论文标题
用于磁性水力学的整体多族
Monolithic Multigrid for Magnetohydrodynamics
论文作者
论文摘要
磁水动力学（MHD）方程模型多种等离子体物理应用，其特征是偏微分方程的非线性系统，该系统与电磁场的演化强烈耦合了带电的流体。离散化和线性化后，由于变量之间的耦合以及线性化过程诱导的异质系数，通常难以求解所得的方程系统。在本文中，我们根据适当解决系统结构和耦合的专业放松方案研究了该系统的多移民预处理。提出了三个范卡松弛的扩展，并将其应用于高达1.7亿自由度，流体和磁性雷诺数的问题，用于固定问题，最高可达20,000，对于时间依赖性问题。
The magnetohydrodynamics (MHD) equations model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of electromagnetic fields. After discretization and linearization, the resulting system of equations is generally difficult to solve due to the coupling between variables, and the heterogeneous coefficients induced by the linearization process. In this paper, we investigate multigrid preconditioners for this system based on specialized relaxation schemes that properly address the system structure and coupling. Three extensions of Vanka relaxation are proposed and applied to problems with up to 170 million degrees of freedom and fluid and magnetic Reynolds numbers up to 400 for stationary problems and up to 20,000 for time-dependent problems.
