Volume 21, Issue 2
An Efficient Implementation of the Divergence Free Constraint in a Discontinuous Galerkin Method for Magnetohydrodynamics on Unstructured Meshes

Christian Klingenberg, Frank Pörner & Yinhua Xia

Commun. Comput. Phys., 21 (2017), pp. 423-442.

Published online: 2018-04

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  • 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 an efficient method at the almost same numerical cost. Finally, numerical experiments are performed to show the capacity and efficiency of the scheme.

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@Article{CiCP-21-423, author = {}, title = {An Efficient Implementation of the Divergence Free Constraint in a Discontinuous Galerkin Method for Magnetohydrodynamics on Unstructured Meshes}, journal = {Communications in Computational Physics}, year = {2018}, volume = {21}, number = {2}, pages = {423--442}, 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 an efficient method at the almost same numerical cost. Finally, numerical experiments are performed to show the capacity and efficiency of the scheme.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.180515.230616a}, url = {http://global-sci.org/intro/article_detail/cicp/11244.html} }
TY - JOUR T1 - An Efficient Implementation of the Divergence Free Constraint in a Discontinuous Galerkin Method for Magnetohydrodynamics on Unstructured Meshes JO - Communications in Computational Physics VL - 2 SP - 423 EP - 442 PY - 2018 DA - 2018/04 SN - 21 DO - http://doi.org/10.4208/cicp.180515.230616a UR - https://global-sci.org/intro/article_detail/cicp/11244.html KW - AB -

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 an efficient method at the almost same numerical cost. Finally, numerical experiments are performed to show the capacity and efficiency of the scheme.

Christian Klingenberg, Frank Pörner & Yinhua Xia. (2020). An Efficient Implementation of the Divergence Free Constraint in a Discontinuous Galerkin Method for Magnetohydrodynamics on Unstructured Meshes. Communications in Computational Physics. 21 (2). 423-442. doi:10.4208/cicp.180515.230616a
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