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首页> 外文期刊>Journal of Computational Physics >Numerical simulation of four-field extended magnetohydrodynamics in dynamically adaptive curvilinear coordinates via Newton-Krylov-Schwarz
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Numerical simulation of four-field extended magnetohydrodynamics in dynamically adaptive curvilinear coordinates via Newton-Krylov-Schwarz

机译：牛顿-克里洛夫-舒瓦兹在动态自适应曲线坐标系中四场扩展磁流体动力学的数值模拟

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摘要

Numerical simulations of the four-field extended magnetohydrodynamics (MHD) equations with hyper-resistivity terms present a difficult challenge because of demanding spatial resolution requirements. A time-dependent sequence of. r-refinement adaptive grids obtained from solving a single Monge-Ampère (MA) equation addresses the high-resolution requirements near the. x-point for numerical simulation of the magnetic reconnection problem. The MHD equations are transformed from Cartesian coordinates to solution-defined curvilinear coordinates. After the application of an implicit scheme to the time-dependent problem, the parallel Newton-Krylov-Schwarz (NKS) algorithm is used to solve the system at each time step. Convergence and accuracy studies show that the curvilinear solution requires less computational effort than a pure Cartesian treatment. This is due both to the more optimal placement of the grid points and to the improved convergence of the implicit solver, nonlinearly and linearly. The latter effect, which is significant (more than an order of magnitude in number of inner linear iterations for equivalent accuracy), does not yet seem to be widely appreciated.
机译：具有高电阻率项的四场扩展磁流体动力学（MHD）方程的数值模拟提出了一个艰巨的挑战，因为对空间分辨率的要求很高。随时间变化的序列。通过求解单个Monge-Ampère（MA）方程获得的r精炼自适应网格满足了附近的高分辨率要求。 x点用于磁性重新连接问题的数值模拟。 MHD方程从笛卡尔坐标转换为解定义的曲线坐标。在将隐式方案应用于时变问题之后，并行牛顿-克里洛夫-舒瓦兹（NKS）算法用于在每个时间步求解系统。收敛性和准确性研究表明，与纯笛卡尔处理相比，曲线解所需的计算量更少。这既是由于网格点的更优化放置，又由于隐式求解器的非线性和线性改进的收敛性。后者的效果很显着（内部线性迭代的数量要比等效精度高一个数量级），似乎尚未得到广泛的认可。

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