论文标题
一种有限体积的方案，用于在恒星内部的低马赫数下建模可压缩的磁性水动力流动
A finite-volume scheme for modeling compressible magnetohydrodynamic flows at low Mach numbers in stellar interiors
论文作者
论文摘要
完全可压缩的磁性水力动力学（MHD）模拟是研究发电机扩增在恒星深对流层中产生磁场中的作用的基本工具。在这种环境中出现的流动的特征是低（声音）马赫数（M_SON <0.01）。在这些制度中，常规的MHD代码通常会显示出过度的耗散性，并且由于Courant-Friedrichs-Lewy（CFL）的限制对时间步的限制变得过于严格。在这项工作中，我们提出了一种新方法，以在空间依赖性重力电位中有效模拟MHD流量，同时仍保留了可压缩性的所有效果。 The proposed scheme is implemented in the finite-volume Seven-League Hydro (SLH) code, and it makes use of a low-Mach version of the five-wave Harten-Lax-van Leer discontinuities (HLLD) solver to reduce numerical dissipation, an implicit-explicit time discretization technique based on Strang splitting to overcome the overly strict CFL constraint, and a well-balancing method that dramatically减少了强大分层设置中空间离散误差的大小。通过在交错网格上使用约束的传输方法来实现磁场上的螺线管约束。我们进行了五项验证测试，包括在M_SON 〜0.001的星形环境中模拟小规模的发电机。我们证明所提出的方案可用于准确模拟低马赫数和强烈分层的设置中的可压缩MHD流动，即使使用中等粗大的网格。
Fully compressible magnetohydrodynamic (MHD) simulations are a fundamental tool for investigating the role of dynamo amplification in the generation of magnetic fields in deep convective layers of stars. The flows that arise in such environments are characterized by low (sonic) Mach numbers (M_son < 0.01 ). In these regimes, conventional MHD codes typically show excessive dissipation and tend to be inefficient as the Courant-Friedrichs-Lewy (CFL) constraint on the time step becomes too strict. In this work we present a new method for efficiently simulating MHD flows at low Mach numbers in a space-dependent gravitational potential while still retaining all effects of compressibility. The proposed scheme is implemented in the finite-volume Seven-League Hydro (SLH) code, and it makes use of a low-Mach version of the five-wave Harten-Lax-van Leer discontinuities (HLLD) solver to reduce numerical dissipation, an implicit-explicit time discretization technique based on Strang splitting to overcome the overly strict CFL constraint, and a well-balancing method that dramatically reduces the magnitude of spatial discretization errors in strongly stratified setups. The solenoidal constraint on the magnetic field is enforced by using a constrained transport method on a staggered grid. We carry out five verification tests, including the simulation of a small-scale dynamo in a star-like environment at M_son ~ 0.001 . We demonstrate that the proposed scheme can be used to accurately simulate compressible MHD flows in regimes of low Mach numbers and strongly stratified setups even with moderately coarse grids.
