A linearity preserving nodal variation limiting algorithm for continuous Galerkin discretization of ideal MHD equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:410

Article

Mabuza, Sibusiso¹  Shadid, John N.^2,3  Cyr, Eric C.²  Pawlowski, Roger P.²  Kuzmin, Dmitri⁴ 

[1] Clemson Univ, Sch Math & Stat Sci, O-110 Martin Hall, Clemson, SC 29634 USA

[2] Sandia Natl Labs, Ctr Comp Res, POB 5800, Albuquerque, NM 87185 USA

[3] Univ New Mexico, Dept Math & Stat, MSC01 1115, Albuquerque, NM 87131 USA

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

关键词: Linearity preservation;    Algebraic flux correction;    Continuous Galerkin methods;    Iterative limiters;    Artificial diffusion;    Magnetohydrodynamics;   

DOI  :  10.1016/j.jcp.2020.109390

来源: Elsevier

【 摘 要 】

In this work, a stabilized continuous Galerkin (CG) method for magnetohydrodynamics (MHD) is presented. Ideal, compressible inviscid MHD equations are discretized in space on unstructured meshes using piecewise linear or bilinear finite element bases to get a semi-discrete scheme. Stabilization is then introduced to the semi-discrete method in a strategy that follows the algebraic flux correction paradigm. This involves adding some artificial diffusion to the high order, semi-discrete method and mass lumping in the time derivative term. The result is a low order method that provides local extremum diminishing properties for hyperbolic systems. The difference between the low order method and the high order method is scaled element-wise using a limiter and added to the low order scheme. The limiter is solution dependent and computed via an iterative linearity preserving nodal variation limiting strategy. The stabilization also involves an optional consistent background high order dissipation that reduces phase errors. The resulting stabilized scheme is a semi-discrete method that can be applied to inviscid shock MHD problems and may be even extended to resistive and viscous MHD problems. To satisfy the divergence free constraint of the MHD equations, we add parabolic divergence cleaning to the system. Various time integration methods can be used to discretize the scheme in time. We demonstrate the robustness of the scheme by solving several shock MHD problems. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free