Abstract
We have considered the modern theory of breakdown of an arbitrary gas-dynamic discontinuity for the space-time dimension equal to two. We consider the Riemann problem of the breakdown of one-dimensional discontinuity of parameters of non-stationary gas flow in application to construction of numerical methods like the Godunov method. The problem is solved as accurate stated and as rough stated (Osher-Solomon difference scheme used in the numerical methods of shock-cupturing): the intensities are determined (static pressure relations) and the flow velocity step on the sides of formed discontinuities and waves, then the other parameters are calculated in all flow areas. We give the classification of the difference schemes using the Riemann problem solution. We compared the results of model flows by means of accurate and rough solutions.
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