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Mathematical simulation of unsteady natural convection and thermal surface radiation within a rotating square enclosure was performed. The considered domain of interest had two isothermal opposite walls subjected to constant low and high temperatures, while other walls are adiabatic. The walls were diffuse and gray. The considered cavity rotated with constant angular velocity relative to the axis that was perpendicular to the cavity and crossed the cavity in the center. Mathematical model, formulated in dimensionless transformed variables “stream function – vorticity” using the Boussinesq approximation and diathermic approach for the medium, was performed numerically using the finite difference method. The vorticity dispersion equation and energy equation were solved using locally one-dimensional Samarskii scheme. The diffusive terms were approximated by central differences, while the convective terms were approximated using monotonic Samarskii scheme. The difference equations were solved by the Thomas algorithm. The approximated Poisson equation for the stream function was solved by successive over-relaxation method. Optimal value of the relaxation parameter was found on the basis of computational experiments. Radiative heat transfer was analyzed using the net-radiation method in Poljak approach. The developed computational code was tested using the grid independence analysis and experimental and numerical results for the model problem.

Numerical analysis of unsteady natural convection and thermal surface radiation within the rotating enclosure was performed for the following parameters: Ra = 10³–10⁶, Ta = 0–10⁵, Pr = 0.7, ε = 0–0.9. All distributions were obtained for the twentieth complete revolution when one can find the periodic behavior of flow and heat transfer. As a result we revealed that at low angular velocity the convective flow can intensify but the following growth of angular velocity leads to suppression of the convective flow. The radiative Nusselt number changes weakly with the Taylor number.

The work is dedicated to the use of the software package Turbulence Problem Solver (TPS) for numerical simulation of a wide range of laser problems. The capabilities of the package are demonstrated by the example of numerical simulation of the interaction of femtosecond laser pulses with thin metal bonds. The software package TPS developed by the authors is intended for numerical solution of hyperbolic systems of differential equations on multiprocessor computing systems with distributed memory. The package is a modern and expandable software product. The architecture of the package gives the researcher the opportunity to model different physical processes in a uniform way, using different numerical methods and program blocks containing specific initial conditions, boundary conditions and source terms for each problem. The package provides the the opportunity to expand the functionality of the package by adding new classes of problems, computational methods, initial and boundary conditions, as well as equations of state of matter. The numerical methods implemented in the software package were tested on test problems in one-dimensional, two-dimensional and three-dimensional geometry, which included Riemann's problems on the decay of an arbitrary discontinuity with different configurations of the exact solution.

Thin films on substrates are an important class of targets for nanomodification of surfaces in plasmonics or sensor applications. Many articles are devoted to this subject. Most of them, however, focus on the dynamics of the film itself, paying little attention to the substrate, considering it simply as an object that absorbs the first compression wave and does not affect the surface structures that arise as a result of irradiation. The paper describes in detail a computational experiment on the numerical simulation of the interaction of a single ultrashort laser pulse with a gold film deposited on a thick glass substrate. The uniform rectangular grid and the first-order Godunov numerical method were used. The presented results of calculations allowed to confirm the theory of the shock-wave mechanism of holes formation in the metal under femtosecond laser action for the case of a thin gold film with a thickness of about 50 nm on a thick glass substrate.

The article deals with the development of the noise-reduction algorithm based on anisotropic nonlinear data filtering of computed tomography (CT). Analysis of domestic and foreign literature has shown that the most effective algorithms for noise reduction of CT data use complex methods for analyzing and processing data, such as bilateral, adaptive, three-dimensional and other types of filtrations. However, a combination of such techniques is rarely used in practice due to long processing time per slice. In this regard, it was decided to develop an efficient and fast algorithm for noise-reduction based on simplified bilateral filtration method with three-dimensional data accumulation. The algorithm was developed on C ++11 programming language in Microsoft Visual Studio 2015. The main difference of the developed noise reduction algorithm is the use an improved mathematical model of CT noise, based on the distribution of Poisson and Gauss from the logarithmic value, developed earlier by our team. This allows a more accurate determination of the noise level and, thus, the threshold of data processing. As the result of the noise reduction algorithm, processed CT data with lower noise level were obtained. Visual evaluation of the data showed the increased information content of the processed data, compared to original data, the clarity of the mapping of homogeneous regions, and a significant reduction in noise in processing areas. Assessing the numerical results of the algorithm showed a decrease in the standard deviation (SD) level by more than 6 times in the processed areas, and high rates of the determination coefficient showed that the data were not distorted and changed only due to the removal of noise. Usage of newly developed context dynamic threshold made it possible to decrease SD level on every area of data. The main difference of the developed threshold is its simplicity and speed, achieved by preliminary estimation of the data array and derivation of the threshold values that are put in correspondence with each pixel of the CT. The principle of its work is based on threshold criteria, which fits well both into the developed noise reduction algorithm based on anisotropic nonlinear filtration, and another algorithm of noise-reduction. The algorithm successfully functions as part of the MultiVox workstation and is being prepared for implementation in a single radiological network of the city of Moscow.

