On the stability of the steady states of the gravitating gas disk

Abstract: The three-dimensional model of the gravitating gas disk, rotating around the gravitating center, is investigated. The numerical algorithm for finding the steady flows in the disk, which uses a solution of the system of nonlinear equations, is built. Density, mass and gravitational potential increase several times in comparison with the model, which does not consider gravity of disk. The parameter Toomre, which determines the stability of steady-state solution, is calculated.Note: Research direction:Mathematical modelling in actual problems of science and technic

Numerical model of the cooling gravitating gas disk

Abstract: Evolution of the gas cloud, rotating around the gravitating center, is investigated. The influence of self-gravitation and cooling of disk on the formation of its configuration is studied. The influence of gravity of central object and self-gravitation leads to the intensive compression of cloud, an increase in the density and temperature. Because of an increase in the temperature the pressure, which counteracts compression, grows, and density gradually is reduced. The calculation of the simple law of cooling reduces temperature, density decreases less. The possibility of the disk fragmentation appears.Note: Research direction:Mathematical modelling in actual problems of science and technic

Numerical model of the viscous gas disk

Abstract: 3D model of the formation of proto-planet disk is described by the equations of the compressible viscous gas in the cylindrical coordinates. The viscosity effect of gas and cooling on the disk configuration is investigated.Note: Research direction:Mathematical modelling in actual problems of science and technic

Calculation of the stress state of the 3-dim. composite body

Abstract: Present preprint is the continuation of the papers [1], [2]. The structure and principles of organization of program are described in this work. They allow to carry out the calculations in the domain of complex form. Adaptive multigrid iterative algorithm is constructed. And the results of the computer experiment are discussed. We’ve paid much attention to the degree of convergence of iterations and the accuracy of approximate solution.Note: Research direction:Mathematical modelling in actual problems of science and technic

Computation of tensions in composite body by the method of finite superelements

Abstract: Present preprint is the continuation of the papers [1], [2]. The structure and principles of organization of program are described in this work. They allow to carry out the calculation in the domain of complex form. Adaptive multigrid iterative algorithm is constructed. And the results of the calculations are given.Note: Research direction:Mathematical modelling in actual problems of science and technic

Nuclear Reactor as Stiff System. 5. Main Eigenvalue Problem.

Abstract: The method of solving the main eigenvalue problem for difference approximation of neutron field equations is described. It is based on the simultaneous relaxation of equations for all energetic groups and on multigrid acceleration of the convergence speed. The results of numerical experiments are cited. They show the efficiency and reliability of the method.Note: Research direction:Mathematical modelling in actual problems of science and technic