In this paper, Euler equations have been solved for the internal compressible flows. In order to have such a solution, at first, the equations were written into the integrated form, and then in CUSP and Scalar schemes, by means of the central difference method, and in Roe scheme, by means of the upwind difference method, they were made into the discritized form. The main problem in the central difference method for solving these equations that occurs as a result of the shock phenomenon, is instability and discontinuity of the solution, which is due to the misuse of the information related to the both sides of the shock. In order to solve this problem, we have to apply the artificial dissipations. However, the upwind methods based on the distribution of the flow information along the defined directions in the physical domain, do not have such a problem. In this paper, these schemes will be introduced, and the results of these methods will be compared and then the CUSP scheme will be amended.

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