Godunov method offers a distinct advantage in that they do not require addition of artificial viscosity or smoothing term in the numerical scheme and in that it has the clear physical picture upon which it is based. This method requires the solution of Riemann Problems for one-dimensional Euler equations and in the present paper we use Gottlieb method published recently as a fast iterative solver of the nonlinear problem.
This thesis describes the first order Godunov scheme for the Euler equations on an unstructure grid system and the second order multidimensional upwind method on a structure grid. Performance and properties of the scheme have been investigated by solving various problems such as shock tube, circular-arc bump, forward step, compression ramp, and airfoil cascades. The computional results show that the present methods offer solutions as high resolution as corresponding operator split methods and other methods do.
