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1、PHYSICALREVIEWE79,0467012009LatticesforthelatticeBoltzmannmethodShyamS.Chikatamarla*LAV,InstituteofEnergyTechnology,ETHZurich,8092Zurich,SwitzerlandIliyaV.KarlinLAV,InstituteofEnergyTechnology,ETHZurich,8092Zurich,SwitzerlandandSchoolofEngineeringSciences,Univer
2、sityofSouthampton,SouthamptonSO171BJ,UnitedKingdomReceived24November2008;published1April2009Arecentlyintroducedtheoryofhigher-orderlatticeBoltzmannmodelsChikatamarlaandKarlin,Phys.Rev.Lett.97,1906012006iselaboratedindetail.Ageneraltheoryoftheconstructionofla
3、tticeBoltzmannmodelsasanapproximationtotheBoltzmannequationispresented.NewlatticesarefoundinallthreedimensionsandareclassifiedaccordingtotheiraccuracydegreeofapproximationoftheBoltzmannequation.Thenumericalstabilityoftheselatticesisarguedbasedontheentropyprincipl
4、e.Theefficiencyandaccuracyofmanynewlatticesaredemonstratedviasimulationsinallthreedimensions.DOI:10.1103/PhysRevE.79.046701PACSnumbers:47.11.j,05.20.DdI.INTRODUCTIONquiredinestablishinghigher-orderlatticesforlatticeBoltz-mannmethods.ThelatticeBoltzmannLBmethod
5、isapowerfulnewToimprovetheaccuracyandisotropyofalattice,alargerapproachtohydrodynamics,withapplicationsrangingfromnumberofdiscretevelocitiesisrequired.Onewayofobtain-largeReynoldsnumberflowstoflowsatthemicrometeringhigher-orderLBmodelsisbydiscretizingtheBoltzmannsca
6、le,porousmedia,andmultiphaseflows1.TheLBequationontherootsofHermitepolynomials6,12.Thismethodsolvesafullydiscretekineticequationforpopula-routeofhigher-orderGauss-Hermitequadraturespromisedationsfix,t,designedtoreproducetheNavier-Stokesequa-systematicderivati
7、onofnewcompleteGalilean-invariantLBtionsinthehydrodynamiclimit.Populationscorrespondtomodels6,12.However,sincetherootsofHermitepolyno-discretevelocitiesci,i=1,...,nd,whichfitintoaregularmialsareirrational,thecorrespondingdiscretevelocitiesspatiallatticewithnodesx
8、.Thisenablesasimpleandhighlycannotbefittedintoaregularspace-fillinglattice.Thus,oneefficientstreamalonglinksandequilibrateatnodesreal-ofthemostimportantadv
