In this paper issues relating to geostationary orbit (GEO) insertion trajectory optimization is considered. The article discusses the GEO transfer trajectory optimization for a spacecraft with an ...electric propulsion (EP) system with the purpose of reduction of ionizing radiation dose absorbed by onboard systems from the Earth's radiation belts. The considering trajectory optimization technique is based on the Pontryagin's maximum principle and the method of numerical continuation. Much attention is paid to smooth approximation of the dose rate dependence on spatial coordinates using biharmonic splines interpolation. The proposed method makes it possible to abandon the methodological simplification of averaging the radiation dose rate over circular orbits to effectively solve this class of problems and directly consider the dependence of the dose rate on time and geographical longitude. Using as an example the minimum time problem for a test transfer, the errors in calculating the dose at the end of the transfer both by the proposed method and by the method of averaging over circular orbits are estimated. The proposed method turned out to be more than 13 times more accurate than the analogue. It can be applied in transfer trajectory optimization problems of an EP spacecraft in order to minimize the total accumulated ionizing radiation dose.
The paper considers a method of the dose exposure decrease from the charged particles of Earth’s radiation belts (ERBs) affecting a reusable orbital transfer vehicle, which is launched from a low ...circular orbit into geostationary orbit using a nuclear electric propulsion system. The main idea of the method consists in numerical continuation of a solution of the minimum time problem with respect to an ionizing radiation dose accumulated at the end of a transfer. To do this, equations of motion of the orbital transfer vehicle are supplemented by an additional equation for the radiation dose, and the boundary condition for the dose at the right end is introduced. In calculating the dose, the AE8/AP8 MIN, AE8/AP8 MAX, and AE9/AP9 models of fluxes of charged particles of ERBs were used. By changing the insertion trajectory shape, it became possible to lower the radiation dose by 25–38% relative to the minimum time trajectory. At the same time, the transfer time increased no more than by 7% of the minimum time of launching into geostationary orbit, and the characteristic velocity expenses increased by 320–560 m/s.
The work is aimed at the study of the flow structure and the distribution of impurities in an idealized street canyon, depending on the intensity of heating of the street canyon walls.
The paper presents the results of studying the influence of the development of meteorological situation in clear weather with a weak wind on the level of atmospheric surface air pollution in the city ...of Tomsk (Russia). Mesoscale meteorological and photochemical models with a new kinetic scheme were applied to the analysis. The main local weather conditions were identified, in which numerical calculations show increased values of the air pollution index. The numerical predictions have confirmed an increase in the ground-level concentration of pollutants in the presence of temperature inversion or isothermy.
The paper describes a modified smooth approximation method for smoothing the dependence of the equivalent fluence of charged particles of the Earth’s Van Allen radiation belts on time and position in ...near-Earth space. It is shown that this method can be effectively used to solve the problems of minimizing radiation-induced degradation of spacecraft solar cell arrays. The latter problems involve the variation of the trajectory that the spacecraft follows during an electric propulsion transfer from an initial orbit to a geostationary one.
The results of mathematical modeling of a nonisothermal turbulent air flow and admixture transport in an idealized street canyon are presented. The simulation is based on the RANS model, numerical ...algorithm, and application package developed by the authors, which are improved to take into account the effect of the buoyancy force on the aerodynamics and admixture transport. The mathematical model includes Reynolds-averaged stationary three-dimensional Navier–Stokes equations, as well as equations of heat transfer and impurity transport. For closing, a k-eps turbulence model is chosen taking into account the buoyancy forces. The numerical algorithm uses the finite volume method, nonuniform structured grids, and the fictitious domain method. The differential problem is approximated using Van Leer’s monotonized linear upwind scheme and piecewise linear interpolation for dependent quantities. The resulting grid equations are solved sequentially by N.I. Buleev’s iterative method. The SIMPLE algorithm is used to match the velocity and pressure fields. Using the developed package of applied programs, it is found that narrow and high street canyons are the least ventilated at a low wind velocity (~1 m/s), and the higher the street canyon with a constant width the higher the average concentration in the breathing zone. When studying the influence of the degree of heating of the surfaces of a street canyon with the same height and width, the least ventilated case is when the surface temperature of the windward vertical side of the canyon is 15–20°C higher than the ambient temperature. The main reason for this is the formation of a secondary vortex above the road surface, due to which the admixture is poorly carried out of the canyon.
A parallel algorithm for numerical solution of a generalized unsteady 3-dimensional advection-diffusion equation for a mesoscale meteorological model is considered. Efficiency of parallel ...implementations of the solver with Message Passing Interface (MPI), Open Multi-Processing (OpenMP), and NVidia Compute Unified Device Architecture (CUDA) technologies was compared. It was shown that on the mesh of 25625632 nodes the speedup of the program reaches 18 for OpenMP and MPI implementations and 38 for CUDA.
A parallel algorithm for numerical solution of a generalized unsteady 3-dimensional advection-diffusion equation for a mesoscale meteorological model TSUNM3 is considered. Efficiency of parallel ...implementation of the solver with Message Passing Interface (MPI), Open Multi-Processing (OpenMP), Open Accelerators (OpenACC), and NVidia Compute Unified Device Architecture (CUDA) technologies was compared. The efficiency of the MPI-parallelized code of TSUNM3 model with a two-dimensional domain decomposition strategy applied is not less than 75% on 256-512 processes on Cyberia supercomputer of Tomsk State University.
This paper presents a parallel algorithm for numerical solution of equations for the non-hydrostatic mesoscale meteorological model TSUNM3. To justify the choice of the Message Passing Interface ...technology, computational experiments were performed to compare the effectiveness of the following parallelizing technologies: MPI, OpenMP, OpenACC, and CUDA. 2D decomposition of the gridded domain for the TSUNM3 model has been carried out with MPI technology. It allows for a numerical forecast for the next day in 17 minutes of CPU time on 144 cores of the TSU Cyberia computing cluster.
This paper illustrates the problem of optimizing the trajectory of a direct landing from a halo orbit to the lunar surface with given coordinates. The study is considered in circular restricted three ...body problem. The descent operation consists of two stages: change in velocity for descent from orbit (the descent is considered as an instantaneous change in velocity of a spacecraft) and the main stage of braking, which is considered as a task of optimal performance of the spacecraft with finite thrust. The formulation and solution of the optimal control problem is presented, as well as numerical examples illustrating the accessibility of various regions of the lunar surface and examples of landing trajectories.
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