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Calculations acceleration and stability improvement methods for hydrodynamic turbulent processes model on CUDA

A.A. Gudukhina, I.F. Yasinskiy

Vestnik IGEU, 2018 issue 6, pp. 72—80

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Abstract in English: 

Background. High computational complexity of computer calculations remains one of the main problems in the construction of mathematical models of turbulent hydro and gas dynamic environments, since it is necessary to obtain a solution to a non-stationary problem with a grid of such a spatial step, which corresponds to the size of the smallest vortex structures. The authors took into account the recommendations on the use of differential computational schemes for the turbulent dynamics of a liquid, obtained in the work on modeling the bottling of oil products on the water surface. The purpose of this work is to obtain the mathematical model stable calculation of the viscous incompressible fluid dynamics according to the Euler description, taking into account the influence of turbulence, and the acceleration of calculations in a parallel CUDA interface.

Materials and methods. The method of mathematical modeling of physical objects and the method of differential equations numerical integration are used. The method of countercurrent derivatives is used to increase the stability of differential schemes. The Sekundov’s method of turbulent viscosity estimation of a continuous medium is used, as well as the analysis of the computational experiments results.

Results. A stable parallel realization has been created for numerical simulation of processes in a continuous medium. It takes into account the influence of turbulizing hydro- and gas-dynamic structures. Stability is achieved by using the counter-current derivative method and replacing traditional difference schemes, when calculating the velocity and pressure fields, with four-point counterparts. The method of uniform distribution of the graphics accelerator computing resources with large sizes of the computational grid is proposed. A stable calculation created of a mathematical model of continuous medium dynamics with the Sekundov’s turbulent viscosity estimation at a considerable time interval.

Conclusion. Based on the NVidia CUDA interface, this solution allows acceleration of calculations to be achieved from 2 to 8 times, depending on the capabilities of the hardware configuration. The developed system can be a tool for the study of objects in the energy industry, for which acceleration of control decisions is required, compared with standard software, that does not provide for calculations parallelization. Reliability of the results is caused by the compliance of the system conditions with the configuration of two-phase supply systems of power installations.

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Key words in Russian: 
сплошные среды, гидрогазодинамика, турбулентность, параллельные вычисления, параллельный интерфейс CUDA
Key words in English: 
continuous media, hydro-gas dynamics, turbulence, parallel computing, CUDA parallel interface
The DOI index: 
10.17588/2072-2672.2018.6.072-080
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