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Research on GPU parallel algorithm for direct numerical solution of two-dimensional compressible flows

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Abstract

In this paper, a novel parallel algorithm is proposed to solve the problems of heavy computation and long simulation time in the field of compressible flows. In this algorithm, a third-order upwind scheme and a fourth-order central difference scheme are employed, with a third-order Runge-Kutta method for time stepping. Considering the powerful floating-point computing ability of the Graphics Processing Unit (GPU), this paper establishes the algorithm on the basis of GPU. Moreover, the direct numerical simulation method is adopted in this algorithm to improve the solution accuracy of the simulation results. To further enhance the efficiency of the algorithm, several optimization strategies are explored in the design of the algorithm as well. Both accuracy and feasibility of the algorithm are verified by a classical two-dimensional example. Compared with solving this example on the Central Processing Unit platform, the experimental results demonstrate that the maximum speedup ratio achieved by our approach is 18.03 times.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grand No. 51705390, the Pre-Research Program under Grant No. 61400010111, and the Natural Science Foundation of Shaanxi Province under Grand No. 2018JQ5029.

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Authors and Affiliations

  1. School of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, Jiangsu, China

    Yongzhen Wang & Xuefeng Yan

  2. Collaborative Innovation Center of Novel Software Technology and Industrialization, Nanjing, 210016, Jiangsu, China

    Yongzhen Wang & Xuefeng Yan

  3. School of Mechatronic Engineering, Xi’an Technological University, Xi’an, 710021, Shaanxi, China

    Jun’an Zhang

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  1. Yongzhen Wang
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Correspondence to Xuefeng Yan.

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Wang, Y., Yan, X. & Zhang, J. Research on GPU parallel algorithm for direct numerical solution of two-dimensional compressible flows. J Supercomput 77, 10921–10941 (2021). https://doi.org/10.1007/s11227-021-03704-9

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