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The paper provides a method for selecting the composition of a refrigerant with a given isobaric cooling curve using an artificial neural network (ANN). This method is based on the use of 1D layers of a convolutional neural network. To train the neural network, we applied a technological model of a simple heat exchanger in the UniSim design program, using the Peng – Robinson equation of state.We created synthetic database on isobaric boiling curves of refrigerants of different compositions using the technological model. To record the database, an algorithm was developed in the Python programming language, and information on isobaric boiling curves for 1 049 500 compositions was uploaded using the COM interface. The compositions have generated by Monte Carlo method. Designed architecture of ANN allows select composition of a mixed refrigerant by 101 points of boiling curve. ANN gives mole flows of mixed refrigerant by composition (methane, ethane, propane, nitrogen) on the output layer. For training ANN, we used method of cyclical learning rate. For results demonstration we selected MR composition by natural gas cooling curve with a minimum temperature drop of 3 К and a maximum temperature drop of no more than 10 К, which turn better than we predicted via UniSim SQP optimizer and better than predicted by $k$-nearest neighbors algorithm. A significant value of this article is the fact that an artificial neural network can be used to select the optimal composition of the refrigerant when analyzing the cooling curve of natural gas. This method can help engineers select the composition of the mixed refrigerant in real time, which will help reduce the energy consumption of natural gas liquefaction.

In a number of fundamental and practical problems, it is necessary to describe the dynamics of the motion of complexshaped particles in a high-speed gas flow. An example is the movement of coal particles behind the front of a strong shock wave during an explosion in a coal mine. The paper is devoted to numerical simulation of the dynamics of translational and rotational motion of a square-shaped body, as an example of a particle of a more complex shape than a round one, in a supersonic flow behind a passing shock wave. The formulation of the problem approximately corresponds to the experiments of Professor V. M. Boiko and Professor S. V. Poplavski (ITAM SB RAS).

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 which was developed and verified earlier. 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. To calculate numerical fluxes through the edges of the cell intersected by the boundaries of the body, we use a two-wave approximation for solving the Riemann problem and the Steger – Warming scheme.

The movement of a square with a side of 6 mm was initiated by the passage of a shock wave with a Mach number of 3,0 propagating in a flat channel 800 mm long and 60 mm wide. The channel was filled with air at low pressure. Different initial orientation of the square relative to the channel axis was considered. It is found that the initial position of the square with its side across the flow is less stable during its movement than the initial position with a diagonal across the flow. In this case, the calculated results qualitatively correspond to experimental observations. For the intermediate initial positions of a square, a typical mode of its motion is described, consisting of oscillations close to harmonic, turning into rotation with a constant average angular velocity. During the movement of the square, there is an average monotonous decrease in the distance between the center of mass and the center of pressure to zero.

A method for studying the dispersion characteristics of photonic crystals — media with a dielectric constant that varies periodically in space — is considered. The method is based on the representation of the wave functions and permittivity of a periodic medium in the form of Fourier series and their subsequent substitution into the wave equation, which leads to the formulation of the dispersion equation. Using the latter, for each value of the wave vector it is possible determined a set of eigen frequencies. Each of eigen frequency forms a separate dispersion curve as a continuous function of the wave number. The Fourier expansion coefficients of the permittivity, which depend on the vectors of the reciprocal lattice of the photonic crystal, are determined on the basis of data on the geometric characteristics of the elements that form the crystal, their electrophysical properties and the density of the crystal. The solution of the dispersion equation found makes it possible to obtain complete information about the number of modes propagating in a periodic structure at different frequencies, and about the possibility of forming band gaps, i.e. frequency ranges within which wave propagation through a photonic crystal is impossible. The focus of this work is on the application of this method to the analysis of the dispersion properties of metallic photonic crystals. The difficulties that arise in this case due to the presence of intrinsic dispersion properties of the metals that form the elements of the crystal are overcome by an analytical description of their permittivity based on the model of free electrons. As a result, a dispersion equation is formulated, the numerical solution of which is easily algorithmized. That makes possible to determine the dispersion characteristics of metallic photonic crystals with arbitrary parameters. Obtained by this method the results of calculation of dispersion diagrams, which characterize two-dimensional metal photonic crystals, are compared with experimental data and numerical results obtained using the method of self-consistent equations. Their good agreement is demonstrated.

