and Computational Methods

Rubric: "1.2.2. Mathematical modeling, numerical methods and software packages (technical sciences)"

doi: 10.18698/2309-3684-2022-2-102113

Using the method of dynamics of averages, a "mixed" model of numerous groupings confrontation has been developed with linear dependencies on the time of effective speeds of striking by units of the parties. An algorithm is constructed that allows to investigate the course of the process and calculate its main indicators. It is established that the use of confrontation models with constant effective speed of strikes in many cases leads to significant errors in the calculation of the main indicators of the process. The influence of a preemptive strike by one of the opposing sides on the course of the progress and the final outcome are investigated.

Чуев В.Ю., Дубограй И.В. «Смешанная» модель противоборства многочисленных группировок при линейных зависимостях от времени эффективных скоростей воздействий единицами сторон. Математическое моделирование и численные методы, 2022, № 2, с. 104–115

doi: 10.18698/2309-3684-2023-2-332

In this work, a mathematical model of the thermo-temporal evolution of a cluster in the melt of a heat-resistant nickel alloy ZhS6U is constructed. An initial-boundary value problem with a moving boundary is formulated, for the solution of which numerical modeling is used by the particle trajectory method, and a number of classical physical theories are used to describe evolutionary processes. To check the accuracy of the model, a physical experiment is involved in constructing polytherms and isotherms of the electrical resistance of the alloy under consideration. It has been confirmed that the Brownian diffusion model and Drude's theory of conductivity are applicable to describe both the temporal and temperature evolution of a cluster. The approach to modeling based on "hard balls" also justified itself. According to the simulation results, in the time range from 1690 to 1752 K, the number of particles in the cluster varies from 5000 to 2000, the average dynamic viscosity of the cluster varies from 3 to 2 * 1010 Pa * s, however, it is assumed that the central part is much denser than periphery. The cluster radius varies from 24 to 18 A, and the radius of the free zone around the cluster varies from 56 to 43 A. The directions of further development of the model are determined.

Тягунов А.Г., Зейде К.М., Мильдер О.Б., Тарасов Д.А. Диффузионная модель эволюции кластера в металлическом расплаве жаропрочного никелевого сплава. Математическое моделирование и численные методы, 2023, № 2, с. 3–32.

doi: 10.18698/2309-3684-2023-2-129154

The formation of the supply chain of raw materials is closely related to the production problems of woodworking enterprises. Construction of supply chains for raw materials and the optimal calculation of daily production have been hot topics since the beginning of the second industrial revolution. This article discusses the enterprise of the Primorsky Territory of the woodworking industry, which does not have plots for rent. The purpose of the work is to solve the problem of building a supply chain of raw materials, taking into account the daily loading of production facilities and finding the optimal solution. The source of raw materials is the commodity exchange, where lots appear daily randomly in different mining regions. In the scientific literature, there are many ways to calculate the best profit value, taking into account many restrictions, but they do not take into account many features that are important for woodworking enterprises. Based on a review of the scientific literature, this article presents a mathematical model that acts as a decisionmaking mechanism on each individual day, and it differs in that it can take into account the coefficient of useful volume of raw materials that will reach the warehouse and travel time. The model was tested on the data of the Russian Commodity and Raw Materials Exchange and a company in Primorsky Krai. The result of testing the model is the calculated optimal profit trajectory for each set of data on the volume of raw materials, the time of lots in transit, as well as many important indicators for any production: profit volume, production volume of goods. The analysis of the received solutions showed that there are difficulties in planning supply chains and production volumes. The regions are analyzed as sources of raw materials, from which regions and when it is worth buying raw materials. The shortcomings and positive aspects of the mathematical model are given

Рогулин Р.С. Математическая модель формирования цепочек поставок сырья с товарно-сырьевой биржи в условиях риска с опорой на траекторию прибыли за предыдущие периоды. Математическое моделирование и численные методы, 2023,№ 2, с. 129–154.

