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Results in Journal Computational Mathematics and Information Technologies: 60

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A.A. Filina, V.V. Sidoryakina, A.E. Chistyakov, A.V. Nikitina
Computational Mathematics and Information Technologies; https://doi.org/10.23947/2587-8999-2021-1-1-10-25

Abstract:
The paper covers the research of microbiological destruction processes of petroleum origin pollutants in a shallow water taking into account a number of determining factors that affect the distribution of pollution in the researched water area: the oil fractional composition, the processes of evaporation, dissolution, biological oxidation of petro-hydrocarbons by microorganisms, as well as hydrodynamic and chemical-biological features of the water. A complex of interrelated spatially inhomogeneous mathematical models was proposed that allow researching the dynamics of microbiological destruction processes of petroleum hydrocarbons in shallow water. Schemes with weight taking into account the partial filling of computational cells of the simulated domain were developed at model discretization that made it possible to significantly increase the accuracy of calculations and reduce the calculation time. Based on a multiprocessor computer system, experimental software has been developed for predictive modeling of the ecological situation of shallow water in the event of accidental pollution by oil and other harmful substances during natural and technogenic challenges.
A.I. Sukhinov, V.V. Sidoryakina, E.A. Protsenko
Computational Mathematics and Information Technologies; https://doi.org/10.23947/2587-8999-2021-1-1-36-43

Abstract:
This paper presents the results of wave regime hydrophysical characteristics calculations in the area of the accumulative shore of the Tsimlyansky reservoir northwestern part. Wave hydrodynamics model based on 3D mathematical model that includes three Navier-Stokes motion equations, the continuity equations for an incompressible fluid was used. The discretization of the hydrodynamic equations was performed using the pressure correction method. Numerical algorithms and the software package implementing them are used to determine the pressure field, the water medium velocity vector field and to plot the pressure a given section of the reservoir water area. The results of the study can be used in the study of hydrophysical processes, assessment of the hydrodynamic impact on the formation of the coast-line and the bottom relief of large plaintype reservoirs in the Southern Russia.
A. A. Sukhinov, S. B. Kirilchik
Computational Mathematics and Information Technologies; https://doi.org/10.23947/2587-8999-2021-1-1-1-9

Abstract:
The article is devoted to the suspensions’ distribution mathematical modeling in the Eastern Pacific Ocean for various scenarios for the ferromanganese nodules extraction. The suspensions propagation model with complex granulometric composition that can interact in an aqueous medium takes into account the suspensions microturbulent diffusion caused by the turbulent aqueous medium movement and the suspensions convection caused by the advective movement of water mass in the ocean; gravitational suspensions deposition under the gravity influence; mutual transitions between different fractions that make up the suspension; interaction of particles with the bottom and with the free surface.
, M.I. Chumak
Computational Mathematics and Information Technologies; https://doi.org/10.23947/2587-8999-2021-1-1-44-50

Abstract:
This article is devoted to the development and research of a mathematical model of water fluid dynamics with variable depth. This model describes the water flow movement, the thermodynamics of ice formation and melting, considers the Coriolis force, horizontal and vertical turbulence of the water environment, the complex geometry of the coastline and bottom, friction on the bottom and wind currents, evaporation, wind speed, and atmospheric density, and the deviation of the pressure field value from the hydrostatic approximation. The article describes the influence of the spatial distribution of temperature, salinity, ionic composition, and hydrostatic pressure on the processes of ice cover formation. The Caspian Sea-was chosen as the object of the simulation. The changes in the temperature and salinity distributions measured by the electrical conductivity of the water, considering the ionic composition of the Caspian Sea waters over a long-term period, are used as input data. Modeling the movement of water flow will allow you to respond to man-made threats in an accelerated time mode. The models of hydrodynamics presented in this paper can be adapted for other reservoirs using the appropriate geoinformation systems.
S.V. Protsenko,
Computational Mathematics and Information Technologies; https://doi.org/10.23947/2587-8999-2021-1-1-26-35

