V. M. Chechetkin

Analysis of the development concepts and methods of visual data representation in computational physics

Main steps in the development of scientific visualization as a branch of science are discussed. The evolution and prospects of the development of concepts, methods, and approaches of visual representation of numerical results obtained in computational physics (mainly, in computational fluid dynamics) are discussed.

Physical processes underlying the development of shear turbulence

A physical model of the development of turbulence in free shear flows is proposed. The model is based on the results of numerical simulations of turbulent flow development. The main ideas of the proposed theory of turbulence are stated as follows: the onset of turbulence begins with the formation of large vortices; spectral energy transfer involves both direct and inverse cascades; and the inertial range of the energy spectrum develops as a result of concurrent direct and inverse cascades. The dominant physical factors that determine the spectrum include Joukowski forces.

Numerical stability analysis of the Taylor-Couette flow in the two-dimensional case

The stability of the laminar flow between two rotating cylinders (Taylor-Couette flow) is numerically studied. The simulation is based on the equations of motion of an inviscid fluid (Euler equations). The influence exerted on the flow stability by physical parameters of the problem (such as the gap width between the cylinders, the initial perturbation, and the velocity difference between the cylinders) is analyzed. It is shown that the onset of turbulence is accompanied by the formation of large vortices. The results are analyzed and compared with those of similar studies.

Gas-Dynamic General Circulation Model of the Lower and Middle Atmosphere of the Earth

This paper presents a brief description of the General Circulation Model of the lower and middle atmosphere of the Earth, which is designed to study atmospheric dynamics in a wide range of spatial-temporal scales. The model is based on numerical integration of the complete system of equations that describe the dynamics of a viscous atmospheric gas using a spatial grid with a high resolution. The model takes into account the surface relief and the presence of atmosphere aerosols in the form of microdroplets of water ice particles, as well as the phase transitions of water vapor to aerosol particles and back.

Application of the Kac equation to turbulence simulation

The possibility of applying the Kac equation to the simulation of small-scale turbulence is explored. The hypothesis is substantiated that the formation of a flow regime similar to the actual turbulent one can be qualitatively described as based on the analysis of the properties of the Kac equation.

Mathematical Simulation of a Massive Star Evolution Based on a Gasdynamical Model

The flow method, together with an algorithm for self-gravity computations, is applied for the three-dimensional modeling of astrophysical flows. This method is based on the difference approximations of conservation laws written for finite volumes. It is implemented within the FLUX simulation tool box, designed for computer systems with a cluster architecture. The problem of hydrodynamic simulation in the model of a massive star of the third generation (Pop III), which is a progenitor of a pair-instability supernova (PISN), is considered. Large-scale convective structures are produced under neutral equilibrium conditions that significantly affect the process of a supernova explosion.

Thermodynamic properties of vortex systems

Thermodynamic properties characterizing a system of Onsager’s point-vortex system on a plane are considered. The thermodynamics of the vortex system have been geometrized, the relevant notions have been introduced, and the main properties of the Gibbs surface corresponding to the considered system have been identified.

Coherent hydrodynamic structures and vortex dynamics

Possible approaches to modeling two-dimensional coherent hydrodynamic structures based on the statistical mechanics of local vortices are considered. The exact definitions of coherent structures are given and the mechanisms of their formation are shown. The bases of the kinetic theory of Onsager vortices are given and the possibility of applying the classical molecular-kinetic theory for the explanation of the origin of vortex meso-structures in the shear flows is considered.

Simulation of collisionless ultrarelativistic electron–proton plasma dynamics in a self-consistent electromagnetic field

The evolution of a collisionless electron–proton plasma in the self-consistent approximation is investigated. The plasma is assumed to move initially as a whole in a vacuum with the Lorentz factor. The behavior of the dynamical system is analyzed by applying a three-dimensional model based on the Vlasov–Maxwell equations with allowance for retarded potentials. It is shown that the analysis of the solution to the problem is not valid in the “center-of-mass frame” of the plasmoid (since it cannot be correctly defined for a relativistic plasma interacting via an electromagnetic field) and the transition to a laboratory frame of reference is required. In the course of problem solving, a chaotic electromagnetic field is generated by the plasma particles. As a result, the particle distribution functions in the phase space change substantially and differ from their Maxwell–Juttner form. Computations show that the kinetic energies of the electron and proton components and the energy of the self-consistent electromagnetic field become identical. A tendency to the isotropization of the particle momentum distribution in the direction of the initial plasmoid motion is observed.

Statistical mechanics of vortex hydrodynamic structures

The existing approaches to analyzing the dynamics of coherent vortex structures are considered from the viewpoint of the calculus of variations for Poisson systems. For turbulent hydrodynamic flows with large-scale vortices, a simulation technique in the form of statistical mechanics of the Euler equation in a “coarse-grained” representation is substantiated.