论文标题
带有伪维库姆磁边界的球形壳发电机的平行有限体积模拟
Parallel finite volume simulation of the spherical shell dynamo with pseudo-vacuum magnetic boundary conditions
论文作者
论文摘要
在本文中，我们研究了具有伪磁管磁边界条件的快速旋转的球形壳中磁流失动力（MHD）发电机的平行模拟。基于相互统一的立方体网格网格的二阶有限体积方案应用于MHD Dynamo方程的空间离散化。为了确保磁场的电磁阀条件，我们采用了一种广泛使用的方法，从而将伪压力引入感应方程中。时间整合通过二阶近似分解方法分割，导致两个线性代数系统都通过预处理的Krylov子空间迭代方法求解。然后，将基于域分解和多族方法的多级限制添加剂施瓦茨预处理设计，以提高效率和可扩展性。使用我们的代码获得了两个基准情况的准确数值解决方案，与现有的局部方法结果相当。在Sunway Taihulight超级计算机上进行的几项大规模测试显示出良好的强度和弱的可及性，以及从多达10368处理器核心的多级预处理中明显改进。
In this paper, we study the parallel simulation of the magnetohydrodynamic (MHD) dynamo in a rapidly rotating spherical shell with pseudo-vacuum magnetic boundary conditions. A second-order finite volume scheme based on a collocated quasi-uniform cubed-sphere grid is applied to the spatial discretization of the MHD dynamo equations. To ensure the solenoidal condition of the magnetic field, we adopt a widely-used approach whereby a pseudo-pressure is introduced into the induction equation. The temporal integration is split by a second-order approximate factorization approach, resulting in two linear algebraic systems both solved by a preconditioned Krylov subspace iterative method. A multi-level restricted additive Schwarz preconditioner based on domain decomposition and multigrid method is then designed to improve the efficiency and scalability. Accurate numerical solutions of two benchmark cases are obtained with our code, comparable to the existing local method results. Several large-scale tests performed on the Sunway TaihuLight supercomputer show good strong and weak scalabilities and a noticeable improvement from the multi-level preconditioner with up to 10368 processor cores.
