Inverse Lax-Wendroff procedure for numerical boundary conditions of hyperbolic equations: survey and new developments

Abstract. In this paper, we give a survey and discuss new developments and computational results for a high order accurate numerical boundary condition based on finite difference methods for solving hyperbolic equations on Cartesian grids, while the physical domain can be arbitrarily shaped. The challenges are the wide stencil for the high order scheme and the fact that the physical boundary does not usually coincide with grid lines. There are two main ingredients of the method. The first one is an inverse Lax-Wendroff procedure for inflow boundary conditions and the second one is a robust and high order accurate extrapolation for outflow boundary conditions. The method is high order accurate and stable under standard CFL conditions determined by the interior schemes. We show applications in simulating interactions between compressible inviscid flows and rigid (static or moving) boundaries.