Improved simplified and highly stable lattice Boltzmann methods for incompressible flows

Yuan Gao (), Liuming Yang (), Yang Yu (), Guoxiang Hou and Zhongbao Hou ()
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Yuan Gao: School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, No.1037, Luoyu Road, Wuhan 430074, P. R. China
Liuming Yang: School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, No.1037, Luoyu Road, Wuhan 430074, P. R. China
Yang Yu: School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, No.1037, Luoyu Road, Wuhan 430074, P. R. China
Guoxiang Hou: School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, No.1037, Luoyu Road, Wuhan 430074, P. R. China
Zhongbao Hou: Department of Medical Biotechnoligy and Laboratory Science, Chang Gung University Taoyuan 33302, R.O.C.

International Journal of Modern Physics C (IJMPC), 2021, vol. 32, issue 06, 1-26

Abstract: In this work, improved simplified and highly stable lattice Boltzmann methods (SHSLBMs) are developed for incompressible flows. The SHSLBM is a newly developed scheme within the lattice Boltzmann method (LBM) framework, which utilizes the fractional step technology to resolve the governing equations recovered from lattice Boltzmann equation (LBE) and reconstructs the equations in the Lattice Boltzmann frame. By this treatment, the SHSLBM directly tracks the macroscopic variables in the evolution process rather than the distribution functions of each grid node, which greatly saves virtual memories and simplifies the implementation of physical boundary conditions. However, the Chapman–Enskog expansion analysis reveals that the SHSLBM recover the weakly compressible Navier–Stokes equations with the low Mach number assumption. Therefore, the original SHSLBM can be regarded as an artificial compressible method and may cause some undesired errors. By modifying the evolution equation for the density distribution function, the improved SHSLBMs can eliminate the compressible effects. The incompressible SHSLBMs are compared with the original SHSLBM in terms of accuracy and stability by simulating several two-dimensional steady and unsteady incompressible flow problems, and the results demonstrate that the present SHSLBMs ensure the second order of accuracy and can reduce the compressible effects efficiently, especially for the incompressible flows with large pressure gradients. We then extended the present SHSLBMs to study the more complicated two-dimensional lid-driven flow and found that the present results are in good agreement with available benchmark results.

Keywords: Simplified and highly stable lattice Boltzmann method; compressible effects; incompressible LBGK models; Chapman–Enskog expansion analysis (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0129183121500777

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