scholarly journals New central and central discontinuous Galerkin schemes on overlapping cells of unstructured grids for solving ideal magnetohydrodynamic equations with globally divergence-free magnetic field

2016 ◽  
Vol 327 ◽  
pp. 203-224 ◽  
Author(s):  
Zhiliang Xu ◽  
Yingjie Liu
Keyword(s):  
Magnetic Field ◽  
Discontinuous Galerkin ◽  
Unstructured Grids ◽  
Magnetohydrodynamic Equations ◽  
Divergence Free ◽  
Ideal Magnetohydrodynamic ◽  
Central Discontinuous Galerkin

Solving Magnetohydrodynamic Equations Without Special Treatment for Divergence-Free Magnetic Field

AIAA Journal ◽  
2004 ◽  
Vol 42 (12) ◽  
pp. 2605-2608 ◽  
Author(s):  
Moujin Zhang ◽  
S.-T. John Yu ◽  
Shang-Chuen Lin ◽  
Sin-Chung Chang ◽  
Isaiah Blankson
Keyword(s):  
Magnetic Field ◽  
Special Treatment ◽  
Magnetohydrodynamic Equations ◽  
Divergence Free

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

2017 ◽  
Vol 21 (2) ◽  
pp. 423-442 ◽  
Author(s):  
Christian Klingenberg ◽  
Frank Pörner ◽  
Yinhua Xia
Keyword(s):  
Magnetic Field ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Efficient Method ◽  
Numerical Experiments ◽  
Unstructured Meshes ◽  
Mhd Equations ◽  
Ideal Magnetohydrodynamics ◽  
Divergence Free ◽  
The Ideal

AbstractIn 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.

scholarly journals Divergence-Free WENO Reconstruction-Based Finite Volume Scheme for Solving Ideal MHD Equations on Triangular Meshes

2016 ◽  
Vol 19 (4) ◽  
pp. 841-880 ◽  
Author(s):  
Zhiliang Xu ◽  
Dinshaw S. Balsara ◽  
Huijing Du
Keyword(s):  
Magnetic Field ◽  
Finite Volume ◽  
Normal Component ◽  
Mhd Equations ◽  
Finite Volume Scheme ◽  
Reconstruction Method ◽  
Triangular Meshes ◽  
Weno Reconstruction ◽  
Divergence Free ◽  
Ideal Magnetohydrodynamic

AbstractIn this paper, we introduce a high-order accurate constrained transport type finite volume method to solve ideal magnetohydrodynamic equations on two-dimensional triangular meshes. A new divergence-free WENO-based reconstruction method is developed to maintain exactly divergence-free evolution of the numerical magnetic field. In this formulation, the normal component of the magnetic field at each face of a triangle is reconstructed uniquely and with the desired order of accuracy. Additionally, a new weighted flux interpolation approach is also developed to compute the z-component of the electric field at vertices of grid cells. We also present numerical examples to demonstrate the accuracy and robustness of the proposed scheme.

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