and Computational Methods

#### 621.464.3 Optimization of solid fuel model gas generator design

**Bushuev A. Y. (Bauman Moscow State Technical University), Ryauzov S. S. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2019-4-314

The optimization problem is formulated, which consists in ensuring the maximum time of maintaining the pressure in the filled container in the range from the maximum reached to 70 ATM. A mathematical model of a system consisting of a solid-fuel gas generator and a constant-volume filling tank is constructed. The optimization problem was solved by the Hook-Jeeves method and a genetic algorithm with real coding. The results were compared. A software package has been developed with the help of which a system of ordinary differential equations describing the state of the object under consideration is solved.

Бушуев А.Ю., Ряузов С.С. Оптимизация конструкции твердотопливного модельного газогенератора. Математическое моделирование и численные методы, 2019, № 4, с. 3–14.

#### 629.762 Numerical evaluation of body added mass coefficients introduced by means of acceleration potentials, for the case of slightly compressible liquids

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

doi: 10.18698/2309-3684-2019-4-1530

It is demonstrated that all 36 added mass and inertia coefficients of a body located in an unbounded ideal incompressible liquid may be introduced for the momentary state of rest by using acceleration potentials instead of classical velocity potentials specifying generally not-existent irrotational unseparated flows. The meaning of this conception is investigated with respect to real liquids having the compressibility property, by means of a numerical experiment fulfilled in the framework of an acoustical approach.

Плюснин А.В. Численный расчет коэффициентов присоединенных масс тела, движущегося в слабо-сжимаемой жидкости. Математическое моделирование и численные методы. 2019. № 4. с. 15–30.

#### 531.6.011.32:532.582.4 Simulation of the subsonic detachable body with a bottom cut on the current pattern with an equivalent half-infinite surface at small angles of attack

**Timofeev V. N. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2019-4-3149

The subsonic flow of cylindrical bodies with a detachment located in the vicinity of the bottom cut is considered. The current scheme with an equivalent surface, which is accompanied by a half-infinite section is used. Recommendations have been given on the formation of a configuration of such an equivalent semi-infinite surface at non-zero attack angles. The laboriousness of the calculations is reduced by taking into account the specifics of the applied flow pattern and the use of P-shaped vortex threads in the method of discrete vortexes. The results of mathematical modeling of the flow of cylindrical bodies with a revitalized head and a bottom slice at small angles of attack are presented.

Тимофеев В.Н. Моделирование дозвукового отрывного обтекания тел с донным срезом по схеме течения с эквивалентной полубесконечной поверхностью при малых углах атаки. Математическое моделирование и численные методы, 2019, № 4, с. 31–49.

#### 519.6:621.316:621.396 Modeling and methods of calculation of electric circuits with approximate characteristics

**Arutyunyan R. V. (Bauman Moscow State Technical University), Harutyunyan T. R. (JSC MIC NPO Mashinostroyenia)**

doi: 10.18698/2309-3684-2019-4-5068

The article investigates two approaches to the calculation of electric circuits in the conditions of uncertainty in the initial data or the influence of random influences, noise of different nature. The first approach is based on the application of interval and bilateral methods and is to some extent an example of robust methods. The second approach uses the stochastic Fokker-Planck equation and is the most informative. Although the application of the Fokker-Planck equation is limited by some conditions (random effects have the character of white noise or are subject to the Gaussian distribution law). This method has a wide scope of applicability. In turn, there are various methods for solving this differential equation. The article considers the solution of the corresponding problem using the finite difference method.

Examples of modeling of specific electrical and electronic circuits are given.

Арутюнян Р.В., Арутюнян Т.Р. Моделирование и методы расчета электрических цепей с приближёнными характеристиками. Математическое моделирование и численные методы, 2019, № 4, с. 50–68.

#### 521.3:521.6 Statistical model of space objects distribution in space of orbital parameters

**Borovin G. K. (Keldysh Institute of Applied Mathematics of the Russian Academy of Scienсes), Stepaniants V. A. (Keldysh Institute of Applied Mathematics of the Russian Academy of Scienсes), Zahvatkin M. V. (Keldysh Institute of Applied Mathematics of the Russian Academy of Scienсes), Usovik I. V. (JSC TsNIIMash)**

doi: 10.18698/2309-3684-2019-4-6990

A statistical model of space debris is proposed. The model is based on the catalog of orbits of space objects, constructed using domestic and foreign sources. To build this model, the cataloged objects are clustering using criterion of closeness in a 4d space of orbital parameters characterizing the semimajor axis, eccentricity and position of the plane of the satellite orbits composing a cluster. The distribution of objects in each cluster is determined by the mathematical expectation and the covariance matrix of the spread of the orbital parameters of the cluster.

Боровин Г.К., Захваткин М.В., Степаньянц В.А., Усовик И.В. Статистическая модель распределения космических объектов в пространстве орбитальных параметров. Математическое моделирование и численные методы, 2019, № 4, с. 69–90.

#### 007.51 Simulation model of migration processes in countries taking into account the level of education

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

doi: 10.18698/2309-3684-2019-4-9199

The simulation model of population migration between countries, each of which has its own culture, is considered. The article describes the scheme of the educational process, which assumes the presence of two types of education – technical, which affects the economic well-being of the country and cultural, which affects the mobility of the population and the coefficients of tolerance of intercultural relations. The model takes into account the demographic process. The analysis of the conducted simulation experiments shows that the insufficient development of cultural education of the population, in the case of migration, can lead to social instability in the country.

Белотелов Н.В. Имитационная модель процессов миграции в странах с учетом уровня образования. Математическое моделирование и численные методы, 2019, № 4, с. 91–99.

#### 519.86 The problems of identifying individual customers based on the analysis of large volumes of panel data on cash receipts

**Dimitrienko Y. I. (Bauman Moscow State Technical University), Kotel'nikova A. V. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2019-4-100116

The problems of identifying individual customers are formulated based on the analysis of large amounts of data on cash receipts in a large supermarket. Models of behavior of various categories of individual customers in the supermarket are developed. A computational algorithm is proposed for solving the problems of identifying individual customers using panel data from cash receipts. The algorithm is universal, since it does not use any personal data about the buyer, but is based on an analysis of only buying activity, calculated on the basis of panel data on cash receipts. The algorithm allows you to identify groups of customers, as well as with a certain probability, an individual customer. As an example of the application of the developed models and computational algorithms, commodity checks from the X5Retail Group company supermarket chain for a certain period of time were used.

Димитриенко Ю.И., Котельникова А.В. Задачи идентификации индивидуальных покупателей на основе анализа больших объемов панельных данных о кассовых чеках. Математическое моделирование и численные методы, 2019, № 4, с. 100–116.