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 p roblem that we set up, we use a relaxation scheme to d iscretize 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.
