The work is devoted to the construction of a gas-dynamic model of the accretion disk around a neutron star (NS). The developed multidimensional code is used to study the stability of stationary axially symmetrical models by carry out of evolutionary calculations in 3D taking into account viscosity, as well as taking into account the diffusion of radiation in 2D. It is shown that an arbitrary stationary axially symmetrical disk with a monotonic decrease in density with a cylindrical radius transforms, due to viscosity, braking and spreading of matter along the NS, into a new quasi-stationary toroidal configuration. The stability study of the stationary toroidal configuration confirmed the formation of large-scale vortex structures at the initial periodic disturbance of angular velocity in azimuth, now taking into account the “turbulent” viscosity. It turned out that the presence of large-scale structures leads to an acceleration of braking, i.e., an effective increase in viscosity.

The results of calculations of the magnetic field structure in the kinematic approximation are presented, testifying to the consistency of the constructed numerical model with the structure of the flows of a conducting liquid: the instability of the convective process in a rotating spherical shell is reflected in the evolution of the magnetic field, manifesting itself in the pulsation regime of the field. It is shown that the features of the field evolution in the calculations are most clearly pronounced at high latitudes and have analogs in the behavior of the real geomagnetic field.

We consider a principal problem, that of the possible dominating role of self-consistent gravitational interaction in the formation of cosmic structures: voids and their walls in the local Universe. It is in the context of the Hubble tension as a possible indication of the difference in the descriptions of the late (local) and early (global) Universe. The kinetic Vlasov treatment enables us to consider the evolution of gravitating structures where the fundamental role has the modified gravitational potential with a cosmological constant, leading to the prediction of a local flow with a Hubble parameter that is nonidentical to that of the global Hubble flow. The Poisson equation for a potential with an additional repulsive term, including an integral equation formulation, is analyzed, and we predict the appearance of multiply connected two-dimensional gravitating structures and voids in the local Universe. The obvious consequence of the developed mechanism is that the cosmological constant poses a natural scaling for the voids, along with the physical parameters of their local environment, which can be traced in observational surveys.

We study structure formation in the late Universe within the Vlasov kinetic self-consistent field approach. Our work is principally focused on the use of the modified gravitational potential with a repulsive term of the cosmological constant, which is directly linked to observations that enable characterizations of the Hubble tension as the result of local and global flows. We formulate the criteria for the formation of the semi-periodic gravitating structures, along with the predictions of their quantitative scales associated with observable parameters. Our principal conclusion is that filament formation in the Local (late) Universe can proceed as a deterministic process that is distinct from the structures at larger scales that result from the essentially stochastic dynamics of density perturbations.

The paper proposes and implements a method of obtaining a closed set of Vlasov–Maxwell–Einstein equations (and its weakly relativistic and nonrelativistic analogues) based on variation of the generalized Hilbert–Einstein–Pauli action. This technique also makes it possible to obtain the exact form of the energy-momentum tensor in terms of particle distribution functions. Using a hydrodynamic substitution in the Vlasov equation, the Euler–Lamb equations are obtained, which can be transformed to the form of Hamilton–Jacobi equations. Exact solutions of cosmological type of the hydrodynamic system are demonstrated, and their physical consequences are analyzed (including a generalization of the Milne–McCrea model).

The problem of the gravitational collapse of the core of a massive star is considered, taking into account the neutrino transport in the flux-limited diffusion approximation. To reduce the computational domain of a multidimensional problem on a fixed computational grid, the core of a star, which is already at the stage of collapse, is considered. Since the collapse stage is delayed in time compared to the gas-dynamic time scale for an emerging proto-neutron star, we consider the mathematical problem for the initial configuration in equilibrium and neglected the initial radial velocity. Pressure for a long time at the collapse stage is provided by relativistic degenerate electrons, so the relationship between pressure and density in the initial configuration is described by a polytropic equation with the polytropic index n = 3 . The purpose of this paper is to test the hypothesis that large-scale convection is independent of the 2D and 3D geometry of the mathematical problem and computational grid parameters, as well as the choice of the initial stage of gravitational collapse. The scale of convection is determined by the size of the region of decreasing entropy with neutrino losses, i.e., nonequilibrium neutronization, and the presence of a weak initial rotation.

The emergence of one- and two-dimensional configurations—Zeldovich pancakes—progenitors of the observed filaments and clusters and groups of galaxies is predicted by means of a developed kinetic approach in analyzing the evolution of initial density perturbations. The self-consistent gravitational interaction described by Vlasov–Poisson set of equations with branching conditions is shown to predict two-dimensional structures as of layers of increased density and voids between them, i.e., the cellular macro-structure of the Universe. The modified potential of weak-field General Relativity is involved, which enables one to explain the Hubble tension, revealing the conceptual discrepancy in the local galactic flows and the cosmological expansion. This demonstrates the possible essential role of self-consistent gravity in the formation of the cosmic web.

