An approach for calculating non-stationary thermo-gasdynamic processes in model chambers of solid rocket engines is described. A three-dimensional mathematical model of viscous multicomponent gas mixture is an extended system of Navier-Stokes equations with the component diffusion equations. The computational model and the computer code are based on the developed original mathematical methodology that combines the advantages of splitting method by physical processes, robustness of Godunov's scheme for the convective stage and efficiency of explicit iterative Chebyshev’s scheme for diffusion stage. The code is written in C++ and uses a hybrid three-level parallel structure, including the use of MPI, OpenMP and CUDA technologies.

A method for calculating the nonstationary thermal interaction between a viscous gas flow and a solid body is presented. The method consists in direct joint integration over time of the equations of gas dynamics of a multicomponent mixture and the heat equation in a solid on multi-block unstructured meshes. To calculate one time step, the system of governing equations is split into hyperbolic and parabolic subsystems. The numerical method provides approximation of the matching condition (continuity of temperature and the normal component of the heat flux) at the interface between gas and solid and is efficient for nonstationary calculations. The comparison with the analytical solution of the model problem of the interaction of a high-speed flow and a heated plate confirm the efficiency of the method.

A technique for numerical modeling of unsteady flows of heat-conducting gas in a three-temperature approximation is presented. This technique was built using the fundamental principles of S.K. Godunov. For time integration, the calculation of each time step is carried out by splitting the governing equations into hyperbolic and parabolic subsystems. The first subsystem is solved using a generalization of the Godunov scheme, and the second, using an explicitly iterative Chebyshev scheme. For discretization, moving curvilinear adaptive grids are used; the discrete scheme is written in curvilinear coordinates with preserving the symmetries of the differential problem. The technique is implemented in the form of a parallel code for multiprocessor computers. The main objective is to provide computational studies on the problem of controlled thermonuclear fusion, but it can also be used in other applications of computational aero-gas-dynamics.

Three explicit time integration schemes are compared for solving nonlinear heat conduction problems, local iteration monotone scheme, nonlinear exponential Euler scheme and a scheme based on the hyperbolic model of heat conduction, where an artificial second order time derivative term is added to stabilize the computations. The local iteration monotone and exponential Euler schemes are monotone and allow for a sufficiently large time step size. The local iteration monotone scheme is based on a special Chebyshev polynomial approximation, whereas the exponential Euler scheme employs a restarted Krylov subspace procedure. For these two schemes we propose an adaptive time step selection strategy which leads to a significant reduction in computational costs.

The computational results of a time integration method for thermal interaction between viscous gas flows and solid domains are presented. The methodology is based on simultaneous integration of the multicomponent gas dynamics equations and the thermal conductivity equation of a solid domain. For three-dimensional spatial discretization of the governing equations, multi-block unstructured grids with definition of grid functions at grid nodes are used. On each time step, the governing system is split into hyperbolic and parabolic subsystems. The numerical method provides an approximation of the fluid-solid interface condition (both normal heat flux and temperature are continuous across the interface). To analyze the accuracy and computational efficiency of the scheme, a model problem of high-speed laminar flow around a heated plate is considered. The numerical results demonstrate good agreement with analytical solution and confirm the effectiveness of the developed methodology.

This paper presents the current state of development of 3D methodology for numerical simulation of unsteady thermal interaction of fluid flow and solid bodies. A fluid is a multicomponent mixture of ideal gases. As heat-conducting solid bodies one can consider aircraft elements, shells of combustion chamber, etc. For fluids, the extended system of the unsteady compressible Navier–Stokes equations supplemented by multicomponent diffusion equations is considered. For solids, unsteady heat conduction equation is written. For fluid-solid interfaces, temperature and normal heat flux are continuous across an interface. The developed technique exploits finite-volume discretization of the governing equations and time integration with splitting over physical processes. The time step calculation is split into hyperbolic and parabolic stages. The hyperbolic stage is implemented with the explicit scheme. The parabolic stage is based on the special explicit-iterative Chebyshev scheme. To simulate the fluid–solid thermal interaction within parabolic stage, the energy equation for both fluid and solid is solved as the unified equation. This provides an approximation of the interface continuity condition and coupling in interfacial heat exchange. The proposed method is generalized for multi-block unstructured grids with parallel calculation of the fluid/solid regions and subsequent processing of the fluid-solid interfaces. To demonstrate the features of our technique, the results of solving a test problem is shown and accuracy of the interface condition are discussed.

