Constructing oscillation preventing scheme for advection equation by rational function

Abstract

A numerical scheme for solving advection equations is presented. The scheme is derived from a rational interpolation function. Some properties of the scheme with respect to convex-concave preserving and monotone preserving are discussed. We find that the scheme is attractive in suppressing overshoots and undershoots even in the vicinities of discontinuity. The scheme can also be easily switched as the CIP (Cubic interpolated Pseudo-Particle) method to get a third-order accuracy in smooth region. Numbers of numerical tests are carried out to show the non-oscillatory and less diffusive nature of the scheme.