An Efficient Implementation of the Divergence Free Constraint in a Discontinuous Galerkin Method for Magnetohydrodynamics on Unstructured Meshes. (7th February 2017)

• Record Type: Journal Article
• Authors: Klingenberg, Christian; Pörner, Frank; Xia, Yinhua
• Is Part Of: Communications in computational physics. Volume 21:Number 2(2017:Feb.)
• Page Start: 423
• Page End: 442
• Publication Date: 2017-02-07
• Subjects: 65M12, -- 65M20, -- 65M60, -- 35L65; Ideal magnetohydrodynamics equations, -- discontinuous Galerkin method, -- divergence free constraint, -- locally divergence free projection, -- divergence free cleaning technique; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.180515.230616a
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: In this paper we consider a discontinuous Galerkin discretization of the ideal magnetohydrodynamics (MHD) equations on unstructured meshes, and the divergence free constraint (∇· B =0) of its magnetic field B . We first present two approaches for maintaining the divergence free constraint, namely the approach of a locally divergence free projection inspired by locally divergence free elements [19], and another approach of the divergence cleaning technique given by Dedner et al. [15]. By combining these two approaches we obtain a efficient method at the almost same numerical cost. Finally, numerical experiments are performed to show the capacity and efficiency of the scheme.