A high-order residual-based viscosity finite element method for the ideal MHD equations
Numerical Analysis
2021-12-17 v1 Numerical Analysis
Abstract
We present a high order, robust, and stable shock-capturing technique for finite element approximations of ideal MHD. The method uses continuous Lagrange polynomials in space and explicit Runge-Kutta schemes in time. The shock-capturing term is based on the residual of MHD which tracks the shock and discontinuity positions, and adds a sufficient amount of viscosity to stabilize them. The method is tested up to third order polynomial spaces and an expected fourth-order convergence rate is obtained for smooth problems. Several discontinuous benchmarks such as Orszag-Tang, MHD rotor, Brio-Wu problems are solved in one, two, and three spatial dimensions. Sharp shocks and discontinuity resolutions are obtained.
Cite
@article{arxiv.2112.08885,
title = {A high-order residual-based viscosity finite element method for the ideal MHD equations},
author = {Tuan Anh Dao and Murtazo Nazarov},
journal= {arXiv preprint arXiv:2112.08885},
year = {2021}
}