The virtual element method for resistive magnetohydrodynamics
The virtual element method for resistive magnetohydrodynamics
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DOI：
10.1016/j.cma.2021.113815
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
Sebastian Naranjo Alvarez;V. Bokil;V. Gyrya;G. Manzini
中科院分区：
文献类型：
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作者：
Sebastian Naranjo Alvarez;V. Bokil;V. Gyrya;G. Manzini
本文提出了一种虚拟元法（VEM），用于电阻磁流体力学（MHD）模型的电磁子系统在二维空间上的数值逼近。虚拟元法的主要优点是多边形网格的灵活性和磁场的自动无发散约束。在这项工作中，我们严格地证明了该方法的适定性和离散磁场的螺线形性质。我们也得到了稳定能量估计。该方法的设计包括三种节点质量矩阵的构造选择和准则的选择。这种方法在VEM文献中是新颖的，并且允许我们保留交换图的性质。我们提出了一组独立验证理论结果的数值实验。数值实验包括收敛速率研究、能量估计和磁场无散度条件的验证。所有这些数值实验都是在三角形、摄动四边形和Voronoi网格上进行的。最后，我们在Hartmann流动和磁重联的数值模型上展示了VEM方法的发展。
We present a virtual element method (VEM) for the numerical approximation of the electromagnetics subsystem of the resistive magnetohydrodynamics (MHD) model in two spatial dimensions. The major advantages of the virtual element method include great flexibility of polygonal meshes and automatic divergence-free constraint on the magnetic flux field. In this work, we rigorously prove the well-posedness of the method and the solenoidal nature of the discrete magnetic flux field. We also derive stability energy estimates. The design of the method includes three choices for the construction of the nodal mass matrix and criteria to more alternatives. This approach is novel in the VEM literature and allows us to preserve a commuting diagram property. We present a set of numerical experiments that independently validate theoretical results. The numerical experiments include the convergence rate study, energy estimates and verification of the divergence-free condition on the magnetic flux field. All these numerical experiments have been performed on triangular, perturbed quadrilateral and Voronoi meshes. Finally, we demonstrate the development of the VEM method on a numerical model for Hartmann flows as well as in the case of magnetic reconnection.