For the self-gravitating gas dynamics simulation, an explicit multi-step algorithm is proposed. A spatial three-dimensional programming code on a Cartesian grid in the Euler variables was developed using the Fluid-in-Cell method. The numerical algorithm has the first-order approximation. The corresponding grid viscosity provides the stability of numerical solutions. Computations for a sequence of grid refinements show the convergence of the algorithm. Results of isothermal collapse simulation, isentropic self-gravitating gas rotations, and its self-similar expansion are discussed. The work was supported by the RAS Presidium Program "The Origin, Structure and Evolution of Objects in the Universe", the RAS Presidium Program "The Origin of the Biosphere and Geo-Biological Evolution", and the SB RAS Integration Project No. 26 "Mathematical Models, Numerical Methods and Parallel Algorithms for Solving Large Problems of SB RAS and Their Implementation on Multiprocessor Supercomputers". The computations were performed at the Siberian Supercomputer Center using a common memory computer SMP16x256.

Keywords: splitting methods, large-particle method, gravitational gas dynamics

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