No abstract

No abstract

The results of the study of an explosion point of supernova type Ia (SNIa) with using of mathematical modeling on supercomputers is given in the paper. Hydrodynamical model closed by the stellar equation of state and supplemented by Poisson equation for gravitational potential is used for modeling of a white dwarf. The nuclear combustion of carbon, for which the analytical solution is constructed, is accounted in the model. A multilevel organization of computations on nested grids is used in the solution. The new highorder accuracy numerical method based on the Godunov method, the Rusanov scheme and the piecewise parabolic method on local stencil, adapted for computations on nested grids, is built. The parallel implementation is based on the idea of distributed computations, where the architecture with shared memory is used for modeling of the hydrodynamic evolution of white dwarfs, when the critical values of temperature and density are reached, a new task is launched on the architecture with distributed memory, in which the evolution of hydrodynamic turbulence leading to supersonic nuclear combustion of carbon is simulated.

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.