Vol 9, No 2 (2017)

The influence of the Chelyabinsk meteorite’s bow shock wave on the Earth’s surface is modeled. For solving the problem, a 3D statement is considered for its gas-dynamic and seismic parts. The determining equations of a gas-dynamic model and a seismic model are Euler equations with respect to the radiation heat exchange and the equations of linear elasticity theory, respectively. Two parts of the problem are matched by the direct mechanism of the disturbance transmission. A model seismic signal is compared with the real data. Modeling a seismic effect makes it possible to specify the estimate of the typical parameters of the phenomenon (height of the explosion, and the density and characteristic sizes of the meteorite).

The paper generalizes the conservative volume-centered scheme based on the quasi-onedimensional reconstruction of variables (the BBR scheme) to solve the Euler equations on blockstructured three-dimensional nonstructured grids with sliding interfaces. The calculation of flow by the BBR scheme implies a high volume of calculations, dependent only on the grid geometry. In making calculations on a static grid, these calculations can be carried out at the stage that initialization is calculated. In the presence of sliding interfaces in their neighborhood, these geometrical coefficients have to be recalculated after each offset of one grid block relative to another, that is, for each moment of time. In this paper we propose the modification of the BBR scheme near the grid interface, thus avoiding an excessively high expenditure of the processor time. It is equally applicable for linear schemes and for the use of limiters. On test cases, it is demonstrated that in the use of the implementation scheme described here, the presence of the sliding interface does not have a material effect on the accuracy of the calculations.

The computational experiments on modeling surface waves, which are used for studying the statistics of the occurrence of extremely large surface waves depending on the parameters of the initial waves, are considered. The sudden occurrence of abnormally large waves in the ocean is a big hazard for marine vessels and structures. In recent years, incontrovertible evidence of this phenomenon, such as instrumentation records and photographs, has been presented. The main method of studying the phenomenon of rogue waves in this work is computational experiments based on the complete nonlinear hydrodynamic equations of an ideal liquid with a free surface. The method of conformal variables that is used for the original system of equations enables one to make effective and accurate calculations by computers and computing complexes. According to the experimental results, the statistics of the occurrence of anomalously large surface waves is studied. The use of dissipation and pumping in these computational experiments has made it possible to perform continuous calculations that are not stopped if a rogue wave occurs. The intensity of the occurrence of rogue waves depending on the values of the squares of the mean steepness and wave dispersion is estimated. It is shown that doubling the computational region almost doubles the intensity. The proposed procedure of the computational experiments allows estimating the average waiting time of a rogue wave in the assigned region.

A technique for the numerical simulation of electromagnetic wave propagation in materials with permittivity depending on the frequency is presented. The technique is based on numerical solutions of Maxwell equations with additional integral components in the bias current density. The technique to calculate the bias current density in dispersive media is represented and the corresponding modification of finite-difference scheme for Maxwell equations developed earlier is carried out. The electromagnetic pulse propagation in solid-fuel power systems is calculated.

The Landau (Fokker–Planck) integral of Coulomb collisions is an integral component of the physical and mathematical models of both laboratory and space plasma, in which the intermediate collisionality regime is important. This paper discusses the method for the direct statistical simulation of the Monte Carlo type for a kinetic equation with a nonlinear operator of the Landau–Fokker–Planck (LFP) Coulomb collisions. This method is based on the approximation of the Landau collision integral by the Boltzmann collision integral. The paper has two main objectives: firstly, to obtain numerical estimates of the order of approximation of the Landau collision integral by the Boltzmann integral and, secondly, to explore the possibilities of optimizing the algorithm for multiply charged ions. The results are illustrated by the calculations of the problem on the relaxation of the initial distribution to equilibrium for one and two components.

The author constructs a nonlinear mathematical model of a plane-parallel impact of the medium on a rigid body with a front part of the outer surface shaped as a circular cone. Multivariable analysis of the dynamic equations of motion was performed. A new family of phase patterns on the phase cylinder of quasi-velocities has been obtained. This family consists of infinitely numerous topologically inequivalent phase patterns. The sufficient conditions for the stability of an important mode of motion, i.e., rectilinear translational drag, have been obtained, as well as conditions for the presence of the self-oscillatory modes in the system.