A 2D numerical model of the immersion of a cold oceanic plate into the thickness of the Earth’s upper mantle has been developed, where the stage of the initial immersion of the plate is preceded by the establishment of a regime of thermogravitational convection of the mantle substance. The model approximation of the mantle is a two-dimensional image of an incompressible Newtonian quasi-liquid in a Cartesian coordinate system, where, due to the high viscosity of the medium, the equations of mantle convection are accepted in the Stokes approximation. It is assumed that seawater that has leaked here enters the first horizons of the mantle together with the plate. With depth, the increase in pressure and temperature leads to certain losses of its light fractions and fluids, losses of water and gases of water-containing minerals of the plate, restructuring of their crystal lattice and, as a consequence, phase transformations. These losses cause an increase in the plate density and an uneven distribution of stresses along the plate (the initial sections of the plate are denser), which subsequently, together with the effect of mantle currents on the plate, causes its fragmentation. The state of mantle convection is considered when the plate and its individual fragments have descended to the bottom of the upper mantle. Computational schemes for solving the model equations have been developed. Mantle convection calculations are performed in terms of the Stokes approximation for vorticity and the stream function, and SPH is used to calculate the state and subsidence of the plate. A number of computational experiments have been performed. It is shown that fragmentation of the plate occurs due to the effect of mantle convection on the plate and the development of inhomogeneous stress fields along the plate. Following the equations of the model, the time of the final stage of subduction is estimated, i.e. the time of the entire oceanic plate reaching the bottom of the upper mantle. In geodynamics, this process is determined by the collision of plates that immediately follows subduction and is usually considered as the final stage of the Wilson cycle (i. e., the cycle of development of folded belts).

The paper proposes and investigates a mathematical model of a distributed computing system of parallel interacting processes competing for the use of a limited number of copies of a structured software resource. In cases of unlimited and limited parallelism by the number of processors of a multiprocessor system, the problems of determining operational and exact values of the execution time of heterogeneous and identically distributed competing processes in a synchronous mode are solved, which ensures a linear order of execution of blocks of a structured software resource within each of the processes without delays. The obtained results can be used in a comparative analysis of mathematical relationships for calculating the implementation time of a set of parallel distributed interacting competing processes, a mathematical study of the efficiency and optimality of the organization of distributed computing, solving problems of constructing an optimal layout of blocks of an identically distributed system, finding the optimal number of processors that provide the directive execution time of given volumes of computations. The proposed models and methods open up new prospects for solving problems of optimal distribution of limited computing resources, synchronization of a set of interacting competing processes, minimization of system costs when executing parallel distributed processes.

Modification of the lattice Boltzmann method for computation of viscous Newtonian fluid flows is considered. Modified method is based on the splitting of differential operator in Navier–Stokes equation and on the idea of instantaneous Maxwellisation of distribution function. The problems for the system of lattice kinetic equations and for the system of linear diffusion equations are solved while one time step is realized. The efficiency of the method proposed in comparison with the ordinary lattice Boltzmann method is demonstrated on the solution of the problem of planar flow in cavern in wide range of Reynolds number and various grid resolution.

The paper develops a new mathematical method of the joint signal and noise parameters determination at the Rice statistical distribution by method of moments based upon the analysis of data for the 1-st and the 3-rd raw moments of the random rician value. The explicit equations’ system have been obtained for required parameters of the signal and noise. In the limiting case of the small value of the signal-to-noise ratio the analytical formulas have been derived that allow calculating the required parameters without the necessity of solving the equations numerically. The technique having been elaborated in the paper ensures an efficient separation of the informative and noise components of the data to be analyzed without any a-priori restrictions, just based upon the processing of the results of the signal’s sampled measurements. The task is meaningful for the purposes of the rician data processing, in particular in the systems of magnetic-resonance visualization, in ultrasound visualization systems, at the optical signals’ analysis in range measuring systems, in radio location, etc. The results of the investigation have shown that the two parameter task solution of the proposed technique does not lead to the increase in demanded volume of computing resources compared with the one parameter task being solved in approximation that the second parameter of the task is known a-priori There are provided the results of the elaborated technique’s computer simulation. The results of the signal and noise parameters’ numerical calculation have confirmed the efficiency of the elaborated technique. There has been conducted the comparison of the accuracy of the sought-for parameters estimation by the technique having been developed in this paper and by the previously elaborated method of moments based upon processing the measured data for lower even moments of the signal to be analyzed.

