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In this paper, the system of equations of magnetic hydrodynamics (MHD) is considered. The exact solutions found describe fluid flows in a porous medium and are related to the development of a core simulator and are aimed at creating a domestic technology «digital deposit» and the tasks of controlling the parameters of incompressible fluid. The central problem associated with the use of computer technology is large-dimensional grid approximations and high-performance supercomputers with a large number of parallel microprocessors. Kinetic methods for solving differential equations and methods for «gluing» exact solutions on coarse grids are being developed as possible alternatives to large-dimensional grid approximations. A comparative analysis of the efficiency of computing systems allows us to conclude that it is necessary to develop the organization of calculations based on integer arithmetic in combination with universal approximate methods. A class of exact solutions of the Navier – Stokes system is proposed, describing three-dimensional flows for an incompressible fluid, as well as exact solutions of nonstationary three-dimensional magnetic hydrodynamics. These solutions are important for practical problems of controlled dynamics of mineralized fluids, as well as for creating test libraries for verification of approximate methods. A number of phenomena associated with the formation of macroscopic structures due to the high intensity of interaction of elements of spatially homogeneous systems, as well as their occurrence due to linear spatial transfer in spatially inhomogeneous systems, are highlighted. It is fundamental that the emergence of structures is a consequence of the discontinuity of operators in the norms of conservation laws. The most developed and universal is the theory of computational methods for linear problems. Therefore, from this point of view, the procedures of «immersion» of nonlinear problems into general linear classes by changing the initial dimension of the description and expanding the functional spaces are important. Identification of functional solutions with functions makes it possible to calculate integral averages of an unknown, but at the same time its nonlinear superpositions, generally speaking, are not weak limits of nonlinear superpositions of approximations of the method, i.e. there are functional solutions that are not generalized in the sense of S. L. Sobolev.

The BES-III experiment at the IHEP CAS, Beijing, is running at the high-luminosity e+e- collider BEPC-II to study physics of charm quarks and tau leptons. The world largest samples of J/psi and psi' events are already collected, a number of unique data samples in the energy range 2.5–4.6 GeV have been taken. The data volume is expected to increase by an order of magnitude in the coming years. This requires to move from a centralized computing system to a distributed computing environment, thus allowing the use of computing resources from remote sites — members of the BES-III Collaboration. In this report the general information, latest results and development plans of the BES-III distributed computing system are presented.

Metal hydrides are an interesting class of chemical compounds that can reversibly bind a large amount of hydrogen and are, therefore, of interest for energy applications. Understanding the factors affecting the kinetics of hydride formation and decomposition is especially important. Features of the material, experimental setup and conditions affect the mathematical description of the processes, which can undergo significant changes during the processing of experimental data. The article proposes a general approach to numerical modeling of the formation and decomposition of metal hydrides and solving inverse problems of estimating material parameters from measurement data. The models are divided into two classes: diffusive ones, that take into account the gradient of hydrogen concentration in the metal lattice, and models with fast diffusion. The former are more complex and take the form of non-classical boundary value problems of parabolic type. A rather general approach to the grid solution of such problems is described. The second ones are solved relatively simply, but can change greatly when model assumptions change. Our experience in processing experimental data shows that a flexible software tool is needed; a tool that allows, on the one hand, building models from standard blocks, freely changing them if necessary, and, on the other hand, avoiding the implementation of routine algorithms. It also should be adapted for high-performance systems of different paradigms. These conditions are satisfied by the HIMICOS library presented in the paper, which has been tested on a large number of experimental data. It allows simulating the kinetics of formation and decomposition of metal hydrides, as well as related tasks, at three levels of abstraction. At the low level, the user defines the interface procedures, such as calculating the time layer based on the previous layer or the entire history, calculating the observed value and the independent variable from the task variables, comparing the curve with the reference. Special algorithms can be used for solving quite general parabolic-type boundary value problems with free boundaries and with various quasilinear (i.e., linear with respect to the derivative only) boundary conditions, as well as calculating the distance between the curves in different metric spaces and with different normalization. This is the middle level of abstraction. At the high level, it is enough to choose a ready tested model for a particular material and modify it in relation to the experimental conditions.

