and Computational Methods

#### 004.9:621.7 Mathematical modeling of the metal deformation process on a casting and forging module with a modified drive of the side strikers

**Odinokov V. I. (Komsomolsk-na-Amure State University), Dmitriyev E. A. (Komsomolsk-na-Amure State University), Evstigneev A. I. (Komsomolsk-na-Amure State University), Potianikhin D. A. (Komsomolsk-na-Amure State University), Kvashnin A. E. (Komsomolsk-na-Amure State University)**

doi: 10.18698/2309-3684-2021-3-323

This paper presents the mathematical formulation and the results of calculations of the problem of metal deformation on a casting-forging module with modified side strikers’ drive. A complex spatial problem of determination the stress-strain state of the flow region under loading with an external load that changes over time is considered. The fundamental equations are based on flow theory. At solving the problem, a proven numerical method is used, as well as numerical schemes and the software package used earlier at solving similar problems. The software package implements a step-by-step loading algorithm considering the history of the process and the changing geometry of the flow region. A small time step is associated with a 10° rotation of the eccentric shaft. The deformation area is divided into elements by an orthogonal system of surfaces (elements have an orthogonal shape). For each element, the formulated system of equations is written in a difference form, which is solved according to the developed numerical schemes and algorithms, that consider the initial and boundary conditions. The result of the solution is the fields of stresses and velocities of displacements in the spatial area. The analysis of the obtained results is given. A comparison with the results of the current structure module solving has been made. Lead is taken as a deformed material, the physical properties of which are approximated by an analytical dependence according to the available experimental data. The physical nonlinearity of the system of equations is realized during solving by the iterative method. Local calculations of the solution of the problem were carried out on three variants of division of the area into elements. The choice of the mesh density imposed on the considered deformation region is substantiated. The solution results are presented graphically. The efficiency of the deformation process according to the improved method on a new design of the casting and forging module is shown.

Одиноков В.И., Дмитриев Э.А., Евстигнеев А.И., Потянихин Д.А., Квашнин А.Е. Математическое моделирование процесса деформации металла на литейно-ковочном модуле с измененным приводом боковых бойков. Математическое моделирование и численные методы, 2021, № 3, с. 3–23.

#### 519.63:536.4 Numerical modelling of porcesses of formation, growth, and decomposition of agglomerates in porous medium under different modes of heating

**Donskoy I. G. (Melentiev Energy Systems Institute SB RAS)**

doi: 10.18698/2309-3684-2021-3-2441

The paper considers a numerical model of flow in a porous medium containing particles of a melting component (polymer). When heated, these particles swell, deform and fill the pore spaces, as a result of which the permeability is significantly reduced. The relationship between porosity and permeability is described by a simple Kozeny-Karman formula. Then, near the lower (inlet) boundary, a region with low permeability (i.e.agglomerate) is formed, the growth of which is determined by the conditions at the side wall and inlet boundaries. As a result of calculations, typical scenarios of porous medium blocking at different heating temperatures were obtained. It is shown that when heated through the wall, the polymer may decompose, so the porous medium partially restores its permeability. When heated by the inlet gas, agglomerate is much more stable, since it blocks the heating source.

Донской И.Г. Численное моделирование процессов образования, роста и разложения агломератов в пористой среде при разных режимах нагрева. Математическое моделирование и численные методы, 2021, № 3, с. 24–41.

#### 539.3 Coupled modeling of high-speed aerothermodynamics and internal heat and mass transfer in composite aerospace structures

**Dimitrienko Y. I. (Bauman Moscow State Technical University), Koryakov M. N. (Bauman Moscow State Technical University), Yurin Y. V. (Bauman Moscow State Technical University), Zakharov A. A. (Bauman Moscow State Technical University), Sborschikov S. V. (Bauman Moscow State Technical University), Bogdanov I. O. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2021-3-4261

A coupled problem of high-speed aerothermodynamics and internal heat and mass transfer in heat-shielding structures of reentry spacecraft made of ablative polymer composite materials is considered. To determine the heat fluxes in the shock layer of the reentry vehicle, the chemical composition of the atmosphere is taken into account. The mathematical formulation of the conjugate problem is formulated and an algorithm for the numerical solution is proposed. An example of the numerical solution of the problem for the reentry spacecraft Stardust is presented. It is shown that taking into account chemical reactions in the gas flow around the surface of the reentry vehicle is essential for the correct determination of the gas temperature in the boundary layer. It is also shown that the developed numerical method for solving the problem makes it possible to determine the parameters of phase transformations in a heat-shielding structure depending on the heating time, in particular, it allows calculating the pore pressure field of gaseous products of thermal decomposition of a polymer composite, which, under certain conditions, can lead to material destruction.

