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Modern approach to modernization of the experimental techniques involves design of mathematical models of the wind-tunnel, which are also referred to as Electronic of Digital Wind-Tunnels. They are meant to supplement experimental data with computational analysis. Using Electronic Wind-Tunnels is supposed to provide accurate information on aerodynamic performance of an aircraft basing on a set of experimental data, to obtain agreement between data from different test facilities and perform comparison between computational results for flight conditions and data with the presence of support system and test section.

Completing this task requires some preliminary research, which involves extensive wind-tunnel testing as well as RANS-based computational research with the use of supercomputer technologies. At different stages of computational investigation one may have to model not only the aircraft itself but also the wind-tunnel test section and the model support system. Modelling such complex geometries will inevitably result in quite complex vertical and separated flows one will have to simulate. Another problem is that boundary layer transition is often present in wind-tunnel testing due to quite small model scales and therefore low Reynolds numbers.

In the current article the first stage of the Electronic Wind-Tunnel design program is covered. This stage involves computational investigation of aerodynamic characteristics of the generic flying-wing UAV model previously tested in TsAGI T-102 wind-tunnel. Since this stage is preliminary the model was simulated without taking test-section and support system geometry into account. The boundary layer was considered to be fully turbulent.

For the current research FlowVision computational code was used because of its automatic grid generation feature and stability of the solver when simulating complex flows. A two-equation k–ε turbulence model was used with special wall functions designed to properly capture flow separation. Computed lift force and drag force coefficients for different angles-of-attack were compared to the experimental data.

Seismic survey process is the common method of prospecting and exploration of deposits: oil and natural gas. Invented at the beginning of the XX century, it has received significant development and is currently used by almost all service oil companies. Its main advantages are the acceptable cost of fieldwork (in comparison with drilling wells) and the accuracy of estimating the characteristics of the subsurface area. However, with the discovery of non-traditional deposits (for example, the Arctic shelf, the Bazhenov Formation), the task of improving existing and creating new seismic data processing technologies became important. Significant development in this direction is possible with the use of numerical simulation of the propagation of seismic waves in realistic models of the geological medium, since it is possible to specify an arbitrary internal structure of the medium with subsequent evaluation of the synthetic signal-response.

The present work is devoted to the study of spatial dynamic processes occurring in geological medium containing fractured inclusions in the process of seismic exploration. The authors constructed a three-dimensional model of a layered massif containing a layer of fluid-saturated cracks, which makes it possible to estimate the signal-response when the structure of the inhomogeneous inclusion is varied. To describe physical processes, we use a system of equations for a linearly elastic body in partial derivatives of the second order, which is solved numerically by a grid-characteristic method on hexahedral grid. In this case, the crack planes are identified at the stage of constructing the grid, and further an additional correction is used to ensure a correct seismic response for the model parameters typical for geological media.

In the paper, three-component area seismograms with a common explosion point were obtained. On their basis, the effect of the structure of a fractured medium on the anisotropy of the seismic response recorded on the day surface at a different distance from the source was estimated. It is established that the kinematic characteristics of the signal remain constant, while the dynamic characteristics for ordered and disordered models can differ by tens of percents.

The mathematical model, finite-difference schemes and algorithms for computation of transient thermoand hydrodynamic processes involved in commissioning the unified system including the oil producing well, electrical submersible pump and fractured-porous reservoir with bottom water are developed. These models are implemented in the computer package to simulate transient processes with simultaneous visualization of their results along with computations. An important feature of the package Oil-RWP is its interaction with the special external program GCS which simulates the work of the surface electric control station and data exchange between these two programs. The package Oil-RWP sends telemetry data and current parameters of the operating submersible unit to the program module GCS (direct coupling). The station controller analyzes incoming data and generates the required control parameters for the submersible pump. These parameters are sent to Oil-RWP (feedback). Such an approach allows us to consider the developed software as the “Intellectual Well System”.

