A 3D staggered Lagrangian scheme for ideal magnetohydrodynamics on unstructured meshes

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.