The process of uniform supernovae (SNe) explosions is well investigated for all their types. However, observational data suggests that the SNe may be not spherically symmetric. Modern multidimensional simulations of SNe demonstrate development of hydrodynamical instabilities during the explosion phase. But the configuration of a star and inhomogeneities prior to explosion could strongly affect how the SN develops. A number of papers on numerical modeling of pair-instability SNe explosion considered the case when thermonuclear energy in the central region of a massive star is introduced by a series of several hot spots. It leads to the appearance of many fragments of hot matter behind the divergence shock wave. An observable manifestation of this may be the presence of peaks on light curves of gamma-ray bursts associated with explosions of massive stars. The physical nature of such inhomogeneities is not evident and the number and size of spots is conjecture. In this work, we study the possibility of formation of these inhomogeneities at the stage of core collapse (CC) in a massive star. To check this assumption, we chose an analytic self-similar model of CC and investigated the stability of solutions obtained from it with respect to small multidimensional perturbations. It shows there are no conditions where the collapse of a very massive star may remain stable, although, for a less massive star, it is possible. Using the relations obtained, we found characteristic features of developing instability, thereby making it possible to estimate the amount and characteristic size of the inhomogeneities.

Most of the energy released by the gravitational collapse of the cores of massive stars is carried away by neutrinos. The self-consistent problem of gravitational collapse is solved using 2D gas dynamics considering the spectral transport of neutrinos in the flux-limited diffusion. It is shown that large-scale convection develops in the region near the neutrinosphere and leads to an increase in the average neutrino energy up to 15–18 MeV, which is 1.5 times higher than the results of 1D calculations. This study improves a simple model of neutronization in the central opaque region, which is applicable, strictly speaking, only in the transparent region. The 2D model correctly reproduces the high chemical potential of degenerate electrons ~60 MeV at the center with a high density of matter, as in spherically symmetric calculations with exact account of the weak interaction. Since neutronization at the center is reversible due to trapped neutrinos, the instability development in the center is suppressed, and the high chemical potential of electrons at the center in the refined neutronization model does not affect the energy of outgoing neutrinos. The obtained neutrino energies are important both for explaining the supernova phenomenon and for setting up an experiment to detect neutrinos from a supernova.

To date, the presence of dark matter (DM) can be judged only by its gravitational interaction on the visible matter. It is therefore important to find the consequences of this interaction, which can then help to determine both the DM properties and parameters and the dynamics and evolution of visible matter. The gravitational influence of dark matter on the stability of interstellar medium (ISM), the progenitor of stars and star clusters, was considered. An isothermal self-gravity gas was taken as a suitable model describing ISM, particles interacting only gravitationally were considered as DM. The results obtained by analytical methods show that even a small amount of fast DM particles significantly increases the stable radius of the gas cloud and the corresponding mass while a higher relative density of DM destabilizes the gas. It was shown that with typical parameters of ISM and DM, its presence increases the maximum stable mass of isothermal cloud by a factor of four and the radius by five.

We consider the possibility of generalizing the Newtonian law of gravity and the transition to a general relativistic model for weak fields with the inclusion of a repulsive term identified as a cosmological constant. The analysis includes that of the test particle’s motion in a modified gravitational field of the Hilbert metric and then the problem of the reverse transition from the post-Galilean case to the construction of a modified exact point mass metric which includes the $$\varLambda $$ term.

The model problem of heat transfer from a nonuniformly heated pipe wall to the basic flow is considered, or, in other words, the initial stages of fluid temperature and pressure relaxation in a heated pipe are addressed. The computations are based on computer codes using various combinations of the Navier–Stokes equations, a modified Burnett equation, and the kinetic BGK equation.

A large fraction of the energy released during the gravitational collapse of the core of a massive star is carried by neutrinos. Neutrinos play the main role in explaining core-collapse supernovae. A self-consistent formulation of the gravitational collapse is solved using 2D gas dynamics, taking into account the spectral transport of neutrinos in the framework of neutrino flux-limited diffusion. Large-scale convection leads to an increase in the mean energy of the neutrinos from 10 to 15 MeV, which is important for explaining supernovae, as well as for designing experiments on detecting high-energy neutrinos from supernovae.

We derive from the principle of least action (a slight generalization of the classical one) the right-hand sides of Maxwell and Einstein equations for a system on charged particles in the framework of the Vlasov–Maxwell–Einstein system of equations. The reduced Euler equations are derived using hydrodynamic substitution and are solved within the self-similar class, as a consequence of the Vlasov system of equations. The properties of the generalized non-relativistic Friedmann–Milne–McCrea model are analyzed in context of Gurzadyan’s theorem on the general function satisfying the equivalency of sphere’s and point mass’s gravity.

Описана история развития сотрудничества коллектива ИПМ им. М.В. Келдыша РАН с С.К. Годуновым. В процессе этого сотрудничества получено много интересных результатов в теории кинетических уравнений и вычислительной математике. Библ. 20.

In the current study, the vortex structures that occur in accretion disks are investigated using mathematical modeling methods. The simulation of the processes of formation of large-scale vortex structures in stellar accretion disks is carried out by two methods with different numerical schemes. The first numerical technique is based on conservative difference scheme with “upwind” approximation for fluxes. The second numerical technique is based on an explicit, conservative, monotone in the linear approximation Godunov-type Roe–Einfeldt–Osher scheme, which approximates, with order no higher than the third, the conservation laws in the form of Euler equations. Visualized pictures of the vortex structure are given by both methods for accretion disks. The qualitative similarity of the obtained results is discussed. Evolutionary calculations are carried out on the basis of parallel algorithms implemented on the supercomputing complex of the cluster architecture.

The properties of the solutions of the Klein−Gordon equations for various metrics of the general theory of relativity are considered. It is shown that the presence of singular points of the metric leads to qualitative rearrangement solutions of this equation, and the desingularization of solutions by the choice of a new metric requires a priori assumptions that can lead to formally mathematically correct results, albeit, with paradoxical physical meanings.