Integral-consistent methods for calculating self-gravitating and magnetohydrodynamic phenomena

One of the directions of computational astrophysics is the development of numerical methods for modeling self-gravitating objects. These objects include protoplanetary clouds, supernovas and other clusters of large masses, in the evolution of which an essential role is played by gravity. Discrete modeling in these problems with the significant differences in density and the appearance, for example, of mobile, adaptive, irregular grids, can lead to appreciable disturbances in the balance of gravitational energy. This paper is devoted to the construction of completely conservative difference schemes in the part of integrally-consistent calculations affecting the medium of gravitational and magnetohydrodynamic forces in Lagrangian variables.