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The purpose of this paper is to generalize the macroscopic hydrodynamic vehicular traffic models by using the algorithm for constructing the adequate state equation — dependence the pressure from traffic density by taking into account the real experimental data (possibly using the parametric solutions for model equations). It is proved that this kind of state equation which closed model equations system and obtained from the experimentally observed form of the fundamental diagram — dependence the traffic intensity from its density, completely determines the all properties of the used phenomenological model.

Mathematical simulation on unsteady natural convection in a closed porous cylindrical cavity having finite thickness heat-conducting solid walls in conditions of convective heat exchange with an environment has been carried out. A boundary-value problem of mathematical physics formulated in dimensionless variables such as stream function and temperature on the basis of Darcy–Boussinesq model has been solved by finite difference method. Effect of a porous medium permeability 10^–5≤Da<∞, ratio between a solid wall thickness and the inner radius of a cylinder 0.1≤h/L≤0.3, a thermal conductivity ratio 1≤λ_1,2≤20 and a dimensionless time on both local distributions of isolines and isotherms and integral complexes reflecting an intensity of convective flow and heat transfer has been analyzed in detail.

Modification of the invariant imbedding method to describe the interaction of 3D electromagnetic field with “woodpile” photonic crystal of finite thickness is considered in this paper. This modification allows solving a problem of evanescent modes resonant amplification during numerical calculations for the first layer of photonic crystal. The mathematical model created in this work gives good agreement with physical experiment results.

The article contains results of modeling a meteor entering dense atmosphere layers using Galerkin’s method and smoother particle hydrodynamics. Numerical simulations were run using experimental data gathered for the Chelyabinsk meteor while varying the meteor material characteristics and its orientation when entering the atmosphere.

In this paper, we present new parallel algorithms for finite element analysis implemented in the FEStudio software framework. We describe the programming model of finite element method, which supports parallelism on different stages of numerical simulations. Using this model, we develop parallel algorithms of numerical integration for dynamic problems and local stiffness matrices. For constructing and solving the systems of equations, we use the CUDA programming platform.

The static three-level game-theoretic model of three-level control system of the ship’s water ballast is built. The methods of hierarchical control in view of requirements of keeping the system in the given state are used. A comparison of the results of study of the model in terms of $\Gamma_1$ and $\Gamma_2$ Germeyer’s games is conducted. Numerical calculations for some typical cases are given.

Excitation waves are a prototype of self-organized dynamic patterns in non-equilibrium systems. They develop their own intrinsic dynamics resulting in travelling waves of various forms and shapes. Prominent examples are rotating spirals and scroll waves. It is an interesting and challenging task to find ways to control their behavior by applying external signals, upon which these propagating waves react. We apply external electric fields to such waves in the excitable Belousov–Zhabotinsky (BZ) reaction. Remarkable effects include the change of wave speed, reversal of propagation direction, annihilation of counter-rotating spiral waves and reorientation of scroll wave filaments. These effects can be explained in numerical simulations, where the negatively charged inhibitor bromide plays an essential role. Electric field effects have also been investigated in biological excitable media such as the social amoebae Dictyostelium discoideum. Quite recently we have started to investigate electric field effect in the BZ reaction dissolved in an Aerosol OT water-in-oil microemulsion. A drift of complex patterns can be observed, and also the viscosity and electric conductivity change. We discuss the assumption that this system can act as a model for long range communication between neurons.

The possibility to study temperature fluctuations using URANS approach is studied. The results of numerical simulation of mixing processes for triple-jet sodium at different temperatures are presented. The processes were simulated using FlowVision software system and LMS model for turbulent heat transfer. The analysis and experiment data are compared. Validated was the possibility to determine the energy-carrying frequencies of temperature fluctuations using URANS approach and LMS model when mixing triple-jet sodium at different temperatures.

The article contains results of 3D modeling of seismic responses from fractured geological formations with use of grid-characteristic method on unstructured tetrahedral meshes with use of high-performance computation systems. The method being used is the most suitable for modeling of heterogenic domains exploration seismology problems. The use of unstructured tetrahedral meshes allows modeling of different geometry and space orientation fractures. That gives us possibility to solve the problems in the most real set.

We consider a mathematical model describing the competition for a heterogeneous resource of two populations on a one-dimensional area. Distribution of populations is governed by diffusion and directed migration, species growth obeys to the logistic law. We study the corresponding problem of nonlinear parabolic equations with variable coefficients (function of a resource, parameters of growth, diffusion and migration). Approach on the theory the cosymmetric dynamic systems of V. Yudovich is applied to the analysis of population patterns. Conditions on parameters for which the problem under investigation has nontrivial cosymmetry are analytically derived. Numerical experiment is used to find an emergence of continuous family of steady states when cosymmetry takes place. The numerical scheme is based on the finite-difference discretization in space using the balance method and integration on time by Runge-Kutta method. Impact of diffusive and migration parameters on scenarios of distribution of populations is studied. In the vicinity of the line, corresponding to cosymmetry, neutral curves for diffusive parameters are calculated. We present the mappings with areas of diffusive parameters which correspond to scenarios of coexistence and extinction of species. For a number of migration parameters and resource functions with one and two maxima the analysis of possible scenarios is carried out. Particularly, we found the areas of parameters for which the survival of each specie is determined by initial conditions. It should be noted that dynamics may be nontrivial: after starting decrease in densities of both species the growth of only one population takes place whenever another specie decreases. The analysis has shown that areas of the diffusive parameters corresponding to various scenarios of population patterns are grouped near the cosymmetry lines. The derived mappings allow to explain, in particular, effect of a survival of population due to increasing of diffusive mobility in case of starvation.