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The review considers a wide range of phenomena and problems associated with the explosion. Detailed numerical studies revealed an interesting physical effect — the formation of discrete vortex structures directly behind the front of a shock wave propagating in dense layers of a heterogeneous atmosphere. The necessity of further investigation of such phenomena and the determination of the degree of their connection with the possible development of gas-dynamic instability is shown. The brief analysis of numerous works on the thermal explosion of meteoroids during their high-speed movement in the Earth’s atmosphere is given. Much attention is paid to the development of a numerical algorithm for calculating the simultaneous explosion of several fragments of meteoroids and the features of the development of such a gas-dynamic flow are analyzed. The work shows that earlier developed algorithms for calculating explosions can be successfully used to study explosive volcanic eruptions. The paper presents and discusses the results of such studies for both continental and underwater volcanoes with certain restrictions on the conditions of volcanic activity.

The mathematical analysis is performed and the results of analytical studies of a number of important physical phenomena characteristic of explosions of high specific energy in the ionosphere are presented. It is shown that the preliminary laboratory physical modeling of the main processes that determine these phenomena is of fundamental importance for the development of sufficiently complete and adequate theoretical and numerical models of such complex phenomena as powerful plasma disturbances in the ionosphere. Laser plasma is the closest object for such a simulation. The results of the corresponding theoretical and experimental studies are presented and their scientific and practical significance is shown. The brief review of recent years on the use of laser radiation for laboratory physical modeling of the effects of a nuclear explosion on asteroid materials is given.

As a result of the analysis performed in the review, it was possible to separate and preliminarily formulate some interesting and scientifically significant questions that must be investigated on the basis of the ideas already obtained. These are finely dispersed chemically active systems formed during the release of volcanoes; small-scale vortex structures; generation of spontaneous magnetic fields due to the development of instabilities and their role in the transformation of plasma energy during its expansion in the ionosphere. It is also important to study a possible laboratory physical simulation of the thermal explosion of bodies under the influence of highspeed plasma flow, which has only theoretical interpretations.

In this paper, a gravitational system is understood as a set of point bodies that interact according to Newton's law of attraction and have a negative value of the total energy. The question of the stability (nonstability) of a gravitational system of general position is discussed by direct computational experiment. A gravitational system of general position is a system in which the masses, initial positions, and velocities of bodies are chosen randomly from given ranges. A new method for the numerical solution of ordinary differential equations at large time intervals has been developed for the computational experiment. The proposed method allowed, on the one hand, to ensure the fulfillment of all conservation laws by a suitable correction of solutions, on the other hand, to use standard methods for the numerical solution of systems of differential equations of low approximation order. Within the framework of this method, the trajectory of a gravitational system in phase space is assembled from parts, the duration of each of which can be macroscopic. The constructed trajectory, generally speaking, is discontinuous, and the points of joining of individual pieces of the trajectory act as branch points. In connection with the latter circumstance, the proposed method, in part, can be attributed to the class of Monte Carlo methods. The general conclusion of a series of computational experiments has shown that gravitational systems of general position with a number of bodies of 3 or more, generally speaking, are unstable. In the framework of the proposed method, special cases of zero-equal angular momentum of a gravitational system with a number of bodies of 3 or more, as well as the problem of motion of two bodies, are specially considered. The case of numerical modeling of the dynamics of the solar system in time is considered separately. From the standpoint of computational experiments based on analytical methods, as well as direct numerical methods of high-order approximation (10 and higher), the stability of the solar system was previously demonstrated at an interval of five billion years or more. Due to the limitations on the available computational resources, the stability of the dynamics of the planets of the solar system within the framework of the proposed method was confirmed for a period of ten million years. With the help of a computational experiment, one of the possible scenarios for the disintegration of the solar systems is also considered.

The paper studies the determination for one of the dynamic quality parameter (PDK) of railway vehicles — car body lateral acceleration — by using of computer simulation system for railway vehicles dynamic Simpack Rail. This provide the complex simulation environment with variable velocity depending on the train schedule. The rail vehicle model of typical 1520 mm gauge fright locomotive section used for simulation has been verified by means of the chair “Electric multiple unit cars and locomotives” in the Russian University of Transport (RUT (MIIT)). Due to this homologation the questions of model creating and verification in preprocessor are excluded in this paper. The paper gives the detail description of cartographic track modeling in situation plane, heights plane and superelevation plane based on the real operating data. The statistic parameters (moments) for the rail related track excitation and used cartographic track data of the specified track section in this simulation are given as a numeric and graphical results of reading the prepared data files. The measurement of the car body residual lateral acceleration occur under consideration of the earth gravity acceleration part like the accelerometer measurement in the real world. Finally the desired quality parameter determined by simulation is compared with the same one given by a test drive. The calculation method in both cases is based on the middle value of the absolute maximums picked up within the nonstationary realizations of this parameter. Compared results confirm that this quality factor all the first depends on the velocity and track geometry properties. The simulation of the track in this application uses the strong conformity original track data of the test ride track section. The accepted simplification in the rail vehicle model of fright electric locomotive section (body properties related to the center of gravity, small displacements between the bodies) by keeping the geometric and force law characteristics of the force elements and constraints constant allow in Simpack Rail the simulation with necessary validity of system behavior (reactions).