Some principal results of the simulations can be briefly presented as follows. The transient time between inaction and quasi-steady operation of the producing well depends on the well stream watering, filtration and capacitive parameters of oil reservoir, physical-chemical properties of phases and technical characteristics of the submersible unit. For the large time solution of the nonstationary equations governing the nonsteady processes is practically identical to the inverse quasi-stationary problem solution with the same initial data. The developed software package is an effective tool for analysis, forecast and optimization of the exploiting parameters of the unified oil-producing complex during its commissioning into the operating regime.

Certifying a transport airplane for the flights under icing conditions requires calculations aimed at definition of the dimensions and shapes of the ice bodies formed on the airplane surfaces. Up to date, software developed in Russia for simulation of ice accretion, which would be authorized by Russian certifying supervisory authority, is absent. This paper describes methodology IceVision recently developed in Russia on the basis of software FlowVision for calculations of ice accretion on airplane surfaces.

The main difference of methodology IceVision from the other approaches, known from literature, consists in using technology Volume Of Fluid (VOF — volume of fluid in cell) for tracking the surface of growing ice body. The methodology assumes solving a time-depended problem of continuous grows of ice body in the Euler formulation. The ice is explicitly present in the computational domain. The energy equation is integrated inside the ice body. In the other approaches, changing the ice shape is taken into account by means of modifying the aerodynamic surface and using Lagrangian mesh. In doing so, the heat transfer into ice is allowed for by an empirical model.

The implemented mathematical model provides capability to simulate formation of rime (dry) and glaze (wet) ice. It automatically identifies zones of rime and glaze ice. In a rime (dry) ice zone, the temperature of the contact surface between air and ice is calculated with account of ice sublimation and heat conduction inside the ice. In a glaze (wet) ice zone, the flow of the water film over the ice surface is allowed for. The film freezes due to evaporation and heat transfer inside the air and the ice. Methodology IceVision allows for separation of the film. For simulation of the two-phase flow of the air and droplets, a multi-speed model is used within the Euler approach. Methodology IceVision allows for size distribution of droplets. The computational algorithm takes account of essentially different time scales for the physical processes proceeding in the course of ice accretion, viz., air-droplets flow, water flow, and ice growth. Numerical solutions of validation test problems demonstrate efficiency of methodology IceVision and reliability of FlowVision results.

In this paper, a mathematical model of cellular tissue dynamics is considered. The first part gives the conclusion of the model, the main provisions and the formulation of the problem. In the second part, the final system is investigated numerically and the simulation results are presented. It is postulated that cellular tissue is a three-phase medium that consists of a solid skeleton (which is an extracellular matrix), cells and extracellular fluid. In addition, the presence of nutrients in the tissue is taken into account. The model is based on the equations of conservation of mass, taking into account mass exchange, the equations of conservation of momentum for each phase, as well as the diffusion equation for nutrients. The equation describing the cellular phase also takes into account the term describing the chemical effect on the tissue, which is called chemotaxis — the movement of cells caused by a gradient in the concentration of chemicals. The initial system of equations is reduced to a system of three equations for finding porosity, cell saturation and nutrient concentration. These equations are supplemented by initial and boundary conditions. In the one-dimensional case, the distribution of porosity, concentration of the cell phase and nutrients is set at the initial moment of time. A constant concentration of nutrients is set on the left border, which corresponds, for example, to the supply of oxygen from the vessel, as well as the flow of cell concentration on it is zero. Two types of conditions are considered at the right boundary: the first is the condition of impermeability of the right boundary, the second is the condition of constant concentration of the cell phase and zero flow of nutrient concentration. In both cases, the conditions for the matrix and extracellular fluid are the same, it is assumed that there is a source of nutrients (blood vessel) on the left border of the modeling area. As a result of modeling, it was revealed that chemotaxis has a significant effect on tissue growth. In the absence of chemotaxis, the compaction zone extends to the entire modeling area, but with an increase in the effect of chemotaxis on the tissue, a degradation area is formed in which the concentration of cells becomes lower than the initial one.