The paper presents the physical and mathematical formulation of the problems of internal ballistics of an artillery shot for a charge consisting of a set of powder tubes and their stress-strain state. Combustion and movement of a bundle of powder tubes along the barrel channel is modeled by an equivalent tubular charge of all-round combustion. It is assumed that the equivalent tube moves along the axis of the bore. The speed of movement of an equivalent tubular charge and its current position are determined from Newton’s second law. When calculating the flow parameters, two-dimensional axisymmetric equations of gas dynamics were used, for the solution of which an axisymmetric orthogonalized difference grid is constructed, which adapts to the flow conditions. The control volume method is used to numerically solve the system of gas-dynamic equations. The gas parameters at the boundaries of the control volumes are determined using a self-similar solution to the Godunov’s problem of the decay of an arbitrary discontinuity. The stress-strain state is modeled for a separate burning powder tube located in the field of gas-dynamic parameters. The calculation of the gas-dynamic parameters of the shot is carried out without taking into account the deformed state of the powder elements. The behavior of powder elements during firing is considered under these conditions. The finite element method with the division of the calculation area into triangular elements is used to solve the problem of elasticity. In the process of powder tube burnout, the computational grid on each time layer of the dynamic problem is completely updated due to a change in the boundaries of the powder element due to combustion. The paper shows the time dependences of the parameters of the internal ballistics process and the stress-strain state of powder elements, as well as the distribution of the main parameters of the flow of combustion products at different points in time. It has been established that the tubular powder elements during the shot experience significant deformations, which must be taken into account when solving the basic problem of internal ballistics. The data obtained give an idea of the level of equivalent stresses acting at various points of the powder element. The results obtained indicate the relevance of the conjugate formulation of the problem of gas dynamics and the stress-strain state for charges consisting of tubular powders, since this allows a new approach to the design of tubular charges and opens up the possibility of determining the parameters on which the physics of the combustion process of gunpowder significantly depends, therefore, and the dynamics of the shot process.

A mathematical model of two-phase capillary-nonequilibrium isothermal flows of incompressible phases in a double porosity medium is constructed. A double porosity medium is considered, which is a composition of two porous media with contrasting capillary properties (absolute permeability, capillary pressure). One of the constituent media has high permeability and is conductive, the second is characterized by low permeability and forms an disconnected system of matrix blocks. A feature of the model is to take into account the influence of capillary nonequilibrium on mass transfer between subsystems of double porosity, while the nonequilibrium properties of two-phase flow in the constituent media are described in a linear approximation within the Hassanizadeh model. Homogenization by the method of formal asymptotic expansions leads to a system of partial differential equations, the coefficients of which depend on internal variables determined from the solution of cell problems. Numerical solution of cell problems for a system of partial differential equations is computationally expensive. Therefore, a thermodynamically consistent kinetic equation is formulated for the internal parameter characterizing the phase distribution between the subsystems of double porosity. Dynamic relative phase permeability and capillary pressure in the processes of drainage and impregnation are constructed. It is shown that the capillary nonequilibrium of flows in the constituent subsystems has a strong influence on them. Thus, the analysis and modeling of this factor is important in transfer problems in systems with double porosity.

An algorithm is proposed to identify parameters of a 2D vortex structure used on information about the flow velocity at a finite (small) set of reference points. The approach is based on using a set of point vortices as a model system and minimizing a functional that compares the model and known sets of velocity vectors in the space of model parameters. For numerical implementation, the method of gradient descent with step size control, approximation of derivatives by finite differences, and the analytical expression of the velocity field induced by the point vortex model are used. An experimental analysis of the operation of the algorithm on test flows is carried out: one and a system of several point vortices, a Rankine vortex, and a Lamb dipole. According to the velocity fields of test flows, the velocity vectors utilized for identification were arranged in a randomly distributed set of reference points (from 3 to 200 pieces). Using the computations, it was determined that: the algorithm converges to the minimum from a wide range of initial approximations; the algorithm converges in all cases when the reference points are located in areas where the streamlines of the test and model systems are topologically equivalent; if the streamlines of the systems are not topologically equivalent, then the percentage of successful calculations decreases, but convergence can also take place; when the method converges, the coordinates of the vortices of the model system are close to the centers of the vortices of the test configurations, and in many cases, the values of their circulations also; con-vergence depends more on location than on the number of vectors used for identification. The results of the study allow us to recommend the proposed algorithm for identifying 2D vortex structures whose streamlines are topologically close to systems of point vortices.

This article proposes the sumo-atclib framework, which provides a convenient uniform interface for testing adaptive control algorithms with different limitations, for example, restrictions on phase durations, phase sequences, restrictions on the minimum time between control actions, which uses the open source microscopic transport modeling environment SUMO. The framework shares the functionality of controllers (class TrafficController) and a monitoring and detection system (class StateObserver), which repeats the architecture of real traffic light objects and adaptive control systems and simplifies the testing of new algorithms, since combinations of different controllers and vehicle detection systems can be freely varied. Also, unlike most existing solutions, the road class Road has been added, which combines a set of lanes, this allows, for example, to determine the adjacency of regulated intersections, in cases when the number of lanes changes on the way from one intersection to another, and therefore the road graph is divided into several edges. At the same time, the algorithms themselves use the same interface and are abstracted from the specific parameters of the detectors, network topologies, that is, it is assumed that this solution will allow the transport engineer to test ready-made algorithms for a new scenario, without the need to adapt them to new conditions, which speeds up the development process of the control system, and reduces design overhead. At the moment, the package contains examples of MaxPressure algorithms and the Q-learning reinforcement learning method, the database of examples is also being updated. The framework also includes a set of SUMO scripts for testing algorithms, which includes both synthetic maps and well-verified SUMO scripts such as Cologne and Ingolstadt. In addition, the framework provides a set of automatically calculated metrics, such as total travel time, delay time, average speed; the framework also provides a ready-made example for visualization of metrics.

