Simple Implementation of 1D TVD Scheme for 2D Triangular Finite Volume

Abstract

In this paper a simple implementation of 1D TVD scheme to 2D triangular grid was proposed and sufficient condition for oscillation free solution of advection equation were found using monotone advective K-approximation. The approach was implemented to Superbee and Smart limiter and compared to Barth and Jespersen (BJ) scheme by using the schemes to well known classic case of advection of step and double step of scalar properties. Result indicated that all of the computed solutions are monotone and, apart from highly diffusive first order solution, they show similar level accuracy for test cases. Superbee limiter gives the best performance and follow by Smart limiter and BJ scheme.