An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics

• Published in: Journal of computational physics Vol. 220; no. 2; pp. 791 - 812
• Main Authors: Han, Jianqiang, Tang, Huazhong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 10-01-2007; Elsevier
• Subjects: Adaptive moving mesh method; Algorithms; Computational fluid dynamics; Computational techniques; Constrained transport; Divergence-free; Exact sciences and technology; Finite volume method; Fluid flow; Magnetic fields; Magnetohydrodynamics; Mathematical methods in physics; Mathematical models; MHD; Physics; Two dimensional; Finite volume method; Divergence-free; Magnetohydrodynamics; Adaptive moving mesh method; Constrained transport; Alfven waves; Total energy; Adaptive algorithm; MHD waves; Adaptive method; Finite volume methods; Calculation methods; Interpolation; Shock waves; Divergences; Magnetic potential; Calculation; Magnetic fields; Mesh method; Magnetic properties
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2006.05.031

This paper presents an adaptive moving mesh algorithm for two-dimensional (2D) ideal magnetohydrodynamics (MHD) that utilizes a staggered constrained transport technique to keep the magnetic field divergence-free. The algorithm consists of two independent parts: MHD evolution and mesh-redistribution. The first part is a high-resolution, divergence-free, shock-capturing scheme on a fixed quadrangular mesh, while the second part is an iterative procedure. In each iteration, mesh points are first redistributed, and then a conservative-interpolation formula is used to calculate the remapped cell-averages of the mass, momentum, and total energy on the resulting new mesh; the magnetic potential is remapped to the new mesh in a non-conservative way and is reconstructed to give a divergence-free magnetic field on the new mesh. Several numerical examples are given to demonstrate that the proposed method can achieve high numerical accuracy, track and resolve strong shock waves in ideal MHD problems, and preserve divergence-free property of the magnetic field. Numerical examples include the smooth Alfvén wave problem, 2D and 2.5D shock tube problems, two rotor problems, the stringent blast problem, and the cloud–shock interaction problem.