An Efficient Implementation of the Divergence Free Constraint in a Discontinuous Galerkin Method for Magnetohydrodynamics on Unstructured Meshes

作者：Klingenberg, Christian; Poerner, Frank; Xia, Yinhua^*

来源：Communications in Computational Physics, 2017, 21(2): 423-442.

DOI：10.4208/cicp.180515.230616a

• Ideal magnetohydrodynamics equations
• discontinuous Galerkin method
• divergence free constraint
• locally divergence free projection
• divergence free cleaning technique

In this paper we consider a discontinuous Galerkin discretization of the ideal magnetohydrodynamics (MHD) equations on unstructured meshes, and the divergence free constraint (del. 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. numerical experiments are performed to show the capacity and efficiency of the scheme.

• 出版日期2017-2
• 单位中国科学技术大学