NUMERICAL DISSIPATION FOR THREE-POINT DIFFERENCE SCHEMES TO HYPERBOLIC EQUATIONS WITH UNEVEN MESHES

摘要

The widely used locally adaptive Cartesian grid methods involve a series of abruptly refined interfaces. The numerical dissipation due to these interfaces is studied here for three-point difference approximations of a hyperbolic equation. It will be shown that if the wave moves in the fine-to-coarse direction then the dissipation is positive (stabilizing), and if the wave moves in the coarse-to-fine direction then the dissipation is negative (destabilizing) .