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.

doi: 10.18698/2309-3684-2023-1-92111

The study of the influence of the viscosity grade of the supplied oil ISO VG32 and ISO VG46 in a wide range of rotor speeds and operating clearances on the local and integral characteristics of a thrust plain bearing with fixed pads of the compressor is presented. The studies were carried out using the Sm2Px3Txτ calculation program based on the results of numerical experiments of the bearing. The program is built by numerical implementation of a nonstationary periodic thermoelastohydrodynamic (PTEHD) mathematical model of the thrust bearing operation. The research results indicate a significant influence of the oil viscosity grade on the main characteristics and temperature conditions of the thrust bearing. When changing from ISO VG46 to the lighter oil ISO VG32, there is a noticeable reduction in bearing pad temperatures and power loss. However, the level of this change is determined by the specified operating clearance between the rotating thrust collar and the bearing pads. The influence of oil viscosity grade and the profile of the working surface on the temperature regime of the pad is analyzed. The value and location of the maximum temperature of the thrust bearing pad is determined, as well as the possibility of applying the standard point 75/75 from API-670 in practice.

Соколов Н.В., Хадиев М.Б., Федотов П.Е., Федотов Е.М. Численное исследование влияния класса вязкости смазки на работу упорного подшипника скольжения. Математическое моделирование и численные методы, 2023, No 1, с. 92–111.

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.

doi: 10.18698/2309-3684-2023-3-105124

The purpose of the work is to build and implement an algorithm for finding a numerical solution to a problem for mixed-type equations in an unlimited region. In this case problems are considered in which the process under study is described in some limited area by the thermal conductivity equation or wave equation, and outside it by the Laplace equation. The necessary additional conditions at zero, at infinity and the conditions for conjunction at the border of the inner region are set. There is described an algorithm for finding a numerical solution to a problem with a wave equation in a limited region in one-dimensional and two-dimensional cases, problems with a thermal conductivity equation or a wave equation in a two-dimensional case. Difference schemes are built by the integro–interpolation method. The task is solved in a limited area. Nonlocal boundary conditions are set on its border so the solution of task in limited area coincides with projection of problem in unlimited area. In this case, an artificial boundary is introduced for the solution in the part of the region in which the process is described by the Laplace equation. An iterative algorithm and an algorithm with a non-local boundary condition are built. The results of calculations for examples in various fields are presented.

Галанин М.П., Ухова А.Р. Численное решение уравнений смешанного типа в неограниченной области на плоскости. Математическое моделирование и численные методы, 2023, № 3, с. 105–124.

doi: 10.18698/2309-3684-2023-3-4261

Within the framework of the actual problem of comet-asteroid danger, the physical processes that cause the destruction and fragmentation of meteoric bodies in the Earth's atmosphere, in this case the Tunguska bolide, are numerically studied. The number of possible versions and hypotheses related to the Tunguska phenomenon is extremely large and continues to increase, therefore, an analysis and generalization of all known facts inherent in this non-standard catastrophic event is necessary, and only then proceed to the nomination of certain hypotheses explaining it. Based on the developed physical and mathematical model that determines the movement of space objects of natural origin in the atmosphere and their interaction with it, we have proposed two hypotheses explaining the processes occurring during the fall of the Tunguska body in 1908. The first hypothesis is related to the fragmentation of the body, which is a stone meteoroid into a large number of fragments, which collapsed in the dense layers of the atmosphere under the action of thermal stresses to the size of fine dust. The difficulties in identifying small particles that fell out as a result of the Tunguska event are mainly explained by the following circumstance: the timing of the initial search for traces of the fall of the body was removed from the moment of the event by as much as twenty years, during which a very significant number of other geophysical processes could occur in this area. The second hypothesis is related to phenomena that occur at small angles of entry of a body into the Earth's atmosphere. In this case, there is a change in the ballistics of its flight in the atmosphere, consisting in a transition from the fall mode to the ascent mode. This effect leads to the realization of the following possible scenarios of the event: the return of the body back to outer space at its residual velocity greater than the second cosmic one; the transition of the body to the orbit of the Earth satellite at a residual velocity greater than the first cosmic one; at lower values of the residual velocity of the body, its return after some time to the fall mode and reaching the earth's surface at a considerable distance from the intended crash site. The proposed hypotheses explain, for example, the absence of material traces, including craters, during the search for the remains of the Tunguska bolide in the vicinity of the forest collapse.

Андрущенко В.А., Сызранова Н.Г. Моделирование Тунгусского явления 1908 года в рамках двух возможных гипотез. Математическое моделирование и численные методы, 2023, № 3, с. 42–61.

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.