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arXiv · 2404.09311

A nodal based high order nonlinear stabilization for finite element approximation of Magnetohydrodynamics

Tuan Anh Dao·Murtazo Nazarov
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Abstract

We present a novel high-order nodal artificial viscosity approach designed for solving Magnetohydrodynamics (MHD) equations. Unlike conventional methods, our approach eliminates the need for ad hoc parameters. The viscosity is mesh-dependent, yet explicit definition of the mesh size is unnecessary. Our method employs a multimesh strategy: the viscosity coefficient is constructed from a linear polynomial space constructed on the fine mesh, corresponding to the nodal values of the finite element approximation space. The residual of MHD is utilized to introduce high-order viscosity in a localized fashion near shocks and discontinuities. This approach is designed to precisely capture and resolve shocks. Then, high-order Runge-Kutta methods are employed to discretize the temporal domain. Through a comprehensive set of challenging test problems, we validate the robustness and high-order accuracy of our proposed approach for solving MHD equations.

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Tuan Anh Dao, Murtazo Nazarov. 2024-04-14. A nodal based high order nonlinear stabilization for finite element approximation of Magnetohydrodynamics. https://arxiv.org/abs/2404.09311

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