The work is devoted to the development of a computational algorithm of the Cartesian grid method for studying the interaction of a shock wave with moving bodies with a piecewise linear boundary. The interest in such problems is connected with direct numerical simulation of two-phase media flows. The effect of the particle shape can be important in the problem of dust layer dispersion behind a passing shock wave. Experimental data on the coefficient of aerodynamic drag of non-spherical particles are practically absent.

Mathematical model is based on the two-dimensional Euler equations, which are solved in a region with varying boundaries. The defining system of equations is integrated using an explicit scheme and the Cartesian grid method. The computational algorithm at the time integration step includes: determining the step value, calculating the dynamics of the body movement (determining the force and moment acting on the body; determining the linear and angular velocities of the body; calculating the new coordinates of the body), calculating the gas parameters. At each time step, all cells are divided into two classes – external (inside the body or intersected by its boundaries) and internal (completely filled with gas). The solution of the Euler equations is constructed only in the internal ones. The main difficulty is the calculation of the numerical flux through the edges common to the internal and external cells intersected by the moving boundaries of the bodies. To calculate this flux, we use a two-wave approximation for solving the Riemann problem and the Steger-Warming scheme. A detailed description of the numerical algorithm is presented.

The efficiency of the algorithm is demonstrated on the problem of lifting a cylinder with a base in the form of a circle, ellipse and rectangle behind a passing shock wave. A circular cylinder test was considered in many papers devoted to the immersed boundary methods development. A qualitative and quantitative analysis of the trajectory of the cylinder center mass is carried out on the basis of comparison with the results of simulations presented in eight other works. For a cylinder with a base in the form of an ellipse and a rectangle, a satisfactory agreement was obtained on the dynamics of its movement and rotation in comparison with the available few literary sources. Grid convergence of the results is investigated for the rectangle. It is shown that the relative error of mass conservation law fulfillment decreases with a linear rate.

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.

Based on the modeling method using a mesh system, an algorithm is implemented for solving a unsteady problem with moving bodies The algorithm takes into account the movement and rotation of bodies according to a given law of motion. The algorithm is applied to analysis the flow around an infinite composed of cylinders with an elliptical cross-section, which either move across the flow or rotate with a change in the angle of attack. To simulate the flow of bodies with a sharp edge, characteristic of the profiles of gas turbine machines, an algorithm for constructing a mesh of type C with the inclusion of a certain area behind the profile is implemented. The program for modeling the flow near the profile is implemented within the framework of models of Euler equations, Navier – Stokes equations in the approximation of a thin layer with laminar viscosity and turbulent viscosity in the framework of an algebraic viscosity model. The program has also been adapted to solve the problems of internal gas dynamics of turbomachines. For this purpose, the method of setting the boundary conditions at the entrance and exit from the calculated area from the velocity to the pressure drop, as well as at the lateral boundaries from the free flow to the periodicity, was changed. This made it possible to simulate the flow of gas in the inter-blade channels of compressors and turbines of gas turbine engines. To refine the algorithm, a series of calculations of the aerodynamic parameters of several turbine cascades in various subsonic and supersonic modes and their comparison with the experiment were carried out. Calculations of turbine grating parameters were carried out within the framework of the inviscid and viscous gas model. The calculation and experiment were compared by the distribution of gas parameters near the profile, as well as by the energy losses of the flow in the cascade. Calculations have shown the applicability and correctness of the program to solve this class of problems. To test the program on the problems of external subsonic aerodynamics, calculations of the aerodynamic characteristics of an isolated airfoil in an undisturbed flow were performed. The results obtained allow us to assert the applicability of the hybrid grid method to various classes of problems of applied gas dynamics.

This paper describes the design of an aquatic robot moving on the surface of a fluid and driven by two internal moving masses. The body of the aquatic robot in cross section has the shape of a symmetrical airfoil with a sharp edge. In this prototype, two internal masses move in circles and are rotated by a single DC motor and a gear mechanism that transmits torque from the motor to each mass. Angular velocities of moving masses are used as a control action, and the developed kinematic scheme for transmitting rotation from the motor to the moving masses allows the rotation of two masses with equal angular velocities in magnitude, but with a different direction of rotation. It is also possible to install additional tail fins of various shapes and sizes on the body of this robot. Also in the work for this object, the equations of motion are presented, written in the form of Kirchhoff equations for the motion of a solid body in an ideal fluid, which are supplemented by terms of viscous resistance. A mathematical description of the additional forces acting on the flexible tail fin is presented. Experimental studies on the influence of various tail fins on the speed of motion in the fluid were carried out with the developed prototype of the robot. In this work, tail fins of the same shape and size were installed on the robot, while having different stiffness. The experiments were carried out in a pool with water, over which a camera was installed, on which video recordings of all the experiments were obtained. Next processing of the video recordings made it possible to obtain the object’s movements coordinates, as well as its linear and angular velocities. The paper shows the difference in the velocities developed by the robot when moving without a tail fin, as well as with tail fins having different stiffness. The comparison of the velocities developed by the robot, obtained in experimental studies, with the results of mathematical modeling of the system is given.

