and Computational Methods

#### 532.51 Modeling non-Newtonian liquid permeability in three-dimensional composite structures on the base of asymptotic homogenization method

**Dimitrienko Y. I. (Bauman Moscow State Technical University), Li S. -. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2019-3-1938

The paper describes investigating a mathematical model of the process of a non-Newtonian liquid multiscale filtration in three-dimensional periodic porous media by asymptotic homogenization. The so-called local problem of filtration in a single pore is formulated as well as the local non-Newtonian-viscous defining relationship. An iterative finite element method is developed for solving a local problem in 1/8 periodicity cell, based on the physical symmetry of the structure. The distribution of the components of the filtration rate, pressure micro-fields and non-Newtonian viscosity in a single pore is calculated. On the basis of Darcy's law the nonlinear filtration law is analyzed, the effect of liquid rheological properties on permeability is shown.

Димитриенко Ю.И., Шугуан Ли. Моделирование проницаемости неньютоновских жидкостей в трехмерных композитных структурах на основе метода асимптотической гомогенизации. Математическое моделирование и численные методы. 2019. № 3.c.19–38.

#### 539.3+629.78 Modeling of contact interaction of tetrahedral cell edges in solving problems of spatial body high-speed interaction

**Dobritsa B. T. (Bauman Moscow State Technical University), Dobritsa D. B. (АО "НПО им. С.А. Лавочкина"), Yashchenko B. Y. (АО "НПО им. С.А. Лавочкина")**

doi: 10.18698/2309-3684-2019-3-3956

The paper considers improving techniques of numerical simulation of high-speed interaction of solids, performed for designing spacecraft protection from the impact of micrometeorites and debris particles. An algorithm for the implementation of boundary conditions on the contact surface, designed for numerical simulation using Lagrangian grids and based on the control of mutual penetration of tetrahedral cells of contacting bodies at the intersection of their edges, is proposed. The algorithm is based on the calculation of reaction forces for nodes of tetrahedral cell edges of contacting bodies and correction of velocity vectors of these nodes under condition of non-penetration

Добрица Б.Т., Добрица Д.Б., Ященко Б.Ю. Моделирование контактного взаимодействия ребер тетраэдрических ячеек при решении задач высокоскоростного взаимодействия пространственных тел. Математическое моделирование и численные методы. 2019. № 3.c.39–56.

#### 629.762 Mathematical methods for optimal selection of linear increasing over time mass-flow characteristics of energy devices ensuring aircraft gas-dynamic ejection with specified parameters

**Plyusnin A. V. (Bauman Moscow State Technical University/JSC MIC NPO Mashinostroyenia)**

doi: 10.18698/2309-3684-2019-3-5785

The paper proposes the theory for optimized selection of linear increasing over time mass-flow rates of energy devices designed for craft gas dynamic ejection from a launch container under the specified restrictions on parameters. Theory is also proposed for optimized selection of geometrical parameters of multigrain tubular charge for implementing these mass-flow rates. A visual geometric interpretation of theoretical developments is presented, and their practical feasibility is confirmed by numerical simulations of parameters of gas-dynamic ejection and internal ballistics processes.

Плюснин А.В. Математические методы оптимального выбора линейно нарастающих по времени массорасходных характеристик энергоустройств, обеспечивающих газодинамический выброс летательных аппаратов с заданными параметрами. Математическое моделирование и численные методы, 2019, № 1, с. 57–85.

#### 551.555.9 Numerical simulation of 3d stratified fluid flows around circular cylinder

**Rozhdestvenskaya T. I. (Institute for Computer Aided Design of the Russian Academy of Sciences)**

doi: 10.18698/2309-3684-2019-3-8699

The relevance of study of the liquid stratified density, in particular sea water, is very important for science and technology. The results of such research can be used in the study of the sea water flow around underwater vessels and parts of ships submerged in water, in the study of sea currents behind the islands and, consequently, the safety of navigation. In this paper NaCl salt water solution is considered as a stratified liquid. This is the most common liquid in nature (water in the seas and oceans). The flow of a stratified fluid has characteristics other than flow of a homogeneous fluid. When studying the two-dimensional structure of the flow around the obstacle, such phenomena as outstripping disturbance – fluid blocking in front of obstacle and connected internal waves were discovered. Examining the thin structure of the flow with more details, it is possible to identify other features. This paper investigates numerically a three-dimensional flow of stratified liquid around a circular cylinder in a wide range of Reynolds and Froude numbers. It is found that the region occupied by the internal waves extends to a considerable distance up from the front critical point of the cylinder. The finite difference method of Belotserkovsky-Gushchin-Konshin having the second order of accuracy in spatial coordinates is used as a numerical method of research. The method was repeatedly tested and showed good results. It is implemented in stages: at first the approximate velocity values are computed then the pressure is computed based on these values, after that velocities are revised and finally the salinity is calculated. The software package implementing this method is adapted for machines with parallel architecture using MPI technology. Computations were carried out on the supercomputer MVS-1000.

