and Computational Methods

Rubric: "01.02.00 Mechanics"

doi: 10.18698/2309-3684-2017-1-7890

The research examines the planar and three-dimensional problems of an ice cover perturbed by a point pulse source localized in the depth of an infinitely deep liquid. We studied the ice cover of different thickness and carried out numerical study of its perturbations by sources located at different depths. The main attention is paid to the ice cover perturbations that arise directly above the source.

Savin A., Gorlova N., Strunin P. Numerical simulation of the point pulse source impact in a liquid on the ice cover. Маthematical Modeling and Coтputational Methods, 2017, №1 (13), pp. 78-90

doi: 10.18698/2309-3684-2016-4-1733

We obtained a mathematical model for determining the parameters of longitudinal selfoscillations, excited in the pressure gas flow at local flow heat supply. In our research we established that under certain conditions the gas heat supply alters the flow hydraulic characteristics, creating the "negative" resistance effect. In this case, the self-oscillation excitation is possible even with the monotonically decreasing supercharger pressure characteristic.

Basok B., Gotsulenko V. Simulation of pressure gas flow self-oscillation excited by heat supply. Маthematical Modeling and Coтputational Methods, 2016, №4 (12), pp. 17-33

doi: 10.18698/2309-3684-2014-4-317

On the basis of mathematical model of thermal interaction between inclusion and the matrix we estimated influence of inclusions deviations from spherical shape on the effective thermal conductivity coefficient of the composite and associated with such deviation a possible occurrence of the anisotropy of the composite with respect to the property of thermal conductivity. Using the dual variational formulation of the stationary problem of heat conduction in an inhomogeneous body we built bilateral estimates of effective thermal conductivity.

Zarubin V., Kuvyrkin G., Savelyeva I. Effective thermal conductivity of a composite in case of inclusions shape deviations from spherical ones. Маthematical Modeling and Coтputational Methods, 2014, №4 (4), pp. 3-17

doi: 10.18698/2309-3684-2014-2-115126

During the last decades we are witnessing climate changes. Scientists assume global warming to be the result of man-generated increase of green house gases in the atmosphere, the most important one being СО2. The article deals with the problem and describes cutting-edge solutions for stabilising climate. The research makes use of a seasonal global combined threedimensional hydrodynamic model of climate. This model of climate includes model of the World Ocean with real depths and configuration of continents, model of evolution of sea ice and energy — moisture balance model of the atmosphere. The first stage covers estimation of climate change through 2100 following IPCC A2 СО2 increase scenario. The calculations yield rise of average annual surface temperature of the atmosphere by 3,5 С. A number of calculations have been made to estimate possibility of stabilising climate at the level of 2010 by means of controlled release of sulphate aerosol into stratosphere. The aerosol will reflect and disperse a part of the coming solar radiation. We have calculated concentration (albedo) of the aerosol from 2010 to 2100 which will enable us to stabilise the average annual temperature of the surface layer of atmosphere. We have shown that by this way it is impossible to achieve the seasonal uniform approximation to the existing climate, although it is possible to significantly reduce the greenhouse warming effect. Provided that the aerosol is distributed evenly in space in stratosphere, we can stabilize the average annual temperature of the atmosphere, herewith in middle and low latitudes the climate will be colder by 0,1…0,2 С and in high latitudes it will be warmer by 0,2…1,2 С. Besides, these differences are essentially seasonal in nature, they increase in winter. If we stop releasing the aerosol in 2080 the average annual global temperature of the atmosphere will rise, reaching the former value without the aerosol by the year 2100.

Parkhomenko V. Modelling global climate stabilisation by controlled emission of stratospheric aerosol. Маthematical Modeling and Coтputational Methods, 2014, №2 (2), pp. 115-126

doi: 10.18698/2309-3684-2014-1-1835

The author offers a method (PGRM) of numerical-analytical solving the equation system in partial derivatives describing the natural thermal convection in the complicated-shaped dimensional cavity with arbitrary boundary conditions. The new approach is based on a combination of Petrov – Galerkin method and R-functions (Rvachev functions) and makes it possible to obtain temperature, vortex and current functions satisfying the boundary condi-tions in the form of expansions in certain bases. The coordinated choice of bases provides a natural way to approximate the boundary conditions for the flow function. Unsteady convec-tion problems are solved by combining PGRM and Rothe method.

Basarab M. Numerical-analytical method of solving two-dimensional problems of natural convection in a closed cavity. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 18-35

doi: 10.18698/2309-3684-2015-1-5066

The dispersion relation for a symmetric 3-layered elastic plate is derived and analysed, both numerically and asymptotically. Each layer is assumed to be composed of a linear isotropic elastic material. Numerical solutions of the relation are first presented. After presentation of these numerical solutions, particular focus is applied to the short wave regime, within which appropriate asymptotic approximations are established. These are shown to provide excellent agreement with the numerical solution over a surprisingly larger than might be expected wave number regime. It is envisaged that these solutions might offer some potential for estimation of truncation error for wave number integrals and thereby enable the development of hybrid numerical-asymptotic methods to determine transient structural response to impact.

Lashab M., Rogerson G., Sandiford K. A short wave asymptotic analysis of the dispersion relation for a symmetric three-layered elastic plate. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 50-66

doi: 10.18698/2309-3684-2015-1-6782

The article presents a suggested method of numerical finite-element solving the ‘hole ovalization’ problem. This method can be applied for experimental development of advanced aviation materials with the aim of determining structure element resistance against deforming with stress concentrators, mainly, connectors. The method is based on three-dimensional finite element solution of the problem of lastoplastic deformation of plates with a hole under crushing. It is appropriate for reduction of xperimental studies and replacing them by the numerical experiments. The Ilyushin model of small lastoplastic deformations has been used. The results of numerical simulation of a threedimensional stress-strain state of elastoplastic plates under crushing are presented as well as results of experimental nvestigations of deforming plates of Al-alloy 163. It is shown that the results of numerical and experimental modeling for deforming plates under crushing agree quite well.

Dimitrienko Y., Gubareva E., Sborschikov S., Erasov V., Yakovlev N. Computational modeling and experimental investigation of elastic-plastic plates deforming under crushing. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 67-82

doi: 10.18698/2309-3684-2014-4-7487

The article describes performed simulation of force action on streamlined horizontal elements of engineering structures in the upper layer of sharply stratified flow associated with the generation of waves at the interface between the liquid layers. We obtained an integral representation of the wave drag and lift, made numerical calculations for a real marine environment. The conditions under which there is a significant increase in the hydrodynamic reactions on streamlined structural elements were revealed.

Vladimirov I., Korchagin N., Savin A. Simulation of wave action on horizontal structure elements in the upper layer of stratified flow. Маthematical Modeling and Coтputational Methods, 2014, №4 (4), pp. 74-87

doi: 10.18698/2309-3684-2015-2-2345

The article describes a class of promising anisogrid structures representing mesh shell of unidirectional carbon. A brief analysis of existing approaches to modeling deformation of grid structures is presented. New mathematical and numerical models are proposed for reliable description of complex behavior of anisogrid structures under different kinds of loads. A high degree of accuracy and stability of the numerical model based on the expansions of unknown functions in Chebyshev polynomials and Fourier series is caused by the lack of saturation of such approximations. Efficiency of the proposed models and techniques is demonstrated on the example of solving test boundary-value problems and a problem of axial compression of anisogrid cylindrical shell.

Golushko S., Semisalov B. Numerical modeling of anisogrid structures deformation using schemes of high accuracy without saturation. Маthematical Modeling and Coтputational Methods, 2015, №2 (6), pp. 23-45