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Mathematical simulation on unsteady natural convection in a closed porous cylindrical cavity having finite thickness heat-conducting solid walls in conditions of convective heat exchange with an environment has been carried out. A boundary-value problem of mathematical physics formulated in dimensionless variables such as stream function and temperature on the basis of Darcy–Boussinesq model has been solved by finite difference method. Effect of a porous medium permeability 10^–5≤Da<∞, ratio between a solid wall thickness and the inner radius of a cylinder 0.1≤h/L≤0.3, a thermal conductivity ratio 1≤λ_1,2≤20 and a dimensionless time on both local distributions of isolines and isotherms and integral complexes reflecting an intensity of convective flow and heat transfer has been analyzed in detail.

We consider two versions of the maximum cross section method for the solutions of the stationary equation of radiative transfer in dimensional inhomogeneous medium. Both are based on the application Monte-Carlo method to the summation of the Neumann series for the solution transport equation. First modification is traditional and second is based on the use of branching Markov chains. We carried out numerical comparison of these algorithms.

The possibility to study temperature fluctuations using URANS approach is studied. The results of numerical simulation of mixing processes for triple-jet sodium at different temperatures are presented. The processes were simulated using FlowVision software system and LMS model for turbulent heat transfer. The analysis and experiment data are compared. Validated was the possibility to determine the energy-carrying frequencies of temperature fluctuations using URANS approach and LMS model when mixing triple-jet sodium at different temperatures.

This article is dedicated to applicability justification as well as advantages and disadvantages analysis of discrete models in population dynamics. Discretization is the process of transferring continuous functions, models, and equations into discrete counterparts. We consider how temporal, spatial and structural discretization can be applied for solving typical issues in mathematical ecology, and try to estimate corresponding models adequacy and applicability limitations.

Optimization of hull lines for the minimum resistance to movement is a problem of current interest in ship hydrodynamics. In practice, lines design is still to some extent an art. The usual approaches to decrease the ship resistance are based on the model experiment and/or CFD simulation, following the trial and error method. The paper presents a new method of in-detail hull form design based on the wave-based optimization approach. The method provides systematic variation of the hull geometrical form, which corresponds to alteration of longitudinal distribution of the hull volume, while its vertical volume distribution is fixed or highly controlled. It’s well known from the theoretical studies that the vertical distribution can't be optimized by condition of minimum wave resistance, thus it can be neglected for the optimization procedures. The method efficiency was investigated by application to the foreship of KCS, the well-known test object from the workshop Gothenburg-2000. The variations of the longitudinal distribution of the volume were set on the sectional area curve as finite volume increments and then transferred to the lines plan with the help of special frame transformation methods. The CFD towing simulations were carried out for the initial hull form and the six modified variants. According to the simulation results, examined modifications caused the resistance increments in the range 1.3–6.5 %. Optimization process was underpinned with the respective data analysis based on the new hypothesis, according to which, the resistance increments caused by separate longitudinal segments of hull form meet the principle of superposition. The achieved results, which are presented as the optimum distribution of volume present in the optimized designed hull form, which shows the interesting characteristics that its resistance has decrease by 8.9 % in respect to initial KCS hull form. Visualization of the wave patterns showed an attenuation of the transversal wave components, and the intensification of the diverging wave components.

We present results of a study aimed at identification of a controlled object’s channels based on postprocessing of measurements with development of a model of a multiple-input controlled object and subsequent active modelling experiment. The controlled object model is developed using approximation of its behavior by a neural network model using trends obtained during a passive experiment in the mode of normal operation. Recurrent neural network containing feedback elements allows to simulate behavior of dynamic objects; input and feedback time delays allow to simulate behavior of inertial objects with pure delay. The model was taught using examples of the object’s operation with a control system and is presented by a dynamic neural network and a model of a regulator with a known regulation function. The neural network model simulates the system’s behavior and is used to conduct active computing experiments. Neural network model allows to obtain the controlled object’s response to an exploratory stimulus, including a periodic one. The obtained complex frequency response is used to evaluate parameters of the object’s transfer system using the least squares method. We present an example of identification of a channel of the simulated control system. The simulated object has two input ports and one output port and varying transport delays in transfer channels. One of the input ports serves as a controlling stimulus, the second is a controlled perturbation. The controlled output value changes as a result of control stimulus produced by the regulator operating according to the proportional-integral regulation law based on deviation of the controlled value from the task. The obtained parameters of the object’s channels’ transfer functions are close to the parameters of the input simulated object. The obtained normalized error of the reaction for a single step-wise stimulus of the control system model developed based on identification of the simulated control system doesn’t exceed 0.08. The considered objects pertain to the class of technological processes with continuous production. Such objects are characteristic of chemical, metallurgic, mine-mill, pulp and paper, and other industries.

Numerical study of unsteady mixed convection in an open partially porous horizontal channel with a heatgenerating source was performed. The outer surfaces of horizontal walls of finite thickness were adiabatic. In the channel there was a Newtonian heat-conducting fluid with a temperature-dependent viscosity. The discrete heatconducting and heat-generating source is located inside the bottom wall. The temperature of the fluid phase was equal to the temperature of the porous medium, and calculations were performed using the local thermal equilibrium model. The porous insertion is isotropic, homogeneous and permeable to fluid. The Darcy–Brinkman model was used to simulate the transport process within the porous medium. Governing equations formulated in dimensionless variables “stream function – vorticity – temperature” using the Boussinesq approximation were solved numerically by the finite difference method. The vorticity dispersion equation and energy equation were solved using locally one-dimensional Samarskii scheme. The diffusive terms were approximated by central differences, while the convective terms were approximated using monotonic Samarskii scheme. The difference equations were solved by the Thomas algorithm. The approximated Poisson equation for the stream function was solved separately by successive over-relaxation method. Optimal value of the relaxation parameter was found on the basis of computational experiments. The developed computational code was tested using a set of uniform grids and verified by comparing the results obtained of other authors.

