Hydrodynamic modeling of self-gravitating astrophysical objects on tetrahedral meshes

Abstract

Abstract The paper proposes a new numerical method for solving the equations of gravitational hydrodynamics on a tetrahedral mesh. The proposed numerical method is focused on modeling the evolution of astrophysical objects of spherical shape, which is appropriate for gravitational collapse and star formation, and also for supernova explosion. The construction of tetrahedral grids is carried out in three stages. At the first stage, a geodesic grid methodology is used to construct a triangular grid on the surface of the sphere, which encompasses the computational domain. At the second stage, the resulting triangular mesh is serialized from the surface of the sphere to its center, and at the third stage, the obtained prisms are divided into tetrahedra. This approach allows us to simulate spherical objects without singularities that occur when using spherical or cylindrical coordinates. The paper describes numerical methods for solving the equations of hydrodynamics and the Poisson equation. Numerical examples are given that verify the developed numerical methods.