Inverse design of mesoscopic models for compressible flow using the Chapman-Enskog analysis

作     者：Tao Chen Lian-Ping Wang Jun Lai Shiyi Chen 

作者机构：State Key Laboratory for Turbulence and Complex SystemsCollege of engineeringPeking University100871 BeijingP.R.China Guangdong Provincial Key Laboratory of Turbulence Research and ApplicationsCenter 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 EngineeringUniversity of Delaware19716-3140 NewarkDEUSA. 

出 版 物：《Advances in Aerodynamics》 (空气动力学进展（英文）)

年 卷 期：2021年第3卷第1期

页      面：86-110页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the U.S.National Science Foundation(CNS-1513031,CBET-1706130) the National Natural Science Foundation of China(91852205,91741101&11961131006) the National Numerical Wind Tunnel program,Guangdong Provincial Key Laboratory of Turbulence Research and Applications(2019B21203001) Shenzhen Science&Technology Program(Grant No.KQTD20180411143441009). 

主　　题：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 

摘      要：In this paper,based on simplified Boltzmann equation,we explore the inverse-design of mesoscopic models for compressible flow using the Chapman-Enskog analysis.Starting 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 term.Under 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 analysis.Next,five basic constraints for the design of the two source terms are obtained in order to recover the NSF system in the continuum limit.These constraints allow for adjustable bulk-to-shear viscosity ratio,Prandtl number as well as a thermal energy source.The specific forms of the two source terms can be determined through proper physical considerations and numerical implementation requirements.By employing the truncated Hermite expansion,one design for the two source terms is proposed.Moreover,three well-known mesoscopic models in the literature are shown to be compatible with these five constraints.In addition,the consistent implementation of boundary conditions is also explored by using the Chapman-Enskog expansion at the NSF order.Finally,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 flux.Some underlying physics can be further explored using the DNS simulation data based on the proposed model.