The problem discrete statement by the smoothed particle hydrodynamics method (SPH) include a discretization constants parameters set. Of them particular note is the model sound speed $c_0$, which relates the SPH-particle instantaneous density to the resulting pressure through the equation of state.

The paper describes an approach to the exact determination of the model sound speed required value. It is on the analysis based, how SPH-particle density changes with their relative shift. An example of the continuous medium motion taken the plane shear flow problem; the analysis object is the relative compaction function $\varepsilon_\rho$ in the SPH-particle. For various smoothing kernels was research the functions of $\varepsilon_\rho$, that allowed the pulsating nature of the pressures occurrence in particles to establish. Also the neighbors uniform distribution in the smoothing domain was determined, at which shaping the maximum of compaction in the particle.

Through comparison the function $\varepsilon_\rho$ with the SPH-approximation of motion equation is defined associate the discretization parameter $c_0$ with the smoothing kernel shape and other problem parameters. As a result, an equation is formulated that the necessary and sufficient model sound speed value provides finding. For such equation the expressions of root $c_0$ are given for three different smoothing kernels, that simplified from polynomials to numerical coefficients for the plane shear flow problem parameters.

The article is devoted to modeling the shallow water hydrodynamic processes using the example of the Azov Sea. The article presents a mathematical model of the hydrodynamics of a shallow water body, which allows one to calculate three-dimensional fields of the velocity vector of movement of the aquatic environment. Application of regularizers according to B.N.Chetverushkin in the continuity equation led to a change in the method of calculating the pressure field, based on solving the wave equation. A discrete finite-difference scheme has been constructed for calculating pressure in an area whose linear vertical dimensions are significantly smaller than those in horizontal coordinate directions, which is typical for the geometry of shallow water bodies. The method and algorithm for solving grid equations with a tridiagonal preconditioner are described. The proposed method is used to solve grid equations that arise when calculating pressure for the three-dimensional problem of hydrodynamics of the Azov Sea. It is shown that the proposed method converges faster than the modified alternating triangular method. A parallel implementation of the proposed method for solving grid equations is presented and theoretical and practical estimates of the acceleration of the algorithm are carried out taking into account the latency time of the computing system. The results of computational experiments for solving problems of hydrodynamics of the Sea of Azov using the hybrid MPI + OpenMP technology are presented. The developed models and algorithms were used to reconstruct the environmental disaster that occurred in the Sea of Azov in 2001 and to solve the problem of the movement of the aquatic environment in estuary areas. Numerical experiments were carried out on the K-60 hybrid computing cluster of the Keldysh Institute of Applied Mathematics of Russian Academy of Sciences.

This article presents the results of an analytical and computer study of the chaotic evolution of a regular velocity field generated by a large-scale harmonic forcing. The authors obtained an analytical solution for the flow stream function and its derivative quantities (velocity, vorticity, kinetic energy, enstrophy and palinstrophy). Numerical modeling of the flow evolution was carried out using the OpenFOAM software package based on incompressible model, as well as two inhouse implementations of CABARET and McCormack methods employing nearly incompressible formulation. Calculations were carried out on a sequence of nested meshes with 64², 128², 256², 512², 1024² cells for two characteristic (asymptotic) Reynolds numbers characterizing laminar and turbulent evolution of the flow, respectively. Simulations show that blow-up of the analytical solution takes place in both cases. The energy characteristics of the flow are discussed relying upon the energy curves as well as the dissipation rates. For the fine mesh, this quantity turns out to be several orders of magnitude less than its hydrodynamic (viscous) counterpart. Destruction of the regular flow structure is observed for any of the numerical methods, including at the late stages of laminar evolution, when numerically obtained distributions are close to analytics. It can be assumed that the prerequisite for the development of instability is the error accumulated during the calculation process. This error leads to unevenness in the distribution of vorticity and, as a consequence, to the variance vortex intensity and finally leads to chaotization of the flow. To study the processes of vorticity production, we used two integral vorticity-based quantities — integral enstrophy ($\zeta$) and palinstrophy $(P)$. The formulation of the problem with periodic boundary conditions allows us to establish a simple connection between these quantities. In addition, $\zeta$ can act as a measure of the eddy resolution of the numerical method, and palinstrophy determines the degree of production of small-scale vorticity.