A mathematical model of fluid movement in the portal vein is considered. The fundamental circumstance determining the whole variety of portal hemodynamic phenomena is the absence of a valve apparatus. The flow direction is solely a function of the pressure gradient, and, therefore, it is fundamentally reversible when the boundary conditions of the system change.

Calculations were performed in the area representing a CT image fragment of the portal vein of a particular patient, which does not contain vascular bifurcations. The interpolation of patient Dopplerography data published in the press was used as boundary conditions for the flow. The calculations were carried out using the FlowVision industrial hydrodynamics software package. A comparison of calculations using the ideal fluid model and the Kuemada model of viscoplastic flow is carried out.

Calculations were performed for different values of the resistance coefficient corresponding to the physiological norm and with an increased value of the resistance coefficient.

At a normal value of the resistance coefficient, the flow in the portal vein is characterized by strong convective mixing.

As a result of calculations, it was found that when using the Kuemada model, the flow in the portal vein is stratified. The nature of the stratification depends on the hematocrit. At a normal value of the resistance coefficient, a plastic core of the flow is formed as the velocity decreases. With an increased value of the resistance coefficient during flow inversion, the flow core is also formed. When the flow is inverted, the plastic core continues to move in the forward direction, while the wall layers of the liquid begin to move in the opposite direction.

It is noted that in order to obtain correct modeling results, it is necessary to refine the blood composition of the portal vein and, possibly, refine the rheological model. Such information can be obtained both from comparing simulation data with clinical data, and by laboratory examination of portal vein blood.

The difference scheme for numerical solution of a time-dependant system of two Schrödinger equations with the operator of a spin-orbit interaction for a two-component spinor wave function is offered on the basis of a split method for a time-dependant Schrödinger equations. The computer simulation of the external neutrons’ wave functions evolution with different values of the full moment projection upon internuclear axis and probabilities of their transfer are executed for head-on collisions of ¹⁸O and ⁵⁸Ni nuclei.

The paper describes the results of computer simulation of time-dependent temperature fields arising in polar dielectrics irradiated by focused electron bunches with average electron energy when analyzing with electron microscopy techniques. The mathematical model was based on solving several-dimensional nonstationary heat conduction equation with use of numerical finite element method. The approximation of thermal source was performed taking into account the estimation of initial electron distribution determined by Monte-Carlo simulation of electron trajectories. The simulation program was designed in Matlab. The geometrical modeling and calculation results demonstrated the main features of model sample heating by electron beam were presented at the given experimental parameters as well as source approximation.

An algorithm of applied problem solving was described to calculate electrical characteristics of electrical field effects in ferroelectrics electron-beam charged. The algorithm was based on implementation of the deterministic model using finite element method as well as taking into account Monte-Carlo simulation results of electron transport. The program application was developed to perform computing experiments.

The physical and mathematical model of combustion of the polydisperse suspension of coal dust was developed. The formulation of the problem takes into account the evaporation of particle volatile components during the heating, the particle emitting and the gas heat transfer to a surrounding area via the sphere volume side surface, heat transfer coefficient as a function of temperature. The polydisperse of coal-dust is taken into consideration. N — the number of fraction. Fractions are subdivided into inert and reacting particles. The oxidizer mass balance equation takes into consideration the oxidizer consumption per each reaction (heterogeneous on the particle surface and homogenous in the gas). Exothermic chemical reactions in gas are determined by Arrhenius equation with second-order kinetics. The heterogeneous reaction on the particle surface was first-order reaction. The numerical simulation was solved by Runge–Kutta–Merson method. Reliability of the calculations was verified by solving the partial problems. During the numerical calculation the percentage composition of inert and reacting particles in coal-dust and their total mass were changed for each simulation. We have determined the influence of the percentage composition of inert and reacting particles on burning characteristics of polydisperse coal-dust methane-air mixture. The results showed that the percent increase of volatile components in the mixture lead to the increase of total pressure in the volume. The value of total pressure decreases with the increasing of the inert components in the mixture. It has been determined that there is the extremism radius value of coarse particles by which the maximum pressure reaches the highest value.