A Study of Solutions to Euler Equations for a One Dimensional Unsteady Flow

Abstract

In this paper we deal with the Euler equations for Isothermal gas. In analyzing the equations we obtain two real and distinct eigenvalues which enables us to determine the wave structure of the possible solutions to the Riemann problem set up. By considering the Rankine-Hugoniot condition we obtain the shock wave solution analytically. The rarefaction wave solution is determined analytically by considering the fact that rarefaction wave lies along integral curves. To obtain the numerical solution to the Riemann problem that we set up, we use a relaxation scheme to discretize the Euler equations for isothermal gas. Finally we present the simulation results of the numerical solutions, that is, the approximate shock and rarefaction wave solutions are shown, graphically, and explained.