Inverse Lax–Wendroff Procedure for Numerical Boundary Conditions of Hyperbolic Equations: Survey and New Developments
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 result from the wide stencil of the high order interior 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 other one is a robust and high order accurate extrapolation for outflow boundary conditions. The method is high order accurate, stable under standard CFL conditions determined by the interior schemes, and easy to implement. We show applications in simulating interactions between compressible inviscid flows and rigid (static or moving) boundaries.
KeywordsNumerical boundary conditions Hyperbolic conservation laws Cartesian mesh Inverse Lax-Wendroff procedure Extrapolation
Research is supported by AFOSR grant FA9550-09-1-0126 and NSF grant DMS-1112700.
- 1.Appelö, D., Petersson, N.A.: A fourth-order accurate embedded boundary method for the wave equation. Preprint. www.its.caltech.edu/~appelo/preprints/PadeEBPaper.pdf
- 9.Forrer, H., Berger, M.: Flow simulations on Cartesian grids involving complex moving geometries. In: Jeltsch, R. (ed.) Proc. 7th Intl. Conf. on Hyperbolic Problems, pp. 315–324. Birkhäuser, Basel (1998) Google Scholar