мДимитриенко Ю.И., Коряков М.Н., Юрин Ю.В., Захаров А.А., Сборщиков С.В., Богданов И.О. Сопряженное моделирование высокоскоростной аэротермодинамики и внутреннего тепломассопереноса в композитных аэрокосмических конструкциях. Математическое моделирование и численные методы, 2021, № 3, с. 42–61.

#### 519.6:629.7.02 Application of a genetic algorithm in the problem of modeling and optimization of hydraulic systems for synchronous movement of actuators

**Bushuev A. Y. (Bauman Moscow State Technical University), Reznikov A. O. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2021-3-6273

A model of genetic algorithm with binary coding with independent Schaeffer selection is constructed, which allows one to search for a global optimum by several criteria without their scalarization. The calculations take into account the range of all possible motions of actuators under uncertain external influences in some predetermined range. An algorithm has been developed that allows storing intermediate results to eliminate the problem of a large number of repeated calculations in the course of the evolutionary algorithm, which reduced the computation time. The effectiveness of the optimization algorithm is demonstrated on the example of solving a model problem.

Бушуев А.Ю., Резников А.О. Применение генетического алгоритма в задаче моделирования и оптимизации пневмогидравлической системы синхронизации исполнительных органов. Математическое моделирование и численные методы, 2021, № 3, с. 62–73.

#### 519.6 Modeling and optimization of low–mass satellite control when flying from Earth orbit to Mars orbit under a solar sail

**Mozzhorina T. Y. (Bauman Moscow State Technical University), Rakhmankulov D. A. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2021-3-7487

In this paper, the optimization of the transfer of a low–mass satellite from the Earth's orbit to the Mars orbit under a solar sail is considered. Optimization of the control of the pitch angle of the solar sail is carried out using the Pontryagin maximum principle while minimizing the flight time. In contrast to previous works on this topic, the solution of the boundary value problem, to the solution of which the maximum principle is reduced, was obtained by the false position method. The calculation program is written in the C++ programming language. Despite the computational difficulties arising when using the false position method, it was possible to achieve good convergence of the Newton method underlying the algorithm. The analysis of the accuracy of the results obtained is carried out and the possibility of using the false position method in solving such problems is shown. A comparison is made with the data of previously published works. Despite some assumptions used in the development of the calculation algorithm, the work has its value in terms of assessing the possibility of using the false position method, which gives the most accurate numerical optimization results.

Мозжорина Т.Ю., Рахманкулов Д.А. Моделирование и оптимизация управлением спутника малой массы при перелете с орбиты Земли на орбиту Марса под солнечным парусом. Математическое моделирование и численные методы, 2021, № 3, с. 74–87.

#### 004.85:551.5051 Methods of data mining in the nowcasting model of dangerous phenomena

**Shershakova A. O. (Bauman Moscow State Technical University), Parkhomenko V. P. (ФИЦ ИУ РАН/Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2021-3-88104

This work is devoted to the study and application of methods of intellectual analysis for the implementation of the scheme of the nowcasting of dangerous phenomena. In the course of the work, data sets were formed with differ in the methods of information processing for their preparation. For each set, a number of mathematical models were constructed for classifying cloud cells according to the degree of danger of tornadoes forming from them. The Python programming language has been chosen as the main development language. The work is of great practical importance in the field of forecasting weather events. Its novelty lies in the use of modern machine learning methodology, instead of the traditional approach to data extrapolation, widely used in various schemes of nowcasting.

Шершакова А.О., Пархоменко В.П. Методы интеллектуального анализа данных в модели наукастинга опасных явлений. Математическое моделирование и численные методы, 2021, № 3, с. 88–104.

#### 519.6 Agent-based model of cultural interactions on non-metrizable Hausdorff spaces

**Belotelov N. V. (Bauman Moscow State Technical University/Institution of Russian Academy of Sciences Dorodnicyn Computing Centre of RAS), Pavlov S. A. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2021-3-105119

The need to develop formalized computer-oriented approaches to conducting interdisciplinary research of intercultural interactions is an urgent task. The article describes an approach to the development of agent models of intercultural interactions based on the use of non-metrizable Hausdorff spaces using genetic algorithms to introduce dynamic changes in the structure of cultural agents under consideration. The article considers a prototype of an agent model in which the state of agents is described in Hausdorff spaces. Using the choice of reference points for each agent, the Uryson function is built, which allows you to enter the preferences of agents. Further, using the technology of gentic algorithms, it is possible to obtain the clock dynamics of changes in the entire system of agents. The article describes some simulation experiments. Possible prospects for the development of this approach are discussed.

Белотелов Н.В, Павлов С.А. Агентная модель культурных взаимодействий на неметризуемых хаусдорфовых пространствах. Математическое моделирование и численные методы, 2021, № 3, с. 105–119.