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

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....

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Vydáno v:Journal of computational physics Ročník 512; s. 113146
Hlavní autoři: Dao, Tuan Anh, Nazarov, Murtazo
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.09.2024
Témata:
Artificial viscosity
Beräkningsvetenskap med inriktning mot numerisk analys
High order method
MHD
Residual based shock-capturing
Scientific Computing with specialization in Numerical Analysis
Stabilized finite element method
MHD
Stabilized finite element method
Artificial viscosity
Residual based shock-capturing
High order method
ISSN:0021-9991, 1090-2716, 1090-2716
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Shrnutí: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. •New nodal-based artificial viscosity method for MHD.•The method does not include any ad hoc parameters or explicit definition of the mesh size.•The viscosity coefficient is built in a multigrid strategy.•The method is proven to preserve positivity for scalar conservation laws using linear finite elements.
ISSN:0021-9991
1090-2716
1090-2716
DOI:10.1016/j.jcp.2024.113146