High-order dimensionally split lagrange-remap schemes for ideal magnetohydrodynamics

We first propose a new class of high-order finite volume schemes for solving the 1-D ideal magnetohydrodynamics equations that is particularly well-suited for modern computer architectures. Applicable to arbitrary equations of state, these schemes, based on a Lagrange-remap approach, are high-order accurate in both space and time in the non-linear regime. A multidimensional extension on 2-D Cartesian grids using a high-order dimensional splitting technique is then proposed. Numerical results up to fourth-order on smooth and non-smooth test problems are also provided.