Limiting and divergence cleaning for continuous finite element discretizations of the MHD equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:407

Article

Kuzmin, Dmitri¹  Klyushnev, Nikita¹ 

[1] TU Dortmund Univ, Inst Appl Math LS 3, Vogelpothsweg 87, D-44227 Dortmund, Germany

关键词: Ideal MHD equations;    Positivity preservation;    Finite elements;    Flux-corrected transport;    Limiting;    Divergence cleaning;   

DOI  :  10.1016/j.jcp.2020.109230

来源: Elsevier

【 摘 要 】

This work introduces a new type of constrained algebraic stabilization for continuous piecewise-linear finite element approximations to the equations of ideal magnetohydrodynamics (MHD). At the first step of the proposed flux-corrected transport (FCT) algorithm, the Galerkin element matrices are modified by adding graph viscosity proportional to the fastest characteristic wave speed. At the second step, limited antidiffusive corrections are applied and divergence cleaning is performed for the magnetic field. The limiting procedure developed for this stage is designed to enforce local maximum principles, as well as positivity preservation for the density and thermodynamic pressure. Additionally, it adjusts the magnetic field in a way which penalizes divergence errors without violating conservation laws or positivity constraints. Numerical studies for 2D test problems are performed to demonstrate the ability of the proposed algorithms to accomplish this task in applications to ideal MHD benchmarks. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free