Problems of numerical modeling on the basis of some modifications of the Godunov’s scheme

Abstract

The paper verifies the ability of previously proposed modifications of the Godunov's scheme develop physically justified numerical solutions of the inviscid gas dynamics equations. The modifications constructed using the approach proposed by Kolgan to improve the accuracy of solutions on spatial variables are being considered. As test it is being solved the problems of flow around of semi-infinite rectangle and of a circular cylinder by a coaxial supersonic flow. The calculations are performed on a rectangular uniform grid. It is shown that the numerical solution can correspond both to stationary and a pulsating flow around with different shape of the shock waves in front of the end wall (see figure below) depending on the viscosity of the numerical scheme and the initial parameter distribution.