All issues
 2021 Vol. 13
 2020 Vol. 12
 2019 Vol. 11
 2018 Vol. 10
 2017 Vol. 9
 2016 Vol. 8
 2015 Vol. 7
 2014 Vol. 6
 2013 Vol. 5
 2012 Vol. 4
 2011 Vol. 3
 2010 Vol. 2
 2009 Vol. 1

A universal method for constructing the simulation model of complex multiagent systems
Computer Research and Modeling, 2013, v. 5, no. 4, pp. 513523Views (last year): 5. Citations: 2 (RSCI).This paper presents a universal method for constructing an agentbased model of complex systems for their further clear computer representation by means of objectoriented programming languages. The method specifies both steps of model developing from the mathematical description of the system to the determined architecture of the program simulating the system. The efficiency of the method is illustrated by the construction of the two simulation models for the complex systems of various origins: the interactive simulation of the stock exchange and spacetime simulation of biological species competition.

Numerical approach and parallel implementation for computer simulation of stacked long Josephson Junctions
Computer Research and Modeling, 2016, v. 8, no. 4, pp. 593604Views (last year): 7. Citations: 6 (RSCI).We consider a model of stacked long Josephson junctions (LJJ), which consists of alternating superconducting and dielectric layers. The model takes into account the inductive and capacitive coupling between the neighbor junctions. The model is described by a system of nonlinear partial differential equations with respect to the phase differences and the voltage of LJJ, with appropriate initial and boundary conditions. The numerical solution of this system of equations is based on the use of standard threepoint finitedifference formulae for discrete approximations in the space coordinate, and the applying the fourstep RungeKutta method for solving the Cauchy problem obtained. Designed parallel algorithm is implemented by means of the MPI technology (Message Passing Interface). In the paper, the mathematical formulation of the problem is given, numerical scheme and a method of calculation of the currentvoltage characteristics of the LJJ system are described. Two variants of parallel implementation are presented. The influence of inductive and capacitive coupling between junctions on the structure of the currentvoltage characteristics is demonstrated. The results of methodical calculations with various parameters of length and number of Josephson junctions in the LJJ stack depending on the number of parallel computing nodes, are presented. The calculations have been performed on multiprocessor clusters HybriLIT and CICC of MultiFunctional Information and Computing Complex (Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna). The numerical results are discussed from the viewpoint of the effectiveness of presented approaches of the LJJ system numerical simulation in parallel. It has been shown that one of parallel algorithms provides the 9 times speedup of calculations.

FlowVision: Industrial computational fluid dynamics
Computer Research and Modeling, 2017, v. 9, no. 1, pp. 520Views (last year): 30. Citations: 8 (RSCI).The work submits new release of the FlowVision software designed for automation of engineering calculations in computational fluid dynamics: FlowVision 3.09.05. The FlowVision software is used for solving different industrial problems. Its popularity is based on the capability to solve complex nontradition problems involving different physical processes. The paradigm of complete automation of laborintensive and timetaking processes like grid generation makes FlowVision attractive for many engineers. FlowVision is completely developerindependent software. It includes an advanced graphical interface, the system for specifying a computational project as well as the system for flow visualization on planes, on curvilinear surfaces and in volume by means of different methods: plots, color contours, isolines, isosurfaces, vector fields. Besides that, FlowVision provides tools for calculation of integral characteristics on surfaces and in volumetric regions.
The software is based on the finitevolume approach to approximation of the partial differential equations describing fluid motion and accompanying physical processes. It provides explicit and implicit methods for time integration of these equations. The software includes automated generator of unstructured grid with capability of its local dynamic adaptation. The solver involves twolevel parallelism which allows calculations on computers with distributed and shared memory (coexisting in the same hardware). FlowVision incorporates a wide spectrum of physical models: different turbulence models, models for mass transfer accounting for chemical reactions and radioactive decay, several combustion models, a dispersed phase model, an electrohydrodynamic model, an original VOF model for tracking moving interfaces. It should be noted that turbulence can be simulated within URANS, LES, and ILES approaches. FlowVision simulates fluid motion with velocities corresponding to all possible flow regimes: from incompressible to hypersonic. This is achieved by using an original allspeed velocitypressure split algorithm for integration of the NavierStokes equations.
FlowVision enables solving multiphysic problems with use of different modeling tools. For instance, one can simulate multiphase flows with use of the VOF method, flows past bodies moving across a stationary grid (within Euler approach), flows in rotary machines with use of the technology of sliding grid. Besides that, the software solves fluidstructure interaction problems using the technology of twoway coupling of FlowVision with finiteelement codes. Two examples of solving challenging problems in the FlowVision software are demonstrated in the given article. The first one is splashdown of a spacecraft after deceleration by means of jet engines. This problem is characterized by presence of moving bodies and contact surface between the air and the water in the computational domain. The supersonic jets interact with the airwater interphase. The second problem is simulation of the work of a human heart with artificial and natural valves designed on the basis of tomographic investigations with use of a finiteelement model of the heart. This problem is characterized by twoway coupling between the “liquid” computational domain and the finiteelement model of the hart muscles.

