Study of Simple Hydrodynamic Solutions with the Two-Relaxation-Times Lattice Boltzmann Scheme
作者机构：CemagrefAntony Regional CentreParc de Tourvoie–BP 4492163Antony CedexFrance Department of Metallurgy and Materials EngineeringKatholieke Universiteit LeuvenKasteelpark Arenberg 443001LeuvenBelgium Laboratoire de Physique Statistique´Ecole Normale Sup´erieureassociated to CNRS and P.and M.Curie and D.Diderot Universities24 Rue Lhomond75231 Paris C´edex 05France.
出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)
年 卷 期：2008年第3卷第3期
页 面：519-581页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Lattice Boltzmann equation Dirichlet boundary conditions pressure boundary conditions two-relaxation-time model Knudsen layers exact hydrodynamic solutions staggered invariants pulsatile flow.
摘 要：For simple hydrodynamic solutions, where the pressure and the velocity arepolynomial functions of the coordinates, exact microscopic solutions are constructedfor the two-relaxation-time (TRT) Lattice Boltzmann model with variable forcing andsupported by exact boundary schemes. We show how simple numerical and analyticalsolutions can be interrelated for Dirichlet velocity, pressure and mixed (pressure/tangential velocity) multi-reflection (MR) type schemes. Special care is taken toadapt themfor corners, to examine the uniqueness of the obtained steady solutions andstaggered invariants, to validate their exact parametrization by the non-dimensionalhydrodynamic and a “kinetic (collision) number. We also present an inlet/outlet“constant mass flux condition. We show, both analytically and numerically, that thekinetic boundary schemes may result in the appearance of Knudsen layers which arebeyond the methodology of the Chapman-Enskog analysis. Time dependent Dirichletboundary conditions are investigated for pulsatile flow driven by an oscillating pressuredrop or forcing. Analytical approximations are constructed in order to extend thepulsatile solution for compressible regimes.
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