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A novel median dual finite volume lattice Boltzmann method for incompressible flows on unstructured grids

Author

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  • Lei Xu

    (Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, P. R. China†Shenzhen Key Laboratory for Exascale, Engineering and Scientific Computing, Shenzhen 518055, P. R. China)

  • Wu Zhang

    (#x2021;Institute of Applied Mathematics and Mechanics, Shanghai University Shanghai 200072, P. R. China)

  • Zhengzheng Yan

    (Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, P. R. China†Shenzhen Key Laboratory for Exascale, Engineering and Scientific Computing, Shenzhen 518055, P. R. China)

  • Zheng Du

    (#xA7;Department of Computer Science and Technology, Tsinghua University Beijing 100084, P. R. China)

  • Rongliang Chen

    (Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, P. R. China†Shenzhen Key Laboratory for Exascale, Engineering and Scientific Computing, Shenzhen 518055, P. R. China)

Abstract

A novel median dual finite volume lattice Boltzmann method (FV-LBM) for the accurate simulation of incompressible flows on unstructured grids is presented in this paper. The finite volume method is adopted to discretize the discrete velocity Boltzmann equation (DVBE) on median dual control volumes (CVs). In the previous studies on median dual FV-LBMs, the fluxes for each partial face have to be computed separately. In the present second-order scheme, we assume the particle distribution functions (PDFs) to be constant for all faces grouped around a particular edge. The fluxes are then evaluated using the low-diffusion Roe scheme at the midpoint of the edge, and the PDFs at the faces of the CV are obtained through piecewise linear reconstruction of the left and right states. The gradients of the PDFs are computed with the Green–Gauss approach. The presented scheme is validated on four benchmark flows: (a) pressure driven Poiseuille flow; (b) the backward-facing step flow with Re=50, 100, 200 and 300; (c) the lid-driven flow with Re=400 and 1000; and (d) the steady viscous flow past a circular cylinder with Re=10, 20 and 40.

Suggested Citation

  • Lei Xu & Wu Zhang & Zhengzheng Yan & Zheng Du & Rongliang Chen, 2020. "A novel median dual finite volume lattice Boltzmann method for incompressible flows on unstructured grids," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(12), pages 1-18, December.
    • Handle: RePEc:wsi:ijmpcx:v:31:y:2020:i:12:n:s0129183120501739
    DOI: 10.1142/S0129183120501739
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