A novel methodology of numerical solving is developed for applications of unsteady conjugate heat transfer. It is based on a parallel integration strategy of governing equations in fluid and solid domains. The 3D numerical model takes into account an unsteady thermal interaction of viscous multicomponent flow and a solid body. The fluid dynamic model is based on an extended system of the compressible Navier–Stokes equations with the multicomponent diffusion. In a solid, the unsteady heat conduction equation is stated. In a fluid–solid system the heat transfer is fully coupled. Normal heat flux and temperature are continuous across an interface. The method is based on direct coupling heat transfer due to the time integration of the heat equation in fluid and in solid with an automatic approximation of the interfacial condition. This approach is especially effective for unsteady computations, since it does not require the use of an iterative method at each time step. The proposed method is generalized for multiblock conformal unstructured grids. This approach is especially effective for non-stationary calculations, since it does not require the use of an iterative method at each time step. The results of comparison with a model problem analytical solution confirm an efficiency of the proposed method.

In this paper a variant of nonlinear exponential Euler scheme is proposed for solving nonlinear heat conduction problems. The method is based on nonlinear iterations where at each iteration a linear initial-value problem has to be solved. We compare this method to the backward Euler method combined with nonlinear iterations. For both methods we show monotonicity and boundedness of the solutions and give sufficient conditions for convergence of the nonlinear iterations. Numerical tests are presented to examine performance of the two schemes. The presented exponential Euler scheme is implemented based on restarted Krylov subspace methods and, hence, is essentially explicit (involves only matrix-vector products).

The research software package NOISEtte–MCFL is designed to simulate multicomponent gas dynamic flows taking into account conjugate heat transfer. The NOISEtte–MCFL code is based on the developed original mathematical methodology based on the splitting algorithm for physical processes and an explicit iterative scheme based on Chebyshev polynomials. NOISEtte–MCFL is written in C++ and uses a hybrid three-level parallel structure, including MPI, OpenMP and CUDA technologies. The package is validated and verified on a set of model problems and standard test cases. Comparison with the results of calculations using the commercial ANSYS code and the open source OpenFOAM software is performed.

The results of numerical simulation of a vertical-axis wind turbine (VAWT) based on the solution of three-dimensional Reynolds-averaged Navier–Stokes equations with the Spalart–Allmaras turbulence model are presented. The results of parametric calculations of a viscous compressible flow under conditions simulating urban infrastructure for a helicoid-type wind turbine with three spirally twisted blades are presented.

A structure of an automated aerospace monitoring system for monitoring of forest fires and a model for the joint use of satellite monitoring data of the forest fire situation in Russia and clarifying observations of unmanned aerial vehicles are proposed. A comparison of the effectiveness of each of the methods separately is carried out and an assessment of the improvement of the quality of control when they are used together is given. It is shown at the theoretical level that aerial monitoring using satellite observation data gives a significant reduction in the average time to detect a forest fire. To simulate the movement of unmanned aerial vehicles (UAVs), a non-stationary multidimensional Fokker-Planck equation is used with varying diffusion and drift coefficients, determined both by the initial goal of the flight task and by local measurements of gradients of atmospheric parameters (smoke content, temperature). The simulation principle is formulated, which is proposed to be the basis for the optimization of the projected aerospace monitoring system.

An approach to numerical simulation of three-dimensional electrical and thermal fields in high-temperature superconductors is described. In such a semiconductor, the phenomena of superconductivity are observed at high temperatures above the temperature of liquid nitrogen. The absence of a generally accepted theory of superconductivity leads to the need to study physical processes in semiconductor structures using mathematical simulations. The main attention is paid to the calculation of temperature and electric current distributions in large-size mesas with a self-heating effect. An efficient algorithm for solving the equations describing these distributions is constructed. The basis of the algorithm is an adaptive multigrid method on structured Cartesian grids. The adaptability is based on the Chebyshev iterative method for constructing the smoothing procedures at each grid level and for solving the coarsest grid equations. The adaptive technique allows us to realistically simulate the anisotropic phenomena. The functionality of the algorithm is demonstrated along with an example of solving an anisotropic model problem with discontinuous coefficients.

The 3D numerical model of thermal interaction of a multicomponent flow and a solid body is presented. The approach is based on computational fluid dynamic simulation in which the heat transfer in a fluid domain and in a solid are fully coupled. This is known as the conjugate heat transfer problem. According to the our numerical scheme, the computation of a single time step is split into the sequence of hyperbolic and parabolic stages. The energy equation for solid and fluid domains is solved as a unified equation with the explicit-iteration scheme. At the fluid-solid interfaces the matching conditions are the continuity of temperature and the normal components of the heat flux. The continuity conditions are natural for the unified heat conduction equation and there is no need separate consideration of these conditions. The proposed method is generalized for multiblock frame: we implement the conjugate heat transfer algorithm in the case of interaction of fluid domains with various solid domains using multiblock unstructured conformal grids. Our technique can be used to develop a numerical conjugate heat transfer algorithm for calculating magnetohydrodynamic flows in channels.

