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

Part of: Astronomy and astrophysics (General) Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  12 April 2016

Zhiliang Xu ,
Dinshaw S. Balsara  and
Huijing Du
Zhiliang Xu*
Affiliation:
Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA
Dinshaw S. Balsara*
Affiliation:
Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA
Huijing Du
Affiliation:
Department of Mathematics, University of California, Irvine, Irvine, CA 92697, USA
*
*Corresponding author. Email addresses:zxu2@nd.edu (Z. Xu), Dinshaw.S. Balsara.1@nd.edu (D. S. Balsara), huijingd@uci.edu (H. Du)
*Corresponding author. Email addresses:zxu2@nd.edu (Z. Xu), Dinshaw.S. Balsara.1@nd.edu (D. S. Balsara), huijingd@uci.edu (H. Du)
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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 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.

Keywords

Finite volume methodMHD equationsglobally divergence-free

MSC classification

Secondary: 65M08: Finite volume methods 65Z05: Applications to physics 85-08: Computational methods
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 4 , April 2016 , pp. 841 - 880
Copyright
Copyright © Global-Science Press 2016 

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