Preconditioned central moment lattice Boltzmann method on a rectangular lattice grid for accelerated computations of inhomogeneous flows

作     者：Yahia, Eman Premnath, Kannan N. 

作者机构：Univ Colorado Coll Engn Design & Comp Dept Mech Engn 1200 Larimer St Denver CO 80217 USA 

出 版 物：《JOURNAL OF COMPUTATIONAL SCIENCE》 (计算科学杂志)

年 卷 期：2022年第63卷第0期

核心收录：

学科分类：08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Department of Mechanical Engineering at the University of Colorado Denver US National Science Foundation (NSF) [CBET-1705630] NSF 

主　　题：Lattice Boltzmann method Rectangular lattice Central moments Preconditioning Inhomogeneous and anisotropic flows Convergence acceleration 

摘      要：Convergence acceleration of flow simulations to their steady states at lower Mach numbers can be achieved via preconditioning the lattice Boltzmann (LB) schemes that alleviate the associated numerical stiffness, which have so far been constructed on square lattices. We present a new central moment LB method on rectangular lattice grids for efficient computations of inhomogeneous and anisotropic flows by solving the preconditioned Navier-Stokes (PNS) equations. Moment equilibria corrections are derived via a Chapman-Enskog analysis for eliminating the truncation errors due to grid-anisotropy arising from the use of the rectangular lattice and the non-Galilean invariant cubic velocity errors resulting from an aliasing effect on the standard D2Q9 lattice for consistently recovering the PNS equations. Such corrections depend on the diagonal components of the velocity gradients, which are locally obtained from the second order non-equilibrium moments and parameterized by an associated grid aspect ratio gamma and a preconditioning parameter gamma, and the speed of sound in the collision model is naturally adapted to gamma via a physically consistent strategy. We develop our approach by using a robust non-orthogonal moment basis and the central moment equilibria are based on a matching principle, leading to simpler expressions for the corrections for using the rectangular grids and for representing the viscosities as functions of the relaxation parameters, r and gamma, and its implementation is modular allowing a ready extension of the existing LB schemes based on the square lattice. Numerical simulations of inhomogeneous and anisotropic shear-driven bounded flows using the preconditioned rectangular central moment LB method demonstrate the accuracy and significant reductions in the numbers of steps to reach the steady states for various sets of characteristic parameters.