Integral-Consistent Numerical Technique for Self-gravitating Medium Model

Abstract

The supercompression of matter caused by gravitational coupling or self-gravitational forces leads to density growth by several orders in magnitude. Keeping in mind the importance of self-gravitation in astrophysical processes like supernovae star evolution we consider it reasonable to develop a numerical technique based on the consistent approximation to the terms describing gravitational energy transfer into the kinetic energy of a matter in the star along its life cycle. The so-called completely conservative gas-dynamics difference schemes including the gravitation effects are the proper numerical technique able to simulate correctly the problems concerning gravitational coupling effects. The accounting for gravitational forces in the construction of completely conservative difference schemes is a significant complication. In the paper, we propose an integrally-consistent difference scheme that utilizes the method of support difference operators thus providing a possibility to conform the balance between kinetic and gravitational energy increments or losses. According to this method, we use the result of the total gravitational energy varying and construct the symmetrized strain rate tensor as the base operator. The result of varying the gravitational energy of the system is a discrete convolution of the Newton gravitational tensor in the difference media under study, which exhaustively answers all the gravitational processes unfolding against the background of the hydrodynamic motion of matter. The symmetrized strain tensor governs the kinematic motion in a considered system. The conjugate operator related to the convolution of these tensors automatically gives the approximation to the gravitational forces acting in the interior of the balance volume of the difference model built via the support operator approach.