Flow-oriented difference scheme for multidimensional convection-diffusion equation

Abstract

In this paper one flow-oriented difference scheme for multidimensional convection-diffusion equation is constructed and analysed. The order of the accuracy is $O(\Delta x^2)$, except for convection dominant case when it decreased by one. The stability depends on the diffusion coefficient $D$, and for the square grid the stability condition is $D\,\Delta t/\Delta x^2\le 0.25$. Some examples are presented to illustrate that the scheme is especially applicable for dominantly convection problems and problems with not enough smooth solutions.