High-order dimensionally split Lagrange-remap schemes for compressible hydrodynamics

We first propose a new class of finite volume schemes for solving the 1D Euler equations. Applicable to arbitrary equations of state, these schemes are based on a Lagrange-remap approach and are high-order accurate in both space and time in the nonlinear regime. A multidimensional extension on nD Cartesian grids is then proposed, using a high-order dimensional splitting technique. Numerical results up to 6th-order are provided.