High-order accurate Lagrange-remap hydrodynamic schemes on staggered Cartesian grids

AbstractWe consider a class of staggered grid schemes for solving the 1D Euler equations in internal energy formulation. The proposed schemes are applicable to arbitrary equations of state and high-order accurate in both space and time on smooth flows. Adding a discretization of the kinetic energy equation, a high-order kinetic energy synchronization procedure is introduced, preserving globally total energy and enabling proper shock capturing. Extension to nD Cartesian grids is done via C-type staggering and high-order dimensional splitting. Numerical results are provided up to 8th-order accuracy