The cuFFT code for N-body simulation

The complexity of astrophysical processes lies in the joint consideration of components of various nature. For example, in the collision problem of galaxies, the three-dimensional dynamics of an interstellar gas and a stellar component is considered. The modeling of these components can be based on completely different classes of numerical methods. One possible solution to this problem is to use the Eulerian-Lagrangian approach, in which physical quantities are concentrated at material points, which is typical for the SPH (Smoothed Particle Hydrodynamics) method, and the forces are calculated on an adaptive grid attached to a system of material points. This approach uniformly takes into account both the dynamics of a continuous medium and discrete particles, and also eliminates a number of drawbacks inherent in the original method. The calculation of gravitational interaction is carried out by solving the Poisson equation for the gravitational potential. In this case, all particles are projected onto the computational grid and the potential values in each cell are already calculated on it. The solution of the Poisson equation for the gravitational potential is performed using the fast Fourier transform. The article describes the new cuFFT code Virtual Planetarium for modeling astrophysical objects based on the SPH method, supplemented by the Godunov method for calculating pressure and momentum flows between particles, and the fast Fourier transform method for solving the Poisson equation for the gravitational potential. The paper describes the rationale for the transition to such a computational model, kinetic and hydrodynamic approaches are described in detail. Simulation of the collapse of an isothermal gas cloud is performed. Method to reproduce the evolution of instabilities in form of two density arms is realized.