Modern methods of mathematical modeling of blood flow using reduced order methods
Computer Research and Modeling, 2018, v. 10, no. 5, pp. 581604Views (last year): 62. Citations: 2 (RSCI).The study of the physiological and pathophysiological processes in the cardiovascular system is one of the important contemporary issues, which is addressed in many works. In this work, several approaches to the mathematical modelling of the blood flow are considered. They are based on the spatial order reduction and/or use a steadystate approach. Attention is paid to the discussion of the assumptions and suggestions, which are limiting the scope of such models. Some typical mathematical formulations are considered together with the brief review of their numerical implementation. In the first part, we discuss the models, which are based on the full spatial order reduction and/or use a steadystate approach. One of the most popular approaches exploits the analogy between the flow of the viscous fluid in the elastic tubes and the current in the electrical circuit. Such models can be used as an individual tool. They also used for the formulation of the boundary conditions in the models using one dimensional (1D) and three dimensional (3D) spatial coordinates. The use of the dynamical compartment models allows describing haemodynamics over an extended period (by order of tens of cardiac cycles and more). Then, the steadystate models are considered. They may use either total spatial reduction or two dimensional (2D) spatial coordinates. This approach is used for simulation the blood flow in the region of microcirculation. In the second part, we discuss the models, which are based on the spatial order reduction to the 1D coordinate. The models of this type require relatively small computational power relative to the 3D models. Within the scope of this approach, it is also possible to include all large vessels of the organism. The 1D models allow simulation of the haemodynamic parameters in every vessel, which is included in the model network. The structure and the parameters of such a network can be set according to the literature data. It also exists methods of medical data segmentation. The 1D models may be derived from the 3D Navier – Stokes equations either by asymptotic analysis or by integrating them over a volume. The major assumptions are symmetric flow and constant shape of the velocity profile over a crosssection. These assumptions are somewhat restrictive and arguable. Some of the current works paying attention to the 1D model’s validation, to the comparing different 1D models and the comparing 1D models with clinical data. The obtained results reveal acceptable accuracy. It allows concluding, that the 1D approach can be used in medical applications. 1D models allow describing several dynamical processes, such as pulse wave propagation, Korotkov’s tones. Some physiological conditions may be included in the 1D models: gravity force, muscles contraction force, regulation and autoregulation.

Development of network computational models for the study of nonlinear wave processes on graphs
Computer Research and Modeling, 2019, v. 11, no. 5, pp. 777814In various applications arise problems modeled by nonlinear partial differential equations on graphs (networks, trees). In order to study such problems and various extreme situations arose in the problems of designing and optimizing networks developed the computational model based on solving the corresponding boundary problems for partial differential equations of hyperbolic type on graphs (networks, trees). As applications, three different problems were chosen solved in the framework of the general approach of network computational models. The first was modeling of traffic flow. In solving this problem, a macroscopic approach was used in which the transport flow is described by a nonlinear system of secondorder hyperbolic equations. The results of numerical simulations showed that the model developed as part of the proposed approach well reproduces the real situation various sections of the Moscow transport network on significant time intervals and can also be used to select the most optimal traffic management strategy in the city. The second was modeling of data flows in computer networks. In this problem data flows of various connections in packet data network were simulated as some continuous medium flows. Conceptual and mathematical network models are proposed. The numerical simulation was carried out in comparison with the NS2 network simulation system. The results showed that in comparison with the NS2 packet model the developed streaming model demonstrates significant savings in computing resources while ensuring a good level of similarity and allows us to simulate the behavior of complex globally distributed IP networks. The third was simulation of the distribution of gas impurities in ventilation networks. It was developed the computational mathematical model for the propagation of finely dispersed or gas impurities in ventilation networks using the gas dynamics equations by numerical linking of regions of different sizes. The calculations shown that the model with good accuracy allows to determine the distribution of gasdynamic parameters in the pipeline network and solve the problems of dynamic ventilation management.