Рождественская Т.П. Численное исследование трехмерных течений неоднородной жидкости около кругового цилиндра. Математическое моделирование и численные методы, 2019, № 1, с. 86–99.

#### 533.6.011.5 Method of local surfaces for modeling pressure on a blunted cone in three-dimensional flow

**Kotenev V. P. (Bauman Moscow State Technical University/JSC MIC NPO Mashinostroyenia), Puchkov A. S. (Bauman Moscow State Technical University/JSC MIC NPO Mashinostroyenia), Sapozhnikov D. A. (JSC MIC NPO Mashinostroyenia/МГТУ им.Н.Э.Баумана), Tonkih E. G. (JSC MIC NPO Mashinostroyenia/МГТУ им.Н.Э.Баумана)**

doi: 10.18698/2309-3684-2019-3-100112

The paper considers a method for applying the analytical dependence to calculate the pressure on the surface of blunted cones in a supersonic gas flow at an angle of attack, taking into account the discontinuity in the generatrix curvature. To generalize the dependence on the case of three-dimensional flow, the method of local surfaces was used. The pressure coefficient on the surface of spherical bluntness is calculated separately from the conical part according to known ratios [1, 2]. The results were compared with empirical data and the results of accurate calculations in a strict mathematical formulation. The scope of applicability of the method is determined. From the comparison it follows that using the analytical formula for the pressure distribution on the surface of a blunted cone in three-dimensional flows in applied problems of aerodynamics allows significant simplifying calculations while maintaining good accuracy of the results.

Котенев В.П., Пучков А.С., Сапожников Д.А., Тонких Е.Г. Метод локальных поверхностей для моделирования давления на затупленном конусе при пространственном обтекании. Математическое моделирование и численные методы. 2019. № 3. с. 100–112.

#### 532.59 Numerical simulation of perturbation of two-layer liquid free surface by a point source localized in the lower layer

**Nosov V. N. (Vernadsky Institute of Geochemistry and Analytical Chemistry, RAS), Savin A. S. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2019-3-113124

The paper considers a pulse point source in the lower layer of stratified fluid. An expression for the perturbation of its free surface is obtained. It is shown that two waves arise on the surface of the liquid, associated with the presence of a density jump in it. Examples of numerical calculations for real sea conditions are shown. The pulse point source is a model of elementary perturbation of the liquid medium depth, allowing a complete mathematical study in the framework of the approximation of small waves. This approximation is quite justified in cases of simulating real disturbance sources located at considerable depths, since these sources transmit a very weak signal to the sea surface. The main problem in such cases is the isolation of this signal from background noise, such as wind waves. The solution of the problem should be based on the results of mathematical modeling of sea surface disturbances by different sources in the depth of the marine environment. More complex models can be designed by considering real disturbances of the marine environment as some superpositions of model elementary disturbances from point pulse sources. Furthermore, a complete mathematical solution to the problem of a point pulse source gives an idea of the orders of the sea surface disturbance magnitudes, which creates the basis for obtaining various estimates of possible disturbances and therefore is of considerable interest in the development of requirements for sea surface remote sensing equipment.

Носов В.Н., Савин А.С. Численное моделирование возмущения свободной поверхности двухслойной жидкости точечным источником, локализованным в нижнем слое. Математическое моделирование и численные методы. 2019. № 3. с. 113–124.

#### 539.3 Modeling of coupling effects in the problem of pulsed loading of thermoelastic media

**Valishin A. A. (Bauman Moscow State Technical University), Kartashov E. M. (MIREA - Russian Technological University/Moscow Technological University)**

doi: 10.18698/2309-3684-2019-3-318

Deformation of solids under the action of non-stationary external mechanical, thermal or other effects is accompanied by the inverse thermodynamic effect of the release of additional heat due to internal friction, i.e.a change in the temperature field. This causes additional deformation, which in turn leads to the release of heat. This effect of the interaction of mechanical and temperature fields is called the connectivity effect. The consequence of this effect is the appearance of heat fluxes leading to an increase in the entropy of the thermodynamic system and thermoelastic energy dissipation. The purpose of the work is to study the influence of the interaction of deformation and temperature fields for different materials. For “classical” materials, such as metals and glass, the thermodynamic effect of the interaction of deformation and temperature fields is insignificant and it is usually neglected in the calculation, design and operation of structures. For some polymer materials such as various polyvinylacetals, this effect is significant; it must be taken into account when creating composite materials on their basis and when designing products and structures of them. A dynamic coupled problem of thermoelasticity for an elastic layer of various structural, consumer and construction materials under rapid application of a normal compressive load to thermally insulated surfaces is considered. It is shown that for glass and steel temperature increasing due to the interaction of the deformation and temperature fields being really negligible is 0.180–0.183 K (or 0.061–0.062 %). For polymers, first of all, from the class of polyvinylacetals, it is substantial, and it can no longer be neglected.

Валишин А.А., Карташов Э.М. Моделирование эффектов связанности в задаче об импульсном нагружении термоупругих сред. Математическое моделирование и численные методы, 2019, № 3, с. 3–18.