A 3D staggered Lagrangian scheme for ideal magnetohydrodynamics on unstructured meshes
Xiao Xu
Graduate School of China Academy of Engineering Physics, Beijing, China
Search for more papers by this authorCorresponding Author
Zhiming Gao
Institute of Applied Physics and Computational Mathematics, Beijing, China
Zhiming Gao, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China.
Email: [email protected]
Search for more papers by this authorZihuan Dai
Institute of Applied Physics and Computational Mathematics, Beijing, China
Search for more papers by this authorXiao Xu
Graduate School of China Academy of Engineering Physics, Beijing, China
Search for more papers by this authorCorresponding Author
Zhiming Gao
Institute of Applied Physics and Computational Mathematics, Beijing, China
Zhiming Gao, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China.
Email: [email protected]
Search for more papers by this authorZihuan Dai
Institute of Applied Physics and Computational Mathematics, Beijing, China
Search for more papers by this authorSummary
In this paper, we propose a 3D staggered Lagrangian scheme for the ideal magnetohydrodynamics (MHD) on unstructured meshes. All the thermal variables and the magnetic induction are defined in the cell centers while the fluid velocity is located at the nodes. The meshes are compatibly discretized to ensure the geometric conservation laws in Lagrangian computation by the classical subcell method, then the momentum equation is discretized using the subcell forces and the specific internal energy equation is obtained by the total energy conservation. Invoking the Galilean invariance, magnetic flux conservation, and the thermodynamic consistency, the expressions of subcell force as well as the cell-centered velocity are derived. Besides, the magnetic divergence-free constraint is fulfilled by a projection method after each time step. Various numerical tests are presented to assert the robustness and accuracy of our scheme.
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