The application of a conservative numerical method of fluxes is examined for studying the vortex structures in the massive, fast-turned compact astrophysical objects, which are in self-gravity conditions. The simulation is accomplished for the objects with different mass and rotational speed. The pictures of the vortex structure of objects are visualized. In the calculations the gas-dynamic model is used, in which gas is accepted perfected and nonviscous. Numerical procedure is based on the finite-difference approximation of the conservation laws of the additive characteristics of medium for the finite volume. The “upwind” approximations of the densities of distribution of mass, components of momentum and total energy are applied. For the simulation of the objects, which possess fast-spin motion, the control of conservation for the component of moment of momentun is carried out during calculation. Evolutionary calculation is carried out on the basis of the parallel algorithms, realized on the computer complex of cluster architecture. Algorithms are based on the standardized system of message transfer Message Passing Interface (MPI). The blocking procedures of exchange and non-blocking procedures of exchange with control of the completion of operation are used. The parallelization on the space in two or three directions is carried out depending on the size of integration area and parameters of computational grid. For each subarea the parallelization based on the physical factors is carried out also: the calculations of gas dynamics part and gravitational forces are realized on the different processors, that allows to raise the efficiency of algorithms. The real possibility of the direct calculation of gravitational forces by means of the summation of interaction between all finite volumes in the integration area is shown. For the finite volume methods this approach seems to more consecutive than the solution of Poisson’s equation for the gravitational potential. Numerical calculations were carried out on the computer complex of cluster architecture with the peak productivity 523 TFlops. In the calculations up to thousand processors was used.

The article focuses on the problem of mechanisms’ co-design for robotic systems to perform adaptive physical interaction with an unstructured environment, including physical human robot interaction. The co-design means simultaneous optimization of mechanics and control system, ensuring optimal behavior and performance of the system. Mechanics optimization refers to the search for optimal structure, geometric parameters, mass distribution among the links and their compliance; control refers to the search for motion trajectories for mechanism’s joints. The paper presents a generalized method of structural-parametric synthesis of underactuated mechanisms with closed kinematics for robotic systems for various purposes, e. g., it was previously used for the co-design of fingers’ mechanisms for anthropomorphic gripper and legs’ mechanisms for galloping robots. The method implements the concept of morphological computation of control laws due to the features of mechanical design, minimizing the control effort from the algorithmic component of the control system, which reduces the requirements for the level of technical equipment and reduces energy consumption. In this paper, the proposed method is used to optimize the structure and geometric parameters of the passive mechanism of the back support module of an industrial exosuit. Human movements are diverse and non-deterministic when compared with the movements of autonomous robots, which complicates the design of wearable robotic devices. To reduce injuries, fatigue and increase the productivity of workers, the synthesized industrial exosuit should not only compensate for loads, but also not interfere with the natural human motions. To test the developed exosuit, kinematic datasets from motion capture of an entire human body during industrial operations were used. The proposed method of structural-parametric synthesis was used to improve the ergonomics of a wearable robotic device. Verification of the synthesized mechanism was carried out using simulation: the passive module of the back is attached to two geometric primitives that move the chest and pelvis of the exosuit operator in accordance with the motion capture data. The ergonomics of the back module is quantified by the distance between the joints connecting the upper and bottom parts of the exosuit; minimizing deviation from the average value corresponds to a lesser limitation of the operator’s movement, i. e. greater ergonomics. The article provides a detailed description of the method of structural-parametric synthesis, an example of synthesis of an exosuit module and the results of simulation.

In this paper, the structure of a shock wave in a binary gas mixture is studied on the basis of direct solution of the Boltzmann kinetic equation. The conservative projection method is used to evaluate the collision integral in the kinetic equation. The applied evaluation formulas and numerical methods are described in detail. The model of hard spheres is used as an interaction potential of molecules. Numerical simulation is performed using the developed simulation environment software, which makes it possible to study both steady and non-steady flows of gas mixtures in various flow regimes and for an arbitrary geometry of the problem. Modeling is performed on a cluster architecture. Due to the use of code parallelization technologies, a significant acceleration of computations is achieved. With a fixed accuracy controlled by the simulation parameters, the distributions of macroscopic characteristics of the mixture components through the shock wave front were obtained. Computations were conducted for various ratios of molecular masses and Mach numbers. The total accuracy of at least 1% for the local values of molecular density and temperature and 3% for the shock front width was achieved. The obtained results were compared with existing computation data. The results presented in this paper are of theoretical significance, and can serve as a test computation, since they are obtained using the exact Boltzmann equation.