Ameliorating the Courant-Friedrichs-Lewy condition in spherical coordinates: A double FFT filter method for general relativistic MHD in dynamical spacetimes
Ameliorating the Courant-Friedrichs-Lewy condition in spherical coordinates: A double FFT filter method for general relativistic MHD in dynamical spacetimes
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DOI：
10.1103/physrevd.108.104005
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发表时间：
2023-05
影响因子：
5
通讯作者：
Liwei Ji;V. Mewes;Y. Zlochower;Lorenzo Ennoggi;F. G. L. Armengol;M. Campanelli;F. Cipolletta;Z. E
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文献类型：
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作者：
Liwei Ji;V. Mewes;Y. Zlochower;Lorenzo Ennoggi;F. G. L. Armengol;M. Campanelli;F. Cipolletta;Z. E
对致密天体及其残余物合并的数值模拟是引力波和多信使天文学的理论基础。虽然基于笛卡尔坐标的自适应网格细化通常用于模拟，但由于流体角动量演化中的数值耗散较低，并且需要较少数量的计算单元，类球坐标更适合于近球形残余物和方位角流动。然而，使用球坐标数值求解双曲型偏微分方程可能会导致严重的Courant-Friedrichs-Lewy（CFL）稳定性条件时间步长限制，这可能会使模拟成本过高。本文解决了这个问题的耦合时空和广义相对论磁流体力学演化的数值解，通过引入一个双FFT滤波器，并在完全MPI并行化的SphericalNR框架内实现它在爱因斯坦工具包。我们证明了过滤算法的有效性和鲁棒性，通过将其应用到一些具有挑战性的代码测试，并表明它有效地通过这些测试，证明了收敛性，同时也增加了时间步长显着相比，未经过滤的模拟。
Numerical simulations of merging compact objects and their remnants form the theoretical foundation for gravitational wave and multi-messenger astronomy. While Cartesian-coordinate-based adaptive mesh refinement is commonly used for simulations, spherical-like coordinates are more suitable for nearly spherical remnants and azimuthal flows due to lower numerical dissipation in the evolution of fluid angular momentum, as well as requiring fewer numbers of computational cells. However, the use of spherical coordinates to numerically solve hyperbolic partial differential equations can result in severe Courant-Friedrichs-Lewy (CFL) stability condition timestep limitations, which can make simulations prohibitively expensive. This paper addresses this issue for the numerical solution of coupled spacetime and general relativistic magnetohydrodynamics evolutions by introducing a double FFT filter and implementing it within the fully MPI-parallelized SphericalNR framework in the Einstein Toolkit. We demonstrate the effectiveness and robustness of the filtering algorithm by applying it to a number of challenging code tests, and show that it passes these tests effectively, demonstrating convergence while also increasing the timestep significantly compared to unfiltered simulations.