The virtual element method for a 2D incompressible MHD system
The virtual element method for a 2D incompressible MHD system
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DOI：
10.1016/j.matcom.2023.03.029
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发表时间：
2023-04
期刊：
影响因子：
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通讯作者：
Sebastian Naranjo Alvarez;L. Veiga;V. Bokil;F. Dassi;V. Gyrya;G. Manzini
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文献类型：
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作者：
Sebastian Naranjo Alvarez;L. Veiga;V. Bokil;F. Dassi;V. Gyrya;G. Manzini
提出了一种耦合电磁场模型和流体流动模型的二维不可压缩磁流体力学（MHD）系统的离散化方法。我们的方法遵循虚元法的框架，并提供了两个主要的优点。该方法可以在非结构化网格上实现，使其具有高度通用性，能够处理涉及界面，自由边界或自适应网格细化的广泛问题。第二个优点涉及磁通量场和流体速度的发散。如果磁通量场和流体速度的初始状态没有发散，我们的方法保证了它们的数值近似没有发散。重要的是，流体速度的无发散条件在逐点意义上得到满足。我们包括理论证明的条件下的磁通量场，能量估计和适定性研究。数值测试证实了该方法的鲁棒性及其在各种网格上的收敛性。
We present a novel discretization for the two-dimensional incompressible Magnetohydrodynamics (MHD) system coupling an electromagnetic model and a fluid flow model. Our approach follows the framework of the Virtual Element Method and offers two main advantages. The method can be implemented on unstructured meshes making it highly versatile and capable of handling a broad set of problems involving interfaces, free-boundaries, or adaptive refinements of the mesh. The second advantage concerns the divergence of the magnetic flux field and the fluid velocity. Our approach guarantees that the numerical approximation of the magnetic flux field and the fluid velocity are divergence free if their initial states are divergence free. Importantly, the divergence-free condition for the fluid velocity is satisfied in a pointwise sense. We include a theoretical proof of the condition on the magnetic flux field, energy estimates and a well-posedness study. Numerical testing confirms robustness of the method and its convergence properties on a variety of meshes.