Mathematical model and computer analysis of tests for homogeneity of “dose–effect” dependence
Computer Research and Modeling, 2012, v. 4, no. 2, pp. 267273Views (last year): 6.The given work is devoted to the comparison of two tests for homogeneity: chisquare test based on contingency tables of 2 × 2 and test for homogeneity based on asymptotic distributions of the summarized square error of a distribution function estimators in the model of ”dose–effect” dependence. The evaluation of test power is performed by means of computer simulation. In order to design efficiency functions the method of kernel regression estimator based on Nadaray–Watson estimator is used.

Verification of calculated characteristics of supersonic turbulent jets
Computer Research and Modeling, 2017, v. 9, no. 1, pp. 2135Views (last year): 43.Verification results of supersonic turbulent jets computational characteristics are presented. Numerical simulation of axisymmetric nozzle operating is realized using FlowVision CFD. Open test cases for CFD are used. The test cases include Seiner tests with exit Mach number of 2.0 both fullyexpanded and underexpanded $(P/P_0 = 1.47)$. Fullyexpanded nozzle investigated with wide range of flow temperature (300…3000 K). The considered studies include simulation downstream from the nozzle exit diameter. Next numerical investigation is presented at an exit Mach number of 2.02 and a freestream Mach number of 2.2. Geometric model of convergent divergent nozzle rebuilt from original Putnam experiment. This study is set with nozzle pressure ratio of 8.12 and total temperature of 317 K.
The paper provides a comparison of obtained FlowVision results with experimental data and another current CFD studies. A comparison of the calculated characteristics and experimental data indicates a good agreement. The best coincidence with Seiner's experimental velocity distribution (about 7 % at far field for the first case) obtained using twoequation $k–\varepsilon$ standard turbulence model with Wilcox compressibility correction. Predicted Mach number distribution at $Y/D = 1$ for Putnam nozzle presents accuracy of 3 %.
General guidelines for simulation of supersonic turbulent jets in the FlowVision software are formulated in the given paper. Grid convergence determined the optimal cell rate. In order to calculate the design regime, it is recommended to build a grid, containing not less than 40 cells from the axis of symmetry to the nozzle wall. In order to calculate an offdesign regime, it is necessary to resolve the shock waves. For this purpose, not less than 80 cells is required in the radial direction. Investigation of the influence of turbulence model on the flow characteristics has shown that the version of the SST $k–\omega$ turbulence model implemented in the FlowVision software essentially underpredicts the axial velocity. The standard $k–\varepsilon$ model without compressibility correction also underpredicts the axial velocity. These calculations agree well with calculations in other CFD codes using the standard $k–\varepsilon$ model. The inhome $k–\varepsilon$ turbulence model KEFV with compressibility correction a little bit overpredicts the axial velocity. Since, the best results are obtained using the standard $k–\varepsilon$ model combined with the Wilcox compressibility correction, this model is recommended for the problems discussed.
The developed methodology can be regarded as a basis for numerical investigations of more complex nozzle flows.

Comparative analysis of finite difference method and finite volume method for unsteady natural convection and thermal radiation in a cubical cavity filled with a diathermic medium
Computer Research and Modeling, 2017, v. 9, no. 4, pp. 567578Views (last year): 13. Citations: 1 (RSCI).Comparative analysis of two numerical methods for simulation of unsteady natural convection and thermal surface radiation within a differentially heated cubical cavity has been carried out. The considered domain of interest had two isothermal opposite vertical faces, while other walls are adiabatic. The walls surfaces were diffuse and gray, namely, their directional spectral emissivity and absorptance do not depend on direction or wavelength but can depend on surface temperature. For the reflected radiation we had two approaches such as: 1) the reflected radiation is diffuse, namely, an intensity of the reflected radiation in any point of the surface is uniform for all directions; 2) the reflected radiation is uniform for each surface of the considered enclosure. Mathematical models formulated both in primitive variables “velocity–pressure” and in transformed variables “vector potential functions – vorticity vector” have been performed numerically using finite volume method and finite difference methods, respectively. It should be noted that radiative heat transfer has been analyzed using the netradiation method in Poljak approach.
Using primitive variables and finite volume method for the considered boundaryvalue problem we applied powerlaw for an approximation of convective terms and central differences for an approximation of diffusive terms. The difference motion and energy equations have been solved using iterative method of alternating directions. Definition of the pressure field associated with velocity field has been performed using SIMPLE procedure.
Using transformed variables and finite difference method for the considered boundaryvalue problem we applied monotonic Samarsky scheme for convective terms and central differences for diffusive terms. Parabolic equations have been solved using locally onedimensional Samarsky scheme. Discretization of elliptic equations for vector potential functions has been conducted using symmetric approximation of the secondorder derivatives. Obtained difference equation has been solved by successive overrelaxation method. Optimal value of the relaxation parameter has been found on the basis of computational experiments.
As a result we have found the similar distributions of velocity and temperature in the case of these two approaches for different values of Rayleigh number, that illustrates an operability of the used techniques. The efficiency of transformed variables with finite difference method for unsteady problems has been shown.