The paper presents a physical and numerical analysis of the dynamics and radiation of explosion products formed during the Russian-American experiment in the ionosphere using an explosive generator based on hexogen (RDX) and trinitrotoluene (TNT). The main attention is paid to the radiation of the perturbed region and the dynamics of the products of explosion (PE). The detailed chemical composition of the explosion products is analyzed and the initial concentrations of the most important molecules capable of emitting in the infrared range of the spectrum are determined, and their radiative constants are given. The initial temperature of the explosion products and the adiabatic exponent are determined. The nature of the interpenetration of atoms and molecules of a highly rarefied ionosphere into a spherically expanding cloud of products is analyzed. An approximate mathematical model of the dynamics of explosion products under conditions of mixing rarefied ionospheric air with them has been developed and the main thermodynamic characteristics of the system have been calculated. It is shown that for a time of 0,3–3 sec there is a significant increase in the temperature of the scattering mixture as a result of its deceleration. In the problem under consideration the explosion products and the background gas are separated by a contact boundary. To solve this two-region gas dynamic problem a numerical algorithm based on the Lagrangian approach was developed. It was necessary to fulfill special conditions at the contact boundary during its movement in a stationary gas. In this case there are certain difficulties in describing the parameters of the explosion products near the contact boundary which is associated with a large difference in the size of the mass cells of the explosion products and the background due to a density difference of 13 orders of magnitude. To reduce the calculation time of this problem an irregular calculation grid was used in the area of explosion products. Calculations were performed with different adiabatic exponents. The most important result is temperature. It is in good agreement with the results obtained by the method that approximately takes into account interpenetration. The time behavior of the IR emission coefficients of active molecules in a wide range of the spectrum is obtained. This behavior is qualitatively consistent with experiments for the IR glow of flying explosion products.

This paper proposes the implementation of a coherent transceiver with a constant delay and the ability to select any clock frequency grid used for clocking peripheral DACs and ADCs, tasks of device synchronization and data transmission. The choice of the required clock frequency grid directly affects the data transfer rate in the network, however, it allows one to flexibly configure the network for the tasks of transmitting clock signals and subnanosecond generation of sync signals on all devices in the network. A method for increasing the synchronization accuracy to tenths of nanoseconds by using digital phase detectors and a Phase Locked Loop (PLL) system on the slave device is proposed. The use of high-speed fiber-optic communication lines (FOCL) for synchronization tasks allows simultaneously exchanging control commands and signaling data. To simplify and reduce the cost of devices of a synchronous network of transceivers, it is proposed to use a clock signal restored from a data transmission line to filter phase noise and form a frequency grid in the PLL system for heterodyne signals and clock peripheral devices, including DAC and ADC. The results of multiple synchronization tests in the proposed synchronous network are presented.

The paper gives a detailed description of the developed methods for simulating the turbulent flow around a helicopter rotor and calculating its aerodynamic characteristics. The system of Reynolds-averaged Navier – Stokes equations for a viscous compressible gas closed by the Spalart –Allmaras turbulence model is used as the basic mathematical model. The model is formulated in a non-inertial rotating coordinate system associated with a rotor. To set the boundary conditions on the surface of the rotor, wall functions are used.

The numerical solution of the resulting system of differential equations is carried out on mixed-element unstructured grids including prismatic layers near the surface of a streamlined body.The numerical method is based on the original vertex-centered finite-volume EBR schemes. A feature of these schemes is their higher accuracy which is achieved through the use of edge-based reconstruction of variables on extended quasi-onedimensional stencils, and a moderate computational cost which allows for serial computations. The methods of Roe and Lax – Friedrichs are used as approximate Riemann solvers. The Roe method is corrected in the case of low Mach flows. When dealing with discontinuities or solutions with large gradients, a quasi-one-dimensional WENO scheme or local switching to a quasi-one-dimensional TVD-type reconstruction is used. The time integration is carried out according to the implicit three-layer second-order scheme with Newton linearization of the system of difference equations. To solve the system of linear equations, the stabilized conjugate gradient method is used.

The numerical methods are implemented as a part of the in-house code NOISEtte according to the two-level MPI–OpenMP parallel model, which allows high-performance computations on meshes consisting of hundreds of millions of nodes, while involving hundreds of thousands of CPU cores of modern supercomputers.

Based on the results of numerical simulation, the aerodynamic characteristics of the helicopter rotor are calculated, namely, trust, torque and their dimensionless coefficients.

Validation of the developed technique is carried out by simulating the turbulent flow around the Caradonna – Tung two-blade rotor and the KNRTU-KAI four-blade model rotor in hover mode mode, tail rotor in duct, and rigid main rotor in oblique flow. The numerical results are compared with the available experimental data.

The work is devoted to the construction and analysis of difference schemes for a system of hemodynamic equations obtained by averaging the hydrodynamic equations of a viscous incompressible fluid over the vessel cross-section. Models of blood as an ideal and as a viscous Newtonian fluid are considered. Difference schemes that approximate equations with second order on the spatial variable are proposed. The computational algorithms of the constructed schemes are based on the method of splitting on physical processes. According to this approach, at one time step, the model equations are considered separately and sequentially. The practical implementation of the proposed schemes at each time step leads to a sequential solution of two linear systems with tridiagonal matrices. It is demonstrated that the schemes are $\rho$-stable under minor restrictions on the time step in the case of sufficiently smooth solutions.

