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A new numerical model of a galaxy interaction in gasodynamical approach is considered. In this model the equations of a gas dynamics with a cold function and the Poisson equation for a gravity potential are solved. A total system of equations is illposed. It allows us to describe a gravitational instability of astrophysical processes. As an example, the results of the collapse simulation are presented. The gas dynamic system of equations is solved by the Fluids-in-Cell method with the energy balance correction. Using the 3D Cartesian simulation a rotation, a self-consistent gravitational field, a complex central body geometry and a gas temperature were taken into account. A parallel implementation of the method for the simulation of various galaxy interaction scenarios was used in the model. Also, a research of the numerical model application range for various collision velocities and a mass relation of gas and star components was made here.