Abstract:
The vertical turbulent exchange coefficient parametrization based on the LES approach is constructed in this paper. To implement this approach, water flow velocities pulsations full-scale data at some points of shallow-water systems obtained using an acoustic Doppler flow meter (ADCP) during expedition studies were filtered using two-stage Kalman algorithm, and then averaged, after which the LES approach was applied using subgrid turbulence model. The parametrization of the coefficient of vertical turbulent exchange is used in the wave hydrodynamics mathematical model.
Alexander Sukhinov, Alexander Chistyakov, Inna Kuznetsova, Elena Protsenko, Yulia Belova
Computational Mathematics and Information Technologies, Volume 1; https://doi.org/10.23947/2587-8999-2020-1-1-56-70

Mikhail Stepantsov, Keldysh Institute of Applied Mathematics
Computational Mathematics and Information Technologies, Volume 1; https://doi.org/10.23947/2587-8999-2020-1-1-12-18

Alexander Mikhailov, Keldysh Institute of Applied Mathematics, Gennadiy Pronchev, Lomonosov Moscow State University
Computational Mathematics and Information Technologies, Volume 1; https://doi.org/10.23947/2587-8999-2020-1-2-87-93

Abstract:
The paper studies the model of «Power-Society» system with two clans and bipolar reaction of the society. The «Power-Society» model describes the dynamics of distribution of power in hierarchy. This dynamics is influenced by society. Continuous-time «Power-Society» model has the form of parabolic equation in the case of continuous hierarchy, and the form of system of ordinary differential equations in the case of discrete hierarchy. The discrete-time model considered in this paper has the form of five dynamical equations. Bipolar reaction of the society refers to the situation with two stable distributions of power. In other words, for each government official two values are possible for the volume of power. Each of these values is considered by society as desirable. If each official holds the greater volume, we say that there is the «strong hand» distribution, if they all hold the smaller volume, this is the participatory distribution. Bureaucratic clans are an association of bureaucrats united by common interests and pursuing common goals, generally speaking, different from those of society as a whole. The paper considers a simple hierarchy of five officials, of which one is the head and four others form two competing clans. The system is studied numerically. It is shown, in particular, that in this system, the clan's lust for power significantly affects how quickly it manages to increase its power, however, the achieved amount of power itself almost does not depend on the lust for power, but is determined by the reaction of society.
Alexander Chistyakov, Don State Technical University, Alena Filina, Vladimir Litvinov, Supercomputers and Neurocomputers Research Center, Azov-Black Sea Engineering Institute of FSBEI HE Don State Agrarian University
Computational Mathematics and Information Technologies, Volume 1; https://doi.org/10.23947/2587-8999-2020-1-2-101-113

Abstract:
This paper covers the creation and numerical realization of proposed mathematical model of hydrodynamical processes in shallow water based on contemporary information technology and new computational methods that allow improve the prediction accuracy of the environmental situation using the example of the Taganrog Bay in the Azov Sea basin. The proposed mathematical hydrodynamics model takes into account surges, dynamically reconstructed geometry, elevation of the level and coastline, wind currents and friction against the bottom, Coriolis force, turbulent exchange, evaporation, river flow, deviation of the pressure field value from the hydrostatic approximation, the salinity and temperature impact. The discretization of the mathematical model of hydrodynamics was performed using the splitting schemes for physical processes. The constructed discrete analogs possess the properties of conservatism, stability, and convergence. Numerical algorithms are also proposed for solving the arising SLAEs that improve the accuracy of predictive modeling. The practical significance of this research is software implementation of the developed model and the determination of limits and prospects of its application. The experimental software development was based on a graphics accelerator for mathematical simulation the possible scenarios of shallow water ecosystems in consideration the environmental factors influence. The decomposition methods taking into account the CUDA architecture specifications were used at parallel implementation for computationally labors diffusion-convection problems.
Olga Proncheva, Keldysh Institute of Applied Mathematics, Yulia Danik, Mikhail Dmitriev, Institute for Systems Analysis Federal Research Center Computer Science and Control of Russian Academy of Sciences
Computational Mathematics and Information Technologies, Volume 1; https://doi.org/10.23947/2587-8999-2020-1-2-94-100

