A Simple Positive Definite Advection Scheme with Small Implicit Diffusion

Abstract

The development of negative values for positive definite scalars in the solution of the advection equation is an important difficulty in numerical modeling. This paper proposes a new positively definite advection scheme which has a simple form, small implicit diffusion and low computational cost. Comparisons of the present scheme with some other known positive definite schemes are also presented. Abstract The development of negative values for positive definite scalars in the solution of the advection equation is an important difficulty in numerical modeling. This paper proposes a new positively definite advection scheme which has a simple form, small implicit diffusion and low computational cost. Comparisons of the present scheme with some other known positive definite schemes are also presented.