For the problem with a known analytical solution, it is demonstrated that the numerical solution has a second order convergence in a wide range of spatial grid step. The proposed schemes are compared with well-known explicit schemes, such as the Lax – Wendroff, Lax – Friedrichs and McCormack schemes in computational experiments on modeling blood flow in model vascular systems. It is demonstrated that the results obtained using the proposed schemes are close to the results obtained using other computational schemes, including schemes constructed by other approaches to spatial discretization. It is demonstrated that in the case of different spatial grids, the time of computation for the proposed schemes is significantly less than in the case of explicit schemes, despite the need to solve systems of linear equations at each step. The disadvantages of the schemes are the limitation on the time step in the case of discontinuous or strongly changing solutions and the need to use extrapolation of values at the boundary points of the vessels. In this regard, problems on the adaptation of splitting schemes for problems with discontinuous solutions and in cases of special types of conditions at the vessels ends are perspective for further research.

Numerical simulation of moving sportsman external flow is presented. The unique method is developed for obtaining integral aerodynamic characteristics, which were the function of the flow regime (i.e. angle of attack, flow speed) and body position. Individual anthropometric characteristics and moving boundaries of sportsman (or sports equipment) during the race are taken into consideration.

Numerical simulation is realized using FlowVision CFD. The software is based on the finite volume method, high-performance numerical methods and reliable mathematical models of physical processes. A Cartesian computational grid is used by FlowVision, the grid generation is a completely automated process. Local grid adaptation is used for solving high-pressure gradient and object complex shape. Flow simulation process performed by solutions systems of equations describing movement of fluid and/or gas in the computational domain, including: mass, moment and energy conservation equations; state equations; turbulence model equations. FlowVision permits flow simulation near moving bodies by means of computational domain transformation according to the athlete shape changes in the motion. Ski jumper aerodynamic characteristics are studied during all phases: take-off performance in motion, in-run and flight. Projected investigation defined simulation method, which includes: inverted statement of sportsman external flow development (velocity of the motion is equal to air flow velocity, object is immobile); changes boundary of the body technology defining; multiple calculations with the national team member data projecting. The research results are identification of the main factors affected to jumping performance: aerodynamic forces, rotating moments etc. Developed method was tested with active sportsmen. Ski jumpers used this method during preparations for Sochi Olympic Games 2014. A comparison of the predicted characteristics and experimental data shows a good agreement. Method versatility is underlined by performing swimmer and skater flow simulation. Designed technology is applicable for sorts of natural and technical objects.

Modern power transportation systems are the complex engineering systems. Such systems include both point facilities (power producers, consumers, transformer substations, etc.) and the distributed elements (f.e. power lines). Such structures are presented in the form of the graphs with different types of nodes under creating the mathematical models. It is necessary to solve the system of partial differential equations of the hyperbolic type to study the dynamic effects in such systems.

An approach similar to one already applied in modeling similar problems earlier used in the work. New variant of the splitting method was used proposed by the authors. Unlike most known works, the splitting is not carried out according to physical processes (energy transport without dissipation, separately dissipative processes). We used splitting to the transport equations with the drain and the exchange between Reimann’s invariants. This splitting makes possible to construct the hybrid schemes for Riemann invariants with a high order of approximation and minimal dissipation error. An example of constructing such a hybrid differential scheme is described for a single-phase power line. The difference scheme proposed is based on the analysis of the properties of the schemes in the space of insufficient coefficients.

Examples of the model problem numerical solutions using the proposed splitting and the difference scheme are given. The results of the numerical calculations shows that the difference scheme allows to reproduce the arising regions of large gradients. It is shown that the difference schemes also allow detecting resonances in such the systems.

The grid-characteristic method is successfully used for solving hyperbolic systems of partial differential equations (for example, transport / acoustic / elastic equations). It allows to construct correctly algorithms on contact boundaries and boundaries of the integration domain, to a certain extent to take into account the physics of the problem (propagation of discontinuities along characteristic curves), and has the property of monotonicity, which is important for considered problems. In the cases of two-dimensional and three-dimensional problems the method makes use of a coordinate splitting technique, which enables us to solve the original equations by solving several one-dimensional ones consecutively. It is common to use up to 3-rd order one-dimensional schemes with simple splitting techniques which do not allow for the convergence order to be higher than two (with respect to time). Significant achievements in the operator splitting theory were done, the existence of higher-order schemes was proved. Its peculiarity is the need to perform a step in the opposite direction in time, which gives rise to difficulties, for example, for parabolic problems.

In this work coordinate splitting of the 3-rd and 4-th order were used for the two-dimensional hyperbolic problem of the linear elasticity. This made it possible to increase the final convergence order of the computational algorithm. The paper empirically estimates the convergence in L1 and L∞ norms using analytical solutions of the system with the sufficient degree of smoothness. To obtain objective results, we considered the cases of longitudinal and transverse plane waves propagating both along the diagonal of the computational cell and not along it. Numerical experiments demonstrated the improved accuracy and convergence order of constructed schemes. These improvements are achieved with the cost of three- or fourfold increase of the computational time (for the 3-rd and 4-th order respectively) and no additional memory requirements. The proposed improvement of the computational algorithm preserves the simplicity of its parallel implementation based on the spatial decomposition of the computational grid.