热流科学与工程亚步文源大堂E教育部重点实验室Meaning of "Continuous"weDifferentinterfaces-EEE-viewed from point PWpwThe same interfacePEviewed from twoi-1Zi+2i+1points P and EBy “Continuous"we mean:1(Φ)p =(dw)e;JEoxoxThe piecewise linear profile can meet this conditionCFD-NHT-EHTΦ11/41CENTER
11/41 ( ) ( ) ; e P w E [( ) ] [( ) ] e P w E x x The piecewise linear profile can meet this condition. P E Different interfaces viewed from point P The same interface viewed from two points P and E Meaning of “Continuous” By “Continuous” we mean:
热流科学与工程西步文源大堂E教育部重点实验室Interface-biasedquadratic（界面偏向的二次插值）cannotsatisfysuchrequirementInterface valueTangential to P-Interfacevaluefrom W-P-EE-EEatinterfaceFor west sidePEEfrom P-E-EEpw(2)oftheinterfaceTangential to W-DW, P and E areP-E at interfacePE曲线②在界面的切线used for曲线①在einterpolationBoth first order界面的切线ppderivatives andFor east sideinterface valuesof the interface,wweeare not equal!P,EandEEEEEW0are used forinterpolation7.3.4Discussion-Conservationis expectedbutnotnecessaryforallsimulation.（希望而非必须）中CFD-NHT-EH12/41CENTER
12/41 Interface-biased quadratic (界面偏向的二次插值) can not satisfy such requirement 7.3.4 Discussion－Conservation is expected but not necessary for all simulation.(希望而非必须） For west side of the interface, W, P and E are used for interpolation For east side of the interface, P , E and EE are used for interpolation Tangential to PE-EE at interface Tangential to WP-E at interface Both first order derivatives and interface values are not equal! Interface value from P-E-EE Interface value from W-P-E
热流科学与工程西步文源大堂G教育部重点实验室Contents7.1 Consistence,Convergence and Stability ofDiscretized Equations7.2von Neumann Method for AnalysingStabilityofInitial Problems7.3Conservation of Discretized Eguations7.4TransportivePropertyofDiscretizedEquations7.5Sign-preservationPrincipleforAnalyzingConvective StabilityΦCFD-NHT-EHT13/41CENTER
13/41 7.1 Consistence, Convergence and Stability of Discretized Equations 7.3 Conservation of Discretized Equations Contents 7.4 Transportive Property of Discretized Equations 7.5 Sign-preservation Principle for Analyzing Convective Stability 7.2 von Neumann Method for Analysing Stability of Initial Problems
热流科学与工程西步文源大堂G教育部重点实验室7.4 Transportive (迁移)Character of DiscretizedEquations7.4.1Essential（基本的)differencebetweenconvection and diffusion7.4.2cDof diffusiontermcanpropagate(传播)disturbanceall around（四面八方）uniformly7.4.3Analysis of transport character ofdiscretizedschemeofconvectionterm7.4.4Upwindschemeofconvectiontermpossessestransportcharacter7.4.5DiscussionontransportcharacterofdiscretizedconvectiontermCFD-NHT-EHT中14/41CENTER
14/41 7.4.1 Essential (基本的) difference between convection and diffusion 7.4 Transportive (迁移)Character of Discretized Equations 7.4.2 CD of diffusion term can propagate(传播) disturbance all around (四面八方) uniformly 7.4.3 Analysis of transport character of discretized scheme of convection term 7.4.4 Upwind scheme of convection term possesses transport character 7.4.5 Discussion on transport character of discretized convection term