Efficient, divergence-free, high-order MHD on 3D spherical meshes with optimal geodesic meshing
Efficient, divergence-free, high-order MHD on 3D spherical meshes with optimal geodesic meshing
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DOI：
10.1093/mnras/stz1263
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发表时间：
2019-05
影响因子：
4.8
通讯作者：
D. Balsara;V. Florinski;S. Garain;Sethupathy S.;K. Gurski
中科院分区：
文献类型：
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作者：
D. Balsara;V. Florinski;S. Garain;Sethupathy S.;K. Gurski
在天体物理学和空间物理学的许多领域中，都迫切需要在球面网格上进行高精度、无发散的磁流体动力学模拟。这就要求我们仔细注意网格质量和数值算法之间的相互作用。已经设计的方法，从根本上集成高阶等参映射与其他高精度算法，需要在测地线网格上进行无发散MHD模拟。本文的目标是记录这样的算法，实现了在测地线网格版本的黎曼代码。流体变量的重建使用一种特殊的WENO-AO算法，该算法将网格几何形状从地面向上的重建过程。然后，提出了一种新的无发散的磁场重建策略，该策略在所有阶次都有效地执行，即使在等参映射网格上也是如此。的MHD方程的演变在空间和时间使用一种新的ADER预测算法，有效地适应等参映射的几何形状。然后，在网格上的适当位置处应用一维和多维Riemann解算器提供校正步骤。磁场的校正步骤使用Yee型磁场交错。这导致磁场的无发散更新的方案。ADER的使用实现了一步更新，每个完整的时间步只需要一个消息传递操作。这对并行处理非常有利。几个精度测试是严格的测试问题。PetaScale的性能也在最大的超级计算机上得到了验证。
There is a great need in several areas of astrophysics and space physics to carry out high order of accuracy, divergence-free MHD simulations on spherical meshes. This requires us to pay careful attention to the interplay between mesh quality and numerical algorithms. Methods have been designed that fundamentally integrate high-order isoparametric mappings with the other high accuracy algorithms that are needed for divergence-free MHD simulations on geodesic meshes. The goal of this paper is to document such algorithms that are implemented in the geodesic mesh version of the RIEMANN code. The fluid variables are reconstructed using a special kind of WENO-AO algorithm that integrates the mesh geometry into the reconstruction process from the ground-up. A novel divergence-free reconstruction strategy for the magnetic field that performs efficiently at all orders, even on isoparametrically mapped meshes, is then presented. The MHD equations are evolved in space and time using a novel ADER predictor algorithm that is efficiently adapted to the isoparametrically mapped geometry. The application of one-dimensional and multidimensional Riemann solvers at suitable locations on the mesh then provides the corrector step. The corrector step for the magnetic field uses a Yee-type staggering of magnetic fields. This results in a scheme with divergence-free update for the magnetic field. The use of ADER enables a one-step update that only requires one messaging operation per complete timestep. This is very beneficial for parallel processing. Several accuracy tests are presented as are stringent test problems. PetaScale performance is also demonstrated on the largest available supercomputers.