Combined Compact Difference Scheme for the Grid System in Which the Boundary is Located between Regular GRID Points

Abstract

We propose a Combined Compact Difference (CCD) scheme for the grid system in which the boundary is located between regular grid points. We analyze the stability of the proposed CCD scheme for a 1-D advection diffusion problem by using the matrix method. The finite difference representation of the 1-D equation consists of the CCD scheme for the spatial derivatives and the 4th Runge-Kutta method for the time marching. It is shown that the new numerical method is stable for larger Courant number and diffusion number than those of the original method. We also show a numerical test of a 1-D advection diffusion simulation using this numerical method.