A High-order Weighted Finite Difference Scheme with a Multistate Approximate Riemann Solver for Divergence-free Magnetohydrodynamic Simulations
A High-order Weighted Finite Difference Scheme with a Multistate Approximate Riemann Solver for Divergence-free Magnetohydrodynamic Simulations
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DOI：
10.3847/1538-4365/ab1a36
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发表时间：
2019-03
期刊：
影响因子：
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通讯作者：
T. Minoshima;T. Miyoshi;Y. Matsumoto
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文献类型：
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作者：
T. Minoshima;T. Miyoshi;Y. Matsumoto
我们为理想的磁流体动力学模拟设计了一种保守的有限差分方案，该方案可以获得高阶精度、冲击捕获和磁场的无发散条件。该方案通过高阶非线性加权平均值将逐点物理变量从计算节点插值到中点。通过多态近似黎曼求解器在中点评估数值通量，以实现正确的逆风，并通过高阶线性中心差来近似其空间导数，以按照设计的精度和守恒阶数更新变量。磁场和电场是在 Evans & Hawley 的约束传输 (CT) 方法中使用的交错网格点处定义的。我们提出了一种新的 CT 变体，其中交错电场被评估为与基本一维黎曼求解器一致，并且交错磁场被更新为由高阶有限差分表示设计的无散度。我们演示了各种基准测试来衡量当前方案的性能。我们详细讨论了插值方法、黎曼求解器的选择以及无散条件的处理对数值解质量的影响。
We design a conservative finite difference scheme for ideal magnetohydrodynamic simulations that attains high-order accuracy, shock-capturing, and a divergence-free condition of the magnetic field. The scheme interpolates pointwise physical variables from computational nodes to midpoints through a high-order nonlinear weighted average. The numerical flux is evaluated at the midpoint by a multistate approximate Riemann solver for correct upwinding, and its spatial derivative is approximated by a high-order linear central difference to update the variables with the designed order of accuracy and conservation. The magnetic and electric fields are defined at staggered grid points employed in the constrained transport (CT) method by Evans & Hawley. We propose a new CT variant, in which the staggered electric field is evaluated so as to be consistent with the base one-dimensional Riemann solver, and the staggered magnetic field is updated to be divergence-free as designed by the high-order finite difference representation. We demonstrate various benchmark tests to measure the performance of the present scheme. We discuss the effect of the choice of interpolation methods, Riemann solvers, and the treatment for the divergence-free condition on the quality of numerical solutions in detail.