Inverse Lax-Wendroff procedure for numerical boundary treatment of hyperbolic equations

Abstract We discuss a high order accurate numerical boundary condition for solving hyperbolic conservation laws on fixed Cartesian grids, while the physical domain can be arbitrarily shaped and moving. Compared with body-fitted meshes, the biggest advantage of Cartesian grids is that the grid generation is trivial. The challenge is however that the physical boundary does not usually coincide with grid lines. The wide stencil of the high order interior scheme makes a stable boundary treatment even harder to realize. There are two main ingredients of our method. The first one is an inverse Lax-Wendroff procedure for inflow boundary conditions and the other one is a robust and high order accurate extrapolation for outflow boundary conditions. Our method is high order accurate, stable, and easy to implement. It has been successfully applied to simulate interactions between compressible inviscid flows and rigid (static or moving) bodies with complex geometry.