Volume 19, Issue 4
Divergence-Free WENO Reconstruction-Based Finite Volume Scheme for Solving Ideal MHD Equations on Triangular Meshes

Zhiliang Xu, Dinshaw S. Balsara & Huijing Du

Commun. Comput. Phys., 19 (2016), pp. 841-880.

Published online: 2018-04

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  • Abstract

In this paper, we introduce a high-order accurate constrained transport type finite volume method to solve ideal magnetohydrodynamic equations on twodimensional 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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@Article{CiCP-19-841, author = {}, title = {Divergence-Free WENO Reconstruction-Based Finite Volume Scheme for Solving Ideal MHD Equations on Triangular Meshes}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {4}, pages = {841--880}, abstract = {

In this paper, we introduce a high-order accurate constrained transport type finite volume method to solve ideal magnetohydrodynamic equations on twodimensional 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.050814.040915a}, url = {http://global-sci.org/intro/article_detail/cicp/11111.html} }
TY - JOUR T1 - Divergence-Free WENO Reconstruction-Based Finite Volume Scheme for Solving Ideal MHD Equations on Triangular Meshes JO - Communications in Computational Physics VL - 4 SP - 841 EP - 880 PY - 2018 DA - 2018/04 SN - 19 DO - http://dor.org/10.4208/cicp.050814.040915a UR - https://global-sci.org/intro/article_detail/cicp/11111.html KW - AB -

In this paper, we introduce a high-order accurate constrained transport type finite volume method to solve ideal magnetohydrodynamic equations on twodimensional 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.

Zhiliang Xu, Dinshaw S. Balsara & Huijing Du. (2020). Divergence-Free WENO Reconstruction-Based Finite Volume Scheme for Solving Ideal MHD Equations on Triangular Meshes. Communications in Computational Physics. 19 (4). 841-880. doi:10.4208/cicp.050814.040915a
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