We present the methodology and results of parametric aerodynamic studies of vehicles descending into the planet’s atmosphere. The proposed computational approach might serve as the basis for solving a number of problems such as predicting and optimizing the descent trajectory of the vehicle, the search for a rational aerodynamic layout of the vehicle, i.e., tasks requiring massive parametric calculations. The systematization of such calculations is the first step towards the creation of a specialized database that includes sets of input and output data (flight speed, angles of attack, drag and lift coefficients, aerodynamic pitching moment, etc.) and the corresponding three-dimensional fields of gas-dynamic quantities together with computational meshes of various granularity and parameters of the computational model. Additional information to each element of the database might be a set of variables, parameterizing the geometry of the vehicle, experimental data, etc. The probability of forming the information content of such a data-base using modern supercomputer systems is shown. The capabilities of the domestic supercomputer aerodynamic code NOISEtte are demonstrated in the field of multiparametric three-dimensional calculations of descent vehicles based on the numerical solution of the Navier --- Stokes equations on three-dimensional unstructured meshes

The methodology and results of parametric studies of vertical-axis wind turbines (VAWTs) based on three-dimensional aerodynamic calculations are presented. For a model wind turbine with three twisted blades, the dependence of the torque on the wind speed, the speed of rotation of the turbine, and on the variation of geometric parameters that determine the design of the turbine is studied. Estimates of the amplitude of pulsations of the torque of the wind turbine are obtained, depending on the specified parameters.

Представлены результаты численного моделирования вертикально-осевой ветротурбины на основе решения трехмерных осредненных по Рейнольдсу уравнений Навье--Стокса с моделью турбулентности Спаларта--Аллмареса. Для ветротурбины геликоидного типа с тремя спирально закрученными лопастями приведены результаты параметрических расчетов вязкого сжимаемого обтекания в условиях, моделирующих городскую инфраструктуру.

In this paper, we present results of the development of certain parallel numerical methods for solving three-dimensional evolutionary and stationary problems of diffusion and heat transfer. We present a detailed description of a special, explicit iteration scheme for parabolic equations and discuss a multigrid technology used for solving elliptic equations and implicit schemes for parabolic equations.

This paper presents the development and testing of time integration scheme for the system of hydrodynamic equations of gas mixture. These equations take into account the phenomena of multicomponent diffusion and heat transfer. The governing equation system is discretized by the finite volume approach on three-dimensional unstructured grids. According to the algorithm, computation of any single time step is split into the sequence of hyperbolic and parabolic stages. The hyperbolic subtask is solved using the Godunov-type scheme. The parabolic subtask is solved by the explicit iterative Chebyshev scheme, which is algorithmically simple and does not involve tuning parameters. This stage addresses dissipative fluxes (viscosity, multicomponent diffusion and thermal conductivity). The number of the explicit iterations is determined by the convective time step and by the upper bound for the discrete diffusion operator. The resulting scheme ensures the fulfillment of the conservation laws at the discrete level. The computer code can be used in highly parallel computing for large-scale simulation. The proposed approach is recommended for applied problems in which convective and dissipative processes are in close interaction, particularly for problems of plasma physics and astrophysics.

An approach to the time integration of the Navier–Stokes equations for a compressible heat-conducting gas is developed. According to this approach, the solution algorithm is split into a convective and a diffusion stage. The convective stage represents an explicit Godunov-type scheme. The diffusion stage is addressed using the Chebyshev explicit iterative scheme. The resulting scheme ensures the fulfillment of the fundamental conservation laws at the difference level, and its algorithmic structure is well suited for parallelization.

Предложена новая явно-итерационная схема интегрирования по времени многомерных уравнений Навье-Стокса сжимаемой среды на основе расщепления на конвективный и диффузионный этапы, которые выполняются последовательно на каждом шаге по времени. Конвективный этап реализуется по схеме Годунова, диффузионный - по чебышевской явно-итерационной схеме ЛИ-М, не имеющей ограничения на шаг по времени. Результирующая схема обеспечивает выполнение основных законов сохранения на произвольных нерегулярных сетках. Явный характер вычислений гарантирует эффективность использования схемы в различных параллельных технологиях.