Lattice Boltzmann method with the cell-population equilibrium
Zhou Xiao-Yang(周晓阳)a)†,Cheng Bing(程冰)a)b), and Shi Bao-Chang(施保昌)a)
a Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China; bDepartment of Science Institute, Qingdao Agricultural University, Qingdao 266109, China
Abstract The central problem of the lattice Boltzmann method (LBM) is to construct a discrete equilibrium. In this paper, a multi-speed 1D cell-model of Boltzmann equation is proposed, in which the cell-population equilibrium, a direct non-negative approximation to the continuous Maxwellian distribution, plays an important part. By applying the explicit one-order Chapman--Enskog distribution, the model reduces the transportation and collision, two basic evolution steps in LBM, to the transportation of the non-equilibrium distribution. Furthermore, 1D dam-break problem is performed and the numerical results agree well with the analytic solutions.
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