On some integral-consistent methods for calculating magnetohydrodynamic phenomena in problems of computational astrophysics

When constructing difference schemes for calculating complex problems of computational astrophysics considering magnetohydrodynamic and gravitational phenomena, the processes of matter overcompression (with a change in density by several orders of magnitude) should be taken into account, and it is important at a discrete level to take into account the corresponding energy transformations of magnetohydrodynamic, gravitational, kinetic, and internal energy during the evolution of a star. This problem is solved by constructing completely conservative difference schemes in a view of these magnetohydrodynamic processes and self-gravitating phenomena. In this work, to study and apply the difference methods for solving problems of magnetic gas dynamics, a discrete representation of symmetrized spatial deformations of the medium was obtained. The representation is consistent with changes in the magnetic, kinetic, and internal energies and does not lead to their distortions when the matter is overcompressed.     

Mathematical Modeling of Gas Hydrate Dissociation in Porous Medium Taking into Account Ice and Salinity

Doklady Mathematics - This work is devoted to the mathematical modeling of the dissociation of gas hydrates in a porous medium. Numerical methods are developed for solving problems of underground...     

Multiscale approach to computation of three-dimensional gas mixture flows in engineering microchannels

A multiscale approach to computing real gas flows in engineering microchannels on high-performance computer systems in a wide range of Knudsen numbers is described. The numerical implementation of the approach combines the solution of quasigasdynamic equations and the molecular dynamics method. Following the approach, the parameters of the real gas equation of state are found at the molecular level, the kinetic gas properties are calculated, and the form of boundary conditions on the microchannel walls are determined. The technique is verified by computing several test problems. The results agree well with available theoretical and experimental data.     

An Approach for Solving Three-Dimensional Fluid Dynamics Problems with Allowance for Elastic Processes

Computational Mathematics and Mathematical Physics - A finite-difference approximation of elastic forces on Lagrangian grids is constructed by applying the support operator method. For displacement...     

Completely Conservative Difference Schemes for Fluid Dynamics in a Piezoconductive Medium with Gas Hydrate Inclusions

Computational Mathematics and Mathematical Physics - The dynamics equations for a two-component fluid in a porous medium with gas hydrate inclusions are approximated on a structurally irregular...