A coordinate transformation for the porous media equation that renders the free boundary stationary

Abstract

Abstract : We consider the one dimensional porous media problem. We describe a simple difference scheme based on this transformation and show that, even with a fairly crude mesh, the free boundary is tracked quite accurately. We study degenerate diffusion problems in which free boundaries occur, our major objective being the development of numerical procedures which effectively track these boundaries. For convenience, we introduce our ideas in terms of the one- dimensional porous media problem; generalizations are given. Originator-supplied key words include: Parabolic equations, Porous media, Free boundaries.