A Cell-Centered Lagrangian Method for 2D Ideal MHD Equations

In this work, we present a Lagrangian cell-centered MHD scheme on unstructured quadrilateral grid which need neither corrector steps nor modifications to the original ideal MHD equations but preserve exactly the divergence constraint of the magnetic field. All primary variables in this scheme are cell centered. In order to compute the numerical fluxes through the cell interfaces, we introduce one velocity for each vertex, one subcell force and one subcell magnetic flux for each subcell of the mesh. We construct a nodal solver to compute the vertex velocity and the subcell force. The subcell magnetic fluxes in our scheme are assumed to remain unchanged all the time which guarantees the exact preservation of the divergence-free constraint. Several numerical tests are presented to demonstrate the robustness and the accuracy of this scheme.