Analysis of one dimensional inviscid and two dimensional viscous flows using Entropy Preserving method

Abstract

In this paper, the Entropy Preserving (EP) scheme (which is introduced recently by Jameson) has been considered deeply and compared to the other artificial viscosity and upwind schemes. The discretization of the governing equations in the EP scheme is performed in such a way that the entropy is conserved in all those points with no shock. The purpose of this study is to introduce a stable numerical method that enters a minimum artificial dissipation only in the vicinity of shocks. In this paper, an inviscid one-dimensional flow through a convergent-divergent nozzle and a viscous two-dimensional flow with axial symmetry are considered. It is shown that the EP scheme is more accurate if the number of mesh points is increased; and in contrast to other schemes, there is no limit in increasing the number of points.