一种用于可压缩电阻磁流体动力学的受限传输嵌入边界方法
A constrained-transport embedded boundary method for compressible resistive magnetohydrodynamics
AI总结：
本文提出了一种用于可压缩电阻磁流体动力学的受限传输嵌入边界方法，通过有限体积法和鬼体方法实现任意形状边界，并验证了其在不同条件下的收敛性。
摘要：
受近年来脉冲功率磁惯性聚变装置兴趣增加的启发，我们提出了一种方法，用于在笛卡尔网格上实现任意形状的嵌入边界，同时求解可压缩电阻磁流体动力学方程。该方法围绕方程的有限体积形式构建，其中使用黎曼求解器计算网格单元之间面的通量，并采用以面为中心的受限传输形式求解感应方程。通过始终在笛卡尔网格的面上和边上计算通量，避免了切细胞带来的小时间步问题。我们扩展了该方法，利用鬼体方法建模两种不同性质材料之间的移动界面，并展示了初步结果，包括由冲击波驱动和磁驱动的磁流体静力学平衡的动力压缩。我们对方法进行了详尽验证，显示在无间断情况下收敛为二阶，在材料性质有间断时收敛为一阶。
英文摘要：
Motivated by the increased interest in pulsed-power magneto-inertial fusion devices in recent years, we present a method for implementing an arbitrarily shaped embedded boundary on a Cartesian mesh while solving the equations of compressible resistive magnetohydrodynamics. The method is built around a finite volume formulation of the equations in which a Riemann solver is used to compute fluxes on the faces between grid cells, and a face-centered constrained transport formulation of the induction equation. The small time step problem associated with the cut cells is avoided by always computing fluxes on the faces and edges of the Cartesian mesh. We extend the method to model a moving interface between two materials with different properties using a ghost-fluid approach, and show some preliminary results including shock-wave-driven and magnetically-driven dynamical compressions of magnetohydrostatic equilibria. We present a thorough verification of the method and show that it converges at second order in the absence of discontinuities, and at first order with a discontinuity in material properties.
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