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Inverse design of mesoscopic models for compressible flow using the chapman-enskog analysis

Advances in Aerodynamics 2021年第1期3卷 86-110页

作者： Tao Chen Lian-Ping Wang Jun Lai Shiyi Chen State Key Laboratory for Turbulence and Complex Systems College of engineeringPeking University100871 BeijingP.R.China Guangdong Provincial Key Laboratory of Turbulence Research and Applications Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace EngineeringSouthern University of Science and Technology518055 ShenzhenP.R.China Department of Mechanical Engineering University of Delaware19716-3140 NewarkDEUSA.

In this paper,based on simplified Boltzmann equation,we explore the inverse-design of mesoscopic models for compressible flow using the chapman-enskog *** from the single-relaxation-time Boltzmann equation with an additional source term,two model Boltzmann equations for two reduced distribution functions are obtained,each then also having an additional undetermined source *** this general framework and using Navier-Stokes-Fourier(NSF)equations as constraints,the structures of the distribution functions are obtained by the leading-order chapman-enskog ***,five basic constraints for the design of the two source terms are obtained in order to recover the NSF system in the continuum *** constraints allow for adjustable bulk-to-shear viscosity ratio,Prandtl number as well as a thermal energy *** specific forms of the two source terms can be determined through proper physical considerations and numerical implementation *** employing the truncated Hermite expansion,one design for the two source terms is ***,three well-known mesoscopic models in the literature are shown to be compatible with these five *** addition,the consistent implementation of boundary conditions is also explored by using the chapman-enskog expansion at the NSF ***,based on the higher-order chapman-enskog expansion of the distribution functions,we derive the complete analytical expressions for the viscous stress tensor and the heat *** underlying physics can be further explored using the DNS simulation data based on the proposed model.

关键词： Mesoscopic CFD methods Boltzmann equation Inverse design The Navier-Stokes-Fourier system chapman-enskog analysis Structure of distribution function Thermal forcing Boundary condition Bulk viscosity Prandtl number

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Development of Lattice Boltzmann Flux Solver for Simulation of Incompressible Flows

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Advances in Applied Mathematics and Mechanics 2014年第4期6卷 436-460页

作者： C.Shu Y.Wang C.J.Teo J.Wu Department of Mechanical Engineering National University of Singapore10 Kent Ridge CrescentSingapore 119260 Department of Aerodynamics College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsNanjing 210016China

A lattice Boltzmann flux solver(LBFS)is presented in this work for simulation of incompressible viscous and inviscid *** new solver is based on chapman-enskog expansion analysis,which is the bridge to link Navier-Stokes(N-S)equations and lattice Boltzmann equation(LBE).The macroscopic differential equations are discretized by the finite volume method,where the flux at the cell interface is evaluated by local reconstruction of lattice Boltzmann solution from macroscopic flow variables at cell *** new solver removes the drawbacks of conventional lattice Boltzmann method such as limitation to uniform mesh,tie-up of mesh spacing and time interval,limitation to viscous *** is validated by its application to simulate the viscous decaying vortex flow,the driven cavity flow,the viscous flow past a circular cylinder,and the inviscid flow past a circular *** obtained numerical results compare very well with available data in the literature,which show that LBFS has the second order of accuracy in space,and can be well applied to viscous and inviscid flow problems with non-uniform mesh and curved boundary.

关键词： chapman-enskog analysis flux solver incompressible flow Navier-Stokes equation lattice Boltzmann equation

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A pseudopotential-based multiple-relaxation-time lattice Boltzmann model for multicomponent/multiphase flows

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Acta Mechanica Sinica 2012年第4期28卷 983-992页

作者： Zhen-Hua Chai Tian-Shou Zhao Department of Mechanical Engineering Hong Kong University of Science and TechnologyClear Water Bay Kowloon Hong Kong China

In this paper, a pseudopotential-based multiplerelaxation-time lattice Boltzmann model is proposed for multicomponent/multiphase flow systems. Unlike previous models in the literature, the present model not only enables the study of multicomponent flows with different molecular weights, different viscosities and different Schmidt numbers, but also ensures that the distribution function of each component evolves on the same square lattice without invoking ad- ditional interpolations. Furthermore, the chapman-enskog analysis shows that the present model results in the correct hydrodynamic equations, and satisfies the indifferentiability principle. The numerical validation exercises further demonstrate that the favorable performance of the present model.

关键词： Lattice Boltzman method Multicomponent flows Multiphase flow chapman-enskog analysis

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A Pseudopotential Lattice Boltzmann analysis for Multicomponent Flow

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Communications in Computational Physics 2022年第9期32卷 1156-1178页

作者： Yong Zhao Gerald G.Pereira Shibo Kuang Zhenhua Chai Baochang Shi School of Mathematics and Statistics Changsha University of Science and TechnologyChangsha 410114HunanChina CSIRO Data61 Private Bag 10Clayton South 3168Australia ARC Research Hub for Computational Particle Technology Department of Chemical EngineeringMonash UniversityVictoria 3800Australia School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China

This paper presents a pseudopotential lattice Boltzmann analysis to show the deficiency of previous pseudopotential models,i.e.,inconsistency between equilibrium velocity and mixture *** rectify this problem,there are two strategies:decoupling relaxation time and kinematic viscosity or introducing a system mixture relaxation ***,we constructed two modified models:a two-relaxationtime(TRT)scheme and a triple-relaxation-time(TriRT)scheme to decouple the relaxation time and kinematic ***,inspired by the idea of a system mixture relaxation time,we developed three mixture models under different collision schemes,***-SRT,mix-TRT,and mix-TriRT ***,we derived the advection-diffusion equation for the multicomponent system and derived the mutual diffusivity in a ***,we conducted several numerical simulations to validate the analysis on these *** numerical results show that these models can obtain smaller spurious currents than previous models and have a wider range for the accessible viscosity ratio with fourth-order *** to previous models,presentmodels avoid complex matrix operations and only fourth-order isotropy is *** increased simplicity and higher computational efficiency of these models make them easy to apply to engineering and industrial applications.

关键词： Lattice Boltzmann method multicomponent flows chapman-enskog analysis

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