Limiting and divergence cleaning for continuous finite element discretizations of the MHD equations
Limiting and divergence cleaning for continuous finite element discretizations of the MHD equations
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DOI：
10.1016/j.jcp.2020.109230
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
D. Kuzmin;N. Klyushnev
中科院分区：
文献类型：
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作者：
D. Kuzmin;N. Klyushnev
介绍了一种新的约束代数稳定化方法，用于理想磁流体动力学（MHD）方程的连续分段线性有限元逼近。在所提出的通量校正输运（FCT）算法的第一步中，通过添加与最快特征波速成比例的图形粘性来修改Galerkin单元矩阵。在第二步，应用有限的反扩散校正，并对磁场进行发散清除。为这一阶段开发的限制程序的目的是执行局部最大值原则，以及积极的保存密度和热力学压力。此外，它调整磁场的方式，惩罚发散误差，而不违反守恒定律或积极的约束。二维测试问题的数值研究进行证明所提出的算法来完成这项任务的能力，在理想的MHD基准的应用程序。
This work introduces a new type of constrained algebraic stabilization for continuous piecewise-linear finite element approximations to the equations of ideal magnetohydrodynamics (MHD). At the first step of the proposed flux-corrected transport (FCT) algorithm, the Galerkin element matrices are modified by adding graph viscosity proportional to the fastest characteristic wave speed. At the second step, limited antidiffusive corrections are applied and divergence cleaning is performed for the magnetic field. The limiting procedure developed for this stage is designed to enforce local maximum principles, as well as positivity preservation for the density and thermodynamic pressure. Additionally, it adjusts the magnetic field in a way which penalizes divergence errors without violating conservation laws or positivity constraints. Numerical studies for 2D test problems are performed to demonstrate the ability of the proposed algorithms to accomplish this task in applications to ideal MHD benchmarks.