Numerical analysis of unsteady mixed convection of variable viscosity fluid in the horizontal channel with a heat-generating source was performed for the following parameters: $\mathrm{Pr} = 7.0$, $\varepsilon = 0.8$, $\mathrm{Gr} = 10^5$, $C = 0-1$, $10^{-5} < \mathrm{Da} < 10^{-1}$, $50 < \mathrm{Re} < 500$, $\delta = l/H = 0.6-3$. Distributions of the isolines of the stream function, temperature and the dependences of the average Nusselt number and the average temperature inside the heater were obtained in a steady-state regime, when the stationary picture of the flow and heat transfer is observed. As a result we showed that an addition of a porous insertion leads to an intensification of heat removal from the surface of the energy source. The increase in the porous insertion sizes and the use of working fluid with different thermal characteristics, lead to a decrease in temperature inside the source.

The purpose of this work is to develop a universal computer program (solver) which solves kinetic Boltzmann equation for simulations of rarefied gas flows in complexly shaped devices. The structure of the solver is described in details. Its efficiency is demonstrated on an example of calculations of a modern many tubes Knudsen pump. The kinetic Boltzmann equation is solved by finite-difference method on discrete grid in spatial and velocity spaces. The differential advection operator is approximated by finite difference method. The calculation of the collision integral is based on the conservative projection method.

In the developed computational program the unstructured spatial mesh is generated using GMSH and may include prisms, tetrahedrons, hexahedrons and pyramids. The mesh is denser in areas of flow with large gradients of gas parameters. A three-dimensional velocity grid consists of cubic cells of equal volume.

A huge amount of calculations requires effective parallelization of the algorithm which is implemented in the program with the use of Message Passing Interface (MPI) technology. An information transfer from one node to another is implemented as a kind of boundary condition. As a result, every MPI node contains the information about only its part of the grid.

The main result of the work is presented in the graph of pressure difference in 2 reservoirs connected by a multitube Knudsen pump from Knudsen number. This characteristic of the Knudsen pump obtained by numerical methods shows the quality of the pump. Distributions of pressure, temperature and gas concentration in a steady state inside the pump and the reservoirs are presented as well.

The correctness of the solver is checked using two special test solutions of more simple boundary problems — test with temperature distribution between 2 planes with different temperatures and test with conservation of total gas mass.

The correctness of the obtained data for multitube Knudsen pump is checked using denser spatial and velocity grids, using more collisions in collision integral per time step.

The Arctic region contains large hydrocarbon deposits. The presence of different ice formations, such as icebergs, ice hummocks, ice fields, complicates the process of carrying out seismic works on the territory. The last of them, ice fields, bring multiple reflections, spreading all over the surface of ice, into seismogramms. These multiple reflections are necessary to be taken into account while analyzing the seismograms, and geologists should be able to exclude them in order to obtain the reflected waves from the lower geological layers, including hydrocarbon layers.

In this work, we solve the problem of the seismic waves spread in the heterogeneous medium. The systems of equations for the linear elastic medium and for the acoustic medium describe the geological layers. We present the detailed description of the numerical solution of these systems of equations with the help of the grid-characteristic method. The final 1D transfer equations are solved with the use of the Rusanov scheme of the third order of accuracy. In the work, we examine the way of multiple waves decrease in ice by establishing the source of impulse deep into the ice field on border with water. We present the results of computer modelling of the seismic waves spread in geological layers, where the seismic source of impulse is situated on the contact border between ice and water, and also with the seismic source of impulse on the surface of ice for the 3D case. The results of the numerical modelling are presented by wave fields, graphs of the velocity x-components and seismogramms for the two problem formulations. We carry out the analysis of influence of establishing the source of impulse on the border between ice and water on the decrease of the x-components of seismic wave velocities, on seismogramms and on wave fields. As a result, the model, where the seismic source of impulse is situated on the contact border between ice and water, makes worse the final result. The model with the source of impulse on the surface of ice demonstrates a decrease of the x-components of seismic wave velocities.

A mathematical model of two-phase capillary-nonequilibrium isothermal flows of incompressible phases in a double porosity medium is constructed. A double porosity medium is considered, which is a composition of two porous media with contrasting capillary properties (absolute permeability, capillary pressure). One of the constituent media has high permeability and is conductive, the second is characterized by low permeability and forms an disconnected system of matrix blocks. A feature of the model is to take into account the influence of capillary nonequilibrium on mass transfer between subsystems of double porosity, while the nonequilibrium properties of two-phase flow in the constituent media are described in a linear approximation within the Hassanizadeh model. Homogenization by the method of formal asymptotic expansions leads to a system of partial differential equations, the coefficients of which depend on internal variables determined from the solution of cell problems. Numerical solution of cell problems for a system of partial differential equations is computationally expensive. Therefore, a thermodynamically consistent kinetic equation is formulated for the internal parameter characterizing the phase distribution between the subsystems of double porosity. Dynamic relative phase permeability and capillary pressure in the processes of drainage and impregnation are constructed. It is shown that the capillary nonequilibrium of flows in the constituent subsystems has a strong influence on them. Thus, the analysis and modeling of this factor is important in transfer problems in systems with double porosity.