Simulation of flight and destruction of the Benešov bolid
Computer Research and Modeling, 2018, v. 10, no. 5, pp. 605618Views (last year): 24. Citations: 1 (RSCI).Comets and asteroids are recognized by the scientists and the governments of all countries in the world to be one of the most significant threats to the development and even the existence of our civilization. Preventing this threat includes studying the motion of large meteors through the atmosphere that is accompanied by various physical and chemical phenomena. Of particular interest to such studies are the meteors whose trajectories have been recorded and whose fragments have been found on Earth. Here, we study one of such cases. We develop a model for the motion and destruction of natural bodies in the Earth’s atmosphere, focusing on the Benešov bolid (EN070591), a bright meteor registered in 1991 in the Czech Republic by the European Observation System. Unique data, that includes the radiation spectra, is available for this bolid. We simulate the aeroballistics of the Benešov meteoroid and of its fragments, taking into account destruction due to thermal and mechanical processes. We compute the velocity of the meteoroid and its mass ablation using the equations of the classical theory of meteor motion, taking into account the variability of the mass ablation along the trajectory. The fragmentation of the meteoroid is considered using the model of sequential splitting and the statistical stress theory, that takes into account the dependency of the mechanical strength on the length scale. We compute air flows around a system of bodies (shards of the meteoroid) in the regime where mutual interplay between them is essential. To that end, we develop a method of simulating air flows based on a set of grids that allows us to consider fragments of various shapes, sizes, and masses, as well as arbitrary positions of the fragments relative to each other. Due to inaccuracies in the early simulations of the motion of this bolid, its fragments could not be located for about 23 years. Later and more accurate simulations have allowed researchers to locate four of its fragments rather far from the location expected earlier. Our simulations of the motion and destruction of the Benešov bolid show that its interaction with the atmosphere is affected by multiple factors, such as the mass and the mechanical strength of the bolid, the parameters of its motion, the mechanisms of destruction, and the interplay between its fragments.

The purposeful transformation of mathematical models based on strategic reflection
Computer Research and Modeling, 2019, v. 11, no. 5, pp. 815831The study of complex processes in various spheres of human activity is traditionally based on the use of mathematical models. In modern conditions, the development and application of such models is greatly simplified by the presence of highspeed computer equipment and specialized tools that allow, in fact, designing models from preprepared modules. Despite this, the known problems associated with ensuring the adequacy of the model, the reliability of the original data, the implementation in practice of the simulation results, the excessively large dimension of the original data, the joint application of sufficiency heterogeneous mathematical models in terms of complexity and integration of the simulated processes are becoming increasingly important. The more critical may be the external constraints imposed on the value of the optimized functional, and often unattainable within the framework of the constructed model. It is logical to assume that in order to fulfill these restrictions, a purposeful transformation of the original model is necessary, that is, the transition to a mathematical model with a deliberately improved solution. The new model will obviously have a different internal structure (a set of parameters and their interrelations), as well as other formats (areas of definition) of the source data. The possibilities of purposeful change of the initial model investigated by the authors are based on the realization of the idea of strategic reflection. The most difficult in mathematical terms practical implementation of the author's idea is the use of simulation models, for which the algorithms for finding optimal solutions have known limitations, and the study of sensitivity in most cases is very difficult. On the example of consideration of rather standard discrete event simulation model the article presents typical methodological techniques that allow ranking variable parameters by sensitivity and, in the future, to expand the scope of definition of variable parameter to which the simulation model is most sensitive. In the transition to the “improved” model, it is also possible to simultaneously exclude parameters from it, the influence of which on the optimized functional is insignificant, and vice versa — the introduction of new parameters corresponding to real processes into the model.
Fulltext version of the journal is also available on the web site of the scientific electronic library eLIBRARY.RU
The journal is included in the Russian Science Citation Index
The journal is included in the List of Russian peerreviewed journals publishing the main research results of PhD and doctoral dissertations.
International Interdisciplinary Conference "Mathematics. Computing. Education"
The journal is included in the RSCI
Indexed in Scopus