Том 11, № 2 (2019)

The ideal flow theory is used to determine the optimal die profile for the drawing and extrusion of sheets under the conditions of a plane strain. The solution is based on the theory of characteristics. In contrast to the available solutions based on the ideal flow theory, it is assumed that a portion of the die is prescribed. The solution is reduced to evaluating ordinary integrals. As an example, a die profile is found assuming that a portion of this profile is given and is a circular arc.

This paper numerically simulates turbulent heat transfer in a round pipe in a wide range of Reynolds numbers using the CABARET nonparametric MILES method on grids with an incomplete resolution of the turbulence spectrum and the STAR-CCM+ CFD code in the LES approximation. The calculation results are compared with the DNS calculations of other authors found in the literature and with the RANS calculations implemented in the STAR-CCM+ CFD code. The simulation showed a satisfactory accuracy in determining the mean, root-mean-square, and integral characteristics of the flow; and it allowed us to identify the shortcomings of the existing model relations describing local turbulence characteristics. The authors propose a thermal wall function implemented in the RANS approximations.

A technique for the comprehensive simulation of the destruction of polymers under the impact of intense energy flows is developed. The simulation results of the process of destruction of polymer materials can be used to study their behavior at high-energy impacts, verification of the models of bulk destruction of brittle materials, and validation of wide-range equations of state.

We consider a second-order differential equation that contains a fractional derivative (the Bagley–Torvik equation); here, the order of the derivative is in the range from 1 to 2 and is not known in advance. This model is used for describing oscillation processes in a viscoelastic medium. In order to study the equation, we use the Laplace transform; this makes it possible to obtain (in the explicit form) the image of the solution of the corresponding Cauchy problem. Numerical solutions for the various values of the parameter are constructed. Based on this solution, we propose a numerical technique for the parametric identification of an unknown order of the fractional derivative from the available experimental data. In the range of possible values of the parameter, the deviation function is determined by the least-squares method. The minimum of this function determines the search value of the parameter. The developed technique is tested on the experimental data for samples of polymer concrete, the fractional-derivative parameter in the model is determined, the theoretical and experimental curves are compared, and the accuracy of the parametric identification and the adequacy of the technique are established.

The CABARET algorithm constructed earlier by the authors for calculating the motion of multicomponent gas mixtures is used for the numerical simulation of a physical instability evolving when a shock wave passes through an initially quiescent interface of gaseous media with different physical properties, which is followed by the turbulization of the flow in the planar geometry. The following two problems are simulated: the passage of a shock wave through a rectangular subdomain filled with a heavy gas and the development of a Richtmyer–Meshkov instability during the passage of a shock wave through a sinusoidal media interface. The obtained evolution of the width of the mixing zone is compared with the experimental, theoretical, and numerical results of other authors.

In this paper, we present a methodology for the numerical simulation of the reacting flows of multicomponent fluid mixtures in a scramjet combustor based on solving the Navier-Stokes equation system. The combustion dynamics depending on the oxidizer’s oxidation ratio is studied, and the methodology of the numerical simulation on the multiprocessor supercomputer K-100 is developed using OpenFOAM.

We consider a linear ill-posed problem for the Fredholm equation of the first kind. For its regularization, Tikhonov’s stabilizer is implemented. To solve the problem, we use the mesh method, in which we replace integral operators by the simplest quadratures; and the differential ones, by the simplest finite differences. We investigate experimentally the influence of the regularization parameter and mesh thickening on the algorithm’s accuracy. The best performance is provided by the zeroth-order regularizer. We explain the reason of this result. We use the proposed algorithm for an applied problem of the recognition of two closely situated stars if the telescope instrument function is known. In addition, we show that the stars are clearly distinguished if the distance between them is ~0.2 of the instrumental function’s width and the values of brightness differ by 1–2 stellar magnitudes.

We consider a parallel version of the stabilized second-order incomplete triangular factorization–conjugate gradient method in which the reordering of the coefficient matrix that corresponds to the ordering based on splitting into subdomains with separators is used. The incomplete triangular factorization is constructed using the truncation of the fill-in chosen “by value” at the internal nodes of the subdomains and “by value” and ‘by positions” on the separators. The reliability of the method under consideration is theoretically proved. The reliability and convergence rate of the parallel method are numerically analyzed. The developed algorithms are implemented using a Message Passing Interface (MPI); the computational results are presented for benchmark problems with matrices from the collection of the University of Florida.