wave modes degenerate, ensuring well-posedness and smooth transitions between complete and degenerate wave configurations. Numerical simulations using a Finite Volume (FV) solver show that the proposed approximate Riemann solution is less diffusive than the classic HLLD scheme, particularly for slow mode waves. For example, in a 1D test case with a strong longitudinal magnetic field, the new scheme needs one order of magnitude fewer grid cells compared to the classic HLLD scheme to resolve all wave modes.

发表机构

• Institute of Theoretical Astrophysics, University of Oslo（奥斯陆大学理论天体物理研究所）
• Rosseland Centre for Solar Physics, University of Oslo（奥斯陆大学罗斯兰太阳物理学中心）
• Centre for mathematical Plasma-Astrophysics, Department of Mathematics, KU Leuven（荷语鲁汶大学数学系等离子体天体物理学中心）
• Institute of Physics, University of Maria Curie-Skłodowska（玛丽亚·居里-斯可夫多夫斯卡大学物理研究所）

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