In this paper, a new hydrodynamic numerical simulation of interacting galaxies is proposed. The main subgrid physics processes are: the star formation, the supernovae feedback, the cooling function and the molecular hydrogen formation. The collisionless hydrodynamic approach was used for the simulation of the stars and dark matter. An approach for constructing a high order accurate numerical method for solving hydrodynamic equations is described. This method is based on a combination of the operator-splitting method, the Godunov method, and the piecewise-parabolic method on a local stencil. In addition, the performance of the numerical method is demonstrated on a global test of the central galaxies interaction.