Inverse Lax–Wendroff boundary treatment for compressible Lagrange-remap hydrodynamics on Cartesian grids

Abstract

We propose a new high-order accurate numerical boundary treatment for solving hyperbolic systems of conservation laws and Euler equations using a Lagrange-remap approach on Cartesian grids in cases of physical boundaries not aligned with the mesh. The method is an adaptation of the Inverse Lax–Wendroff procedure [34–38] to the Lagrange-remap approach, which considerably alleviates the algebra. High-order accurate ghost values of conservative variables are imposed using Taylor expansions whose coefficients are found by inverting a (linear or non-linear) system which is well posed in all our examples. For 2D problems, a least-square procedure is added to prevent extrapolation instabilities. The Lagrange-remap formalism also provides a simpler fluid–structure coupling which is also described. Numerical examples are given for the linear case and Euler equations in 1D and 2D.