“Virtual Planetarium” Code for Astrophysical Objects Modeling: Mathematical Model, Methodology and First Results

Abstract

The complexity of astrophysical processes lies in simultaneous consideration of components with different nature. So, for example, in the problem of collision of galaxies the three-dimensional dynamics of interstellar gas and stellar component is considered. The modeling of these components could be based on completely different classes of numerical methods. One possible solution to this problem is the use of the Eulerian-Lagrangian approach, in which the physical quantities are concentrated in material points, which is typical for the SPH method, and the calculation of forces is made on an adaptive grid bound to the system of material points. This approach uniformly takes into account both the dynamics of the continuous medium and discrete particles, and also eliminates a number of disadvantages typical for the original method. The calculation of the gravitational interaction is carried out by solving the Poisson equation for the gravitational potential. Herewith, all the particles are projected onto the computational grid and the potential values in each cell are calculated using this grid. The solution of the Poisson equation for the gravitational potential is performed using Fast Fourier Transform. The new “Virtual Planetarium” code for astrophysical objects modeling based on SPH method, supplemented by Godunov method for calculating pressure and momentum flows between particles, and Fast Fourier Transform method to solve the Poisson equation for the gravitational potential, is described in the paper. Rationale for the transition to such numerical model is given in the paper. Kinetic and hydrodynamic approaches are described in detail. The modeling of collapse of an isothermal gas cloud is performed, the ability of the method to reproduce the development of instabilities in the form of the formation of two density sleeves is shown.