Two difference schemes of the total variation diminishing (TVD) type are proposed for solving the two- and three-dimensional equations of gravitational gas dynamics. The accuracy of these algorithms was certified on a number of test problems: the interaction between a shock wave and a region of low density gas, the formation of a shock wave and a vortex, and the simulation of gas-cloud self-gravity processes. The numerical results show that the proposed difference schemes and the corresponding computer programs allow one to solve problems of gravitational gas dynamics with a sufficient accuracy.

Keywords: mathematical modeling, gas dynamics, graphics processors

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