A 3D cell-centered Lagrangian scheme for the ideal Magnetohydrodynamics equations on unstructured meshes

Abstract We propose a cell-centered Lagrangian numerical scheme for solving the 3D ideal Magnetohydrodynamics (MHD) equations on unstructured meshes. All the variables are cell-centered and the Lagrangian conservative system of ideal MHD equations is compatibly discretized in this scheme. The geometric conservation law (GCL) requirement is satisfied by using the discrete compatible Lagrangian framework of polyhedral meshes. A nodal solver for MHD equations is then constructed through the nodal pressure flux and magnetic field invoking total energy conservation and thermodynamic consistency. 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.