Fast algorithm of calculations of Fourier logarithmic discrete transformation on the basis of Kuli-Tjuki algorithm with thinning out by frequency is developed in details 

An application of boundary analogues of direct variational methods for approximation of the very weak decision of the first boundary value problem for a biharmonic equation is considered in this work. On the basis of a method of least squares, offered in literature [1], a converging, steady boundary analogue of a collocation method having good computing properties is constructed on the boundary 

Explicit formulas for coefficients of boundary analogue of the Reynolds linear equation for the gas greasing theory are obtained at presence of dependence of special coefficients of the initial equation on "fast" and "slow" variables. Estimations of differences between decisions of initial and boundary equation are presented 

A stochastical model of dispersed particle motion in the channel with porous walls is developed in present study. The fluid velosity in the particle motion equation is represented as a sum of averaged component and random variable. The instantaneous fluid velosity is sampled from a normal velosity distribution. The eddy lifetime and eddy lenght relating to the given fluctuation are determined with the turbulence local properties. The approximate method is established for turbulence field computation reproducing the main exceptions of such flows. The realizations of dispersed particle motion random trajectories corresponding to the different boundary conditions and particle sizes are constructed 

Investigation of an influence of pressure boundary conditions on a fluid flow is presented in the article. At a numerical realization of the algorithm a coincident mesh for all components of speed and pressure is used. Problems of flat potential and flat laminar flows as test examples are considered at significant non-uniformity of a pressure field at the outgoing or at presence of return flows on outgoing. Computations have shown that in cases when traditional boundary conditions for pressure at the outgoing are used, the received decision is inadequate to the real flow. Modified boundary conditions for pressure offered in this work allow to obtain a decision which appropriate to real fluid flow in a better way 

An algorithm with a high parallelization efficiency is developed for direct simulation of non-stationary flows. With use of this algorithm a research of the axis-symmetrical outflow of a monatomic gas into vacuum from a source suddenly started to act for a small period of time placed on a flat wall (gas-dynamic model of a laser ablation) is carried out. Parameters of the source correspond to the sound outflow from a round nozzle. The basic attention is paid to description of high-duty algorithm of direct simulation, numerical study of a time evolution of flow structure, fields of gas-dynamic parameters and function of particles distribution by speeds in the considered physical problem. Data on realization efficiency of a parallel algorithm on supercomputer systems are presented 

In the frameworks of two-dimensional Navier-Stokes equations averaged by Reynolds method, closed with the help of various models of turbulence, computations of flowing around the circular cylinder are presented. Questions of existence and stability of stationary and non-stationary decisions of the problem are investigated. Estimation of the various ways for managing of transition from laminar to turbulent flow is presented. It is shown, that averaged on time non-stationary decisions received with use of a new way of management by transition offered in the work conform with experiment in the best way 

Results of experimental investigation of the vortical sound generation with a nozzle are presented. Phenomenon of stabilisation of frequency radiation with grow of pressure ratio is detected 

The article is devoted to the problem of numerical modelling of stochastic systems. Method of approximation of multiple Ito stochastic integrals, based on multiple integral sums and method of approximation of multiple Stratonovich stochastic integrals, based on multiple Fourier series are proposed and proved. Approximations of multiple Stratonovich stochastic integrals with the help of trigonometric and polynomial systems are considered. The general formulas of approximation of multiple Ito and Stratonovich stochastic integrals of multiplicity k are derived. The mean-square convergence of methods is proved 

This work is devoted to a states minimization problem for generalized (defined under any associative body) nonstacionary finite automata with partly defined initial conditions and with periodicall variation of all their structural parameters is formulated. For construction of the minimal forms for these automata is proposed special matrix method