Key Engineering Materials Vol. 685

Abstract: In this paper the laminar stationary power-law fluid flow through an axisymmetric pipe contraction is investigated. The mathematical statement of the problem is formulated using stream function and vorticity variables. For obtaining a stationary solution the relaxation method with following realization of numerical algorithm based on finite difference alternative directions scheme is utilized. Implemented parametrical investigations allow obtaining the dependence of local resistance coefficients on Reynolds number, nonlinearity degree and piping contraction ratio.

Abstract: The results of mathematical modeling of the dynamic interaction of a plane longitudinal shock wave with a plane interface between two isotropic nonlinear elastic materials are presented. The mechanical properties of deformable solid are given by the elastic Murnaghan model. The dynamic processes of deformations distribution are studied in the framework of the theory of singular surfaces. The numerical solutions of the corresponding self-similar problem with strong and weak deformations discontinuities in the reflected and refracted wave packages have been obtained on the basis of the developed scheme of computational experiment.

Abstract: We consider the problem of decreasing the scattering from arbitrary 2D object by surrounding it the shell composed of M layers of homogeneous anisotropic materials. The solution of the scattering problem under study is obtained by solving corresponding 2D Helmholtz equation using cylindrical functions expansion. The coefficients of these expansions are determined by solving system of 4M+3 linear algebraic equations. Efficient numerical algorithm of cloaking problem is developed which is based on singular value decomposition of the coefficient matrix. Properties of the algorithm are studied and the results of numerical experiments are discussed.

Abstract: This paper deals with a diffusion approximation for the radiation transfer equation which takes into account Сompton scattering on electrons. An analytical and a numerical examples are used to compare the solution of radiation transfer equation with its diffusion approximation.

Abstract: By method of molecular dynamics discrete breathers with soft and hard types of non-linearity in the Pt₃Al crystal are studied. Obtained graphs characterize the spatial localization of the discrete breathers, the dependence of the frequency on the oscillation amplitude and the amount of energy localized on the discrete breathers. It is shown that the collision of moving discrete breathers may lead to the energy exchange between the breathers with some portion of the energy given to the Pt₃Al lattice. The probability of excitation of discrete breathers in thermodynamic equilibrium is estimated.

Abstract: The article considers the reconstruction of images by Synthetic Aperture Focusing Technique (SAFT). The work compares additive and multiplicative methods for processing signals from antenna array. We have proven that the multiplicative method gives better resolution. The study includes the estimation of beam trajectories for antenna arrays using analytical and numerical methods. We have shown that the analytical estimation method allows decreasing the image reconstruction time in the case of linear antenna array implementation.

Abstract: The 2D scattering problem is studied for the case of a two-dimensional cylindrical invisibility cloak, incorporating a tiny layer of perfect electromagnetic conductor (PEMC). The solution of the corresponding Helmholtz equation with variable coefficients is seeked as cylindrical functions Fourier series. The coefficients of these series are determined by solving the system of four linear algebraic equations with respect to four unknown coefficients with badly-conditioned matrix. The Singular Value Decomposition (SVD) method is applied for solving the system. Based on this idea the efficient numerical method is developed for solving the cloaking problem under study. The properties of this algorithm are studied and some results of numerical experiments are discussed.

Abstract: The article describes the numerical approach uniting finite volume method, Newton method and one of the MUSCL-type schemes for convective transport approximation for gas mixture components concentrations displaced by the water out of the porous medium. Numerical and analytical solutions for the case of radial two-dimensional flow of incompressible gas mixture and water have been compared. The obtained results allow considering the offered algorithm to be effective.

Abstract: The paper presents a mathematical model for combustion of a frozen nanosized aluminum suspension (ALICE), taking into account the combustion of aluminum in water vapor, the motion of combustion products, and the velocity lag of particles compared to gas. The model was formulated based on Belyaev’s approach to modeling the combustion of volatile fuels [1]. The burning rate calculated is in agreement with the experimental data on the ALICE burning rate and its variation with pressure.

Abstract: A boundary multiplicative control problem for a nonlinear steady-state heat transfer model accounting for heat radiation effects is considered. The aim of control consists in obtaining a prescribed temperature or radiative intensity distributions in a part of the model domain by controlling the boundary reflectivity. The solvability of this control problem is proved, and optimality conditions are derived.