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 with 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 was 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.

Modification ofk-εTurbulent Model Using Kinetic Energy–Preserving Method

“…Previous works by the authors show that the kinetic energy-preserving (KEP) method leads to the same results as the other methods until the number of grids is low [5]. The challenge is to improve the KEP method to gain better results at low points of the grid.…”

“…Moreover, Chandrashekar [15,16], Kok [17], and Yan and Jin [18] scrutinized this method in their articles. Also, Javadi and Pasandideh-Fard [5] have applied the KEP method in a onedimensional inviscid convergent-divergent nuzzle flow, two-dimensional inviscid flow over a bump, and two-dimensional viscous flow over a NACA 0012 airfoil. It was shown that the KEP 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 grid points.…”