A Novel Dynamic Quadrature Scheme for Solving Boltzmann Equation with Discrete Ordinate and Lattice Boltzmann Methods
作者机构：Department of Mechanical EngineeringHong Kong University of Science and TechnologyClear Water BayKowloonHong Kong
出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)
年 卷 期：2012年第11卷第4期
页 面：1397-1414页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金：This work is supported by the ITC of Hong Kong Government through ITF under Contract No.GHP/028/08SZ
主 题：Dynamics quadrature dynamic discrete ordinatemethod dynamic lattice Boltzmann method thermal lattice Boltzmann method
摘 要：The Boltzmann equation(BE)for gas flows is a time-dependent nonlinear differential-integral equation in 6 *** current simplified practice is to linearize the collision integral in BE by the BGK model using Maxwellian equilibrium distribution and to approximate the moment integrals by the discrete ordinatemethod(DOM)using a finite set of velocity quadrature *** simplification reduces the dimensions from 6 to 3,and leads to a set of linearized discrete *** main difficulty of the currently used(conventional)numerical procedures occurs when the mean velocity and the variation of temperature are large that requires an extremely large number of quadrature *** this paper,a novel dynamic scheme that requires only a small number of quadrature points is *** is achieved by a velocity-coordinate transformation consisting of Galilean translation and thermal normalization so that the transformed velocity space is independent of mean velocity and *** enables the efficient implementation of Gaussian-Hermite *** velocity quadrature points in the new velocity space are fixed while the correspondent quadrature points in the physical space change from time to time and from position to *** this dynamic nature in the physical space,this new quadrature scheme is termed as the dynamic quadrature scheme(DQS).The DQS was implemented to the DOM and the lattice Boltzmann method(LBM).These new methods with DQS are therefore termed as the dynamic discrete ordinate method(DDOM)and the dynamic lattice Boltzmann method(DLBM),*** new DDOM and DLBMhave been tested and validated with several testing *** the same accuracy in numerical results,the proposed schemes are much faster than the conventional ***,the new DLBM have effectively removed the incompressible and isothermal restrictions encountered by the conventional LBM.
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