Band 24, Heft 1

Several two- and three-dimensional problems for the system of Navier–Stokes equations are solved numerically in the paper using the minimal residual iterative method. The iteration method uses a matrix of iteration parameters. The choice of elements of this matrix is based on the condition of minimization of residual norms. It is shown that two-dimensional and three-dimensional problems have essentially different solutions.

Numerical simulation of the dynamics of a flat localized zone of turbulent perturbations is performed in a stably stratified medium. This simulation is based on a hierarchy of semiempiric second-order turbulence models.

Nonlinear dispersion Zheleznyak–Pelinovskii equations describing surface water waves are derived in the paper for the case of an unsteady bottom surface. It is shown that the obtained equations and the well-known Green–Naghdi equations are different forms of the same system of shallow water equations of the second approximation taking into account the bottom variations.

Numerical simulation is used for studying the formation and outflow of a jet of low-temperature plasma generated by water evaporation induced by a high-energy electric pulse discharge in a half-closed cylindrical volume. It is shown that a stable bounded comet-shaped high-pressure zone is formed in the leading part of the jet moving in the vertical direction.

The results of numerical simulation of the self-focusing process of a laser pulse in a dielectric based on the nonlinear Schrödinger equation (NSE) with cubic nonlinearity are presented in the paper for initial Gauss and ring distributions. The critical power levels for the collapse of these initial distributions are determined. The Crank–Nicholson scheme is used for approximation of the original equation. A parallel sweep algorithm is used for numerical implementation of the finite-difference scheme. Calculations on a high-speed cluster show a 28-times increase in the computing speed for the parallel code compared to the sequential one.

This paper contains some new results concerning the development of a universal method for the construction of spatial grids. The method is based on numerical solution (a stabilizing correction scheme) of inverted one-, two-, and three-dimensional Beltrami equations and diffusion equations with respect to the control metric. One- and two-dimensional equations are used for the generation of grids on the edges and faces of a domain. Using three-dimensional equations, a grid is constructed inside a domain. Examples of model adaptive spatial hexahedral and prismatic grids and a grid for the calculation of the propagation of a passive impurity in the atmosphere are demonstrated.