Divergence-Free WENO Reconstruction-Based Finite Volume Scheme for Solving Ideal MHD Equations on Triangular Meshes. (12th April 2016)

• Record Type: Journal Article
• Authors: Xu, Zhiliang; Balsara, Dinshaw S.; Du, Huijing
• Is Part Of: Communications in computational physics. Volume 19:Number 4(2016:Apr.)
• Page Start: 841
• Page End: 880
• Publication Date: 2016-04-12
• Subjects: 65M08, -- 65Z05, -- 85-08; Finite volume method, -- MHD equations, -- globally divergence-free; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.050814.040915a
• Languages: English
• ISSNs: 1815-2406

Abstract

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.