Abstract:
The paper presents a discrete optimal control problem with constraints on which a method for calculation of migration flows, where qualified and unskilled workers are distinguished, is discussed. At the same time, the optimality criterion in the problem is associated with the achievement of the maximum output with the minimization of the total number of migrants. Numerical calculations are provided that illustrate the sustainable growth scenario over a 10 year period. The work objectives included the development of an approach for calculating the necessary size of working-age population migration and its components to achieve optimal output growth. A macromodel is proposed, which is a discrete optimal control problem. An algorithm for the control synthesis is pro-posed. Numerical modeling is carried out. The obtained results can be used in migration flows planning and management processes.
Alexander Sukhinov, Don State Technical University
Computational Mathematics and Information Technologies, Volume 1; https://doi.org/10.23947/2587-8999-2020-1-2-71-86

Abstract:
The article considers splitting schemes in geometric directions that approximate the initial-boundary value problem for p-dimensional hyperbolic equation by chain of two-dimensional-one-dimensional problems. Two ways of constructing splitting schemes are considered with an operator factorized on the upper layer, algebraically equivalent to the alternating direction scheme, and additive schemes of total approximation. For the first scheme, the restrictions on the shape of the region G at p=3 can be weakened in comparison with schemes of alternating directions, which are a chain of three-point problems on the upper time layer, the region can be a connected union of cylindrical regions with generators parallel to the axis OX3. In the second case, for a three-dimensional equation of hyperbolic type, an additive scheme is constructed, which is a chain «two-dimensional problem – one-dimensional problem» and approximates the original problem in a summary sense (at integer time steps). For the numerical implementation of the constructed schemes – the numerical solution of two-dimensional elliptic problems – one can use fast direct methods based on the Fourier algorithm, cyclic reduction methods for three-point vector equations, combinations of these methods, and other methods. The proposed two-dimensional splitting schemes in a number of cases turn out to be more economical in terms of total time expenditures, including the time for performing computations and exchanges of information between processors, compared to traditional splitting schemes based on the use of three-point difference problems for multiprocessor computing systems, with different structures of connections between processors type «ruler», «matrix», «cube», with universal switching.
Mykhailo Seleznov, Moscow Institute of Physics and Technology
Computational Mathematics and Information Technologies, Volume 1; https://doi.org/10.23947/2587-8999-2020-1-2-114-119

Abstract:
The paper proposes an algorithm for the formation of a small training set, which ensures a reasonable quality of a surrogate machine learning model trained using this set. The algorithm uses multilayer perceptron to estimate heuristics and select the best next sample for the inclusion in a set. The paper tests the algorithm proposed applying it to the problem of deformation and breaking of a thin thread under the action of a transverse load pulse on it. The possibility to generalize the approach and apply it to building surrogate machine learning models for other physical problems is discussed.
, L.U. Akhmetzianova, B.R. Kuluev, I. M. Gubaydullin, A.V. Chemeris
Computational Mathematics and Information Technologies, Volume 1; https://doi.org/10.23947/2587-8999-2019-1-1-29-34

V.I. Agoshkov, T.O. Sheloput, Institute of Numerical Mathematics of the Russian Academy of Sciences
Computational Mathematics and Information Technologies, Volume 2; https://doi.org/10.23947/2587-8999-2018-2-1-1-8

A. A. Sukhinov, Lithuania) Pixelmator Team (Vilnius, G. B. Ostrobrod, Russia) CVisionLab (Taganrog
Computational Mathematics and Information Technologies, Volume 1; https://doi.org/10.23947/2587-8999-2017-1-1-113-127

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