Comparison of Godunov’s and Relaxation Schemes Approximation of Solutions to the Euler Equations

Abstract

In this paper we deal with the study of Euler equations for isothermal gas that is governed by two hyperbolic equations. By analysing the equations we obtain two real and distinct eigenvalues which enables us to determine the wave structure of the possible solution to the Riemann problem set up. We then obtain the numerical solution to the Riemann problem that we set up using the Godunov scheme and the relaxation scheme. Finally, we compare the results obtained from these two schemes graphically and explain in details