Vol 10, No 2 (2018)

A variant of a numerical algorithm for simulating viscous gasdynamic flows on unstructured hybrid grids and its software implementation for heterogeneous computations is described. The system of Navier–Stokes equations is approximated by the finite-volume method of an increased approximation order with the values of the variables being defined at the mass centers of the grid elements. The distributed software implementation of the numerical algorithm is adapted to running on hybrid computer systems of various architectures. Comparative implementations were created using the MPI, OpenMP, CUDA, and OpenCL software models permitting the use of multicore processors and various types of accelerators, including NVIDIA and AMD graphics processors, and Intel Xeon Phi multicore coprocessors. The data exchange between MPI processes and between processors and accelerators is carried out simultaneously with the execution of calculations (both in MPI + OpenMP mode and when using CUDA or OpenCL). The indicators of parallel efficiency and performance on systems with different types of computing devices are studied in detail. In the tests, up to 260 GPUs were successfully used.

A multicriteria approach to identify and forecast mathematical models is considered. The need for such an approach arises, in particular, when it is necessary to take into account errors that cannot be reduced to one function and in the absence of specific information about the data interference class. The paper deals with a multicriteria version of the identification sets method based on approximating and visualizing the graph of the vector function of identification errors and its projections onto the space of identification parameters. The nearness function is introduced that describes the proximity of a criterion point to the set of nonimprovable (Pareto efficient) solutions of the identification problem. The efficient criteria set (Pareto frontier), the sets of efficient and subefficient parameters, and the corresponding forecast trajectory tubes are studied. To construct these objects, methods for approximating implicitly specified sets are used, in particular, methods for approximating the Edgeworth–Pareto hull and the deep holes method. The technique and examples for two criteria of identification quality are considered in detail.

This paper presents a brief description of the General Circulation Model of the lower and middle atmosphere of the Earth, which is designed to study atmospheric dynamics in a wide range of spatial-temporal scales. The model is based on numerical integration of the complete system of equations that describe the dynamics of a viscous atmospheric gas using a spatial grid with a high resolution. The model takes into account the surface relief and the presence of atmosphere aerosols in the form of microdroplets of water ice particles, as well as the phase transitions of water vapor to aerosol particles and back.

The paper considers methods and algorithms providing the basis for a computer program implementing an axial-symmetric electrostatic version of the particle-in-cell method on unstructured triangular grids. In the presented implementation, the Poisson equation is approximated using the finite volume method. A discrete analog of the Poisson equation is solved by the multigrid method. Charged particle trajectories are calculated using the Boris method. Methods for interpolating electrostatic fields on unstructured grids and obtaining the charge density in the computational domain are considered. Special attention is paid to the specifics of implementing these methods in axisymmetric geometry. The developed computer code is tested on the problem of a flat diode operating in the space charge mode.

A hypersonic flow over an axisymmetric aircraft is numerically simulated in the case of a highly underexpanded exhaust plume (jet) of the main engine. The characteristics of the boundary layer separation occurring on the aircraft’s side surface are investigated for several successive points of its takeoff path. The Mach number at the nozzle exit is 6.5. The Mach number of the incoming flow varies from 4 to 7. In this case, the Reynolds number ranges from 2.5 × 10⁵ to 3 × 10³ and the ratio of the nozzle’s exit pressure to the ambient pressure, from 350 to 5 × 10⁴. In the case of the Mach number of the incoming flow M_∞ = 4, the variation range of the pressure ratio extends to 106. Replacement of the exhaust plume with a rigid simulator is considered. Data are obtained on the pressure ratios for which a separation flow begins to form on the side surface, the recirculation zone length, and the level of pressure in it in comparison with the available empirical dependences. A significant increase of the recirculation zone in front of the exhaust plume is shown when it is replaced by a rigid simulator of the same dimensions.

Rotational-translational energy exchange simulation in the direct simulation Monte Carlo method is considered for the problem of the entry of hypersonic space vehicles in the atmosphere of the Earth, Mars, Venus, Titan, and gas giants. The diatomic and polyatomic molecules’ discrete quantum energy levels are systematized. The energy exchange Larsen-Borgnakke algorithm is described for the molecules with discrete rotational energy levels. The parameters of the model of hard spheres of variable diameters (VHS) are derived for molecules present in the atmospheres from the experimental data on the viscosity of gases and calculation of cross sections of clashing molecules elastic. Analogously, the parameters in Parker’s formula, describing the rotational-translational relaxation, are chosen from the experimental data on the times of relaxation of the rotational energy of the molecules. Close agreement between The calculated and experimental data are in close agreement for moving away and the width of the shock wave before the sphere in nitrogen gas. This means that the used models and their parameters are adequate.

A mathematical model for the compression process of a cylindrically symmetric thermonuclear target is presented. A numerical method of an increased accuracy order is considered, which is used to calculate the basic physical processes that occur in target plasma exposed to an external magnetic field.