This article is devoted to the study of self-propulsion of bodies in a fluid by the action of internal mechanisms, without changing the external shape of the body. The paper presents an overview of theoretical papers that justify the possibility of this displacement in ideal and viscous liquids.

A special case of self-propulsion of a rigid body along the surface of a liquid is considered due to the motion of two internal masses along the circles. The paper presents a mathematical model of the motion of a solid body with moving internal masses in a three-dimensional formulation. This model takes into account the three-dimensional vibrations of the body during motion, which arise under the action of external forces-gravity force, Archimedes force and forces acting on the body, from the side of a viscous fluid.

The body is a homogeneous elliptical cylinder with a keel located along the larger diagonal. Inside the cylinder there are two material point masses moving along the circles. The centers of the circles lie on the smallest diagonal of the ellipse at an equal distance from the center of mass.

Equations of motion of the system (a body with two material points, placed in a fluid) are represented as Kirchhoff equations with the addition of external forces and moments acting on the body. The phenomenological model of viscous friction is quadratic in velocity used to describe the forces of resistance to motion in a fluid. The coefficients of resistance to movement were determined experimentally. The forces acting on the keel were determined by numerical modeling of the keel oscillations in a viscous liquid using the Navier – Stokes equations.

In this paper, an experimental verification of the proposed mathematical model was carried out. Several series of experiments on self-propulsion of a body in a liquid by means of rotation of internal masses with different speeds of rotation are presented. The dependence of the average propagation velocity, the amplitude of the transverse oscillations as a function of the rotational speed of internal masses is investigated. The obtained experimental data are compared with the results obtained within the framework of the proposed mathematical model.

One of the destroying natural processes is the initiation of the regional seismic activity. It leads to a large number of human deaths. Much effort has been made to develop precise and robust methods for the estimation of the seismic stability of buildings. One of the most common approaches is the natural frequency method. The obvious drawback of this approach is a low precision due to the model oversimplification. The other method is a detailed simulation of dynamic processes using the finite-element method. Unfortunately, the quality of simulations is not enough due to the difficulty of setting the correct free boundary condition. That is why the development of new numerical methods for seismic stability problems is a high priority nowadays.

The present work is devoted to the study of spatial dynamic processes occurring in geological medium during an earthquake. We describe a method for simulating seismic wave propagation from the hypocenter to the day surface. To describe physical processes, we use a system of partial differential equations for a linearly elastic body of the second order, which is solved numerically by a grid-characteristic method on parallelepiped meshes. The widely used geological hypocenter model, called the “double-couple” model, was incorporated into this numerical algorithm. In this case, any heterogeneities, such as geological layers with curvilinear boundaries, gas and fluid-filled cracks, fault planes, etc., may be explicitly taken into account.

In this paper, seismic waves emitted during the earthquake initiation process are numerically simulated. Two different models are used: the homogeneous half-space and the multilayered geological massif with the day surface. All of their parameters are set based on previously published scientific articles. The adequate coincidence of the simulation results is obtained. And discrepancies may be explained by differences in numerical methods used. The numerical approach described can be extended to more complex physical models of geological media.

One of the numerical methods for solving problems of scattering of electromagnetic waves by systems formed by parallel oriented cylindrical elements — two-dimensional photonic crystals — is considered. The method is based on the classical method of separation of variables for solving the wave equation. Тhe essence of the method is to represent the field as the sum of the primary field and the unknown secondary scattered on the elements of the medium field. The mathematical expression for the latter is written in the form of infinite series in elementary wave functions with unknown coefficients. In particular, the field scattered by N elements is sought as the sum of N diffraction series, in which one of the series is composed of the wave functions of one body, and the wave functions in the remaining series are expressed in terms of the eigenfunctions of the first body using addition theorems. From satisfying the boundary conditions on the surface of each element we obtain systems of linear algebraic equations with an infinite number of unknowns — the required expansion coefficients, which are solved by standard methods. A feature of the method is the use of analytical expressions describing diffraction by a single element of the system. In contrast to most numerical methods, this approach allows one to obtain information on the amplitude-phase or spectral characteristics of the field only at local points of the structure. The absence of the need to determine the field parameters in the entire area of space occupied by the considered multi-element system determines the high efficiency of this method. The paper compares the results of calculating the transmission spectra of two-dimensional photonic crystals by the considered method with experimental data and numerical results obtained using other approaches. Their good agreement is demonstrated.