Numerical HeatTransfer（数值传热学）Chapter4DiscretizedSchemesofDiffusionandConvectionEquation(1)(Chapter5oftextbook)1/49
1/49 Numerical Heat Transfer (数值传热学) Chapter 4 Discretized Schemes of Diffusion and Convection Equation (1) （Chapter 5 of textbook）
（40学时教学主线）Ourteachingprinciple lineYou cansolveturbulentprobsHighlightsfor solvingin irregular regionincompressibleFFHT.ThreemathfeaturesTurbulencemodelsSolutionofIrregulardomainFlow prob.DescretizationAlgorithms:Of convectionAppliedtoSIMPLE,termsolveSIMPLER...DiffusionSchemes:prob.FUD,CD,SUD,QUICK...TDMA;MostASTM;IntermidiatefundamentalsLinearizationBasicpartpartGoverning eqs.You can solvelaminarflowYou have laid a solidDomaindiscretizationandheattransferproblemsfoundationforadvancedEq.discretizationinirregularregionstudyofCFDand NHT250
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Chapter4Discretizeddiffusion-convectionequation4.1 Two ways of discretization of convection term4.2CDandUDschemesoftheconvectionterm4.3Hybridandpower-lawschemes4.4Characteristicsoffivethree-pointschemes4.5 Discussion on false diffusion4.6Methodsforovercomingoralleviatingeffectsoffalsediffusion4.7 Discretization of multi-dimensional problem andB.C.treatment3/49
3/49 4.1 Two ways of discretization of convection term 4.2 CD and UD schemes of the convection term 4.3 Hybrid and power-law schemes Chapter 4 Discretized diffusion－convection equation 4.4 Characteristics of five three-point schemes 4.5 Discussion on false diffusion 4.6 Methods for overcoming or alleviating effects of false diffusion 4.7 Discretization of multi-dimensional problem and B.C. treatment
4.1 Two ways of discretization of convection term4.1.1Importanceofdiscretizedschemeofconvectionterm1.Accuracy2.Stability3.Economics4.1.2Two ways forconstructing discretizationschemesofconvectiveterm4.1.3Relationshipbetweenthetwoways4/49
4/49 4.1.1 Importance of discretized scheme of convection term 4.1.2 Two ways for constructing discretization schemes of convective term 1. Accuracy 2. Stability 3. Economics 4.1 Two ways of discretization of convection term 4.1.3 Relationship between the two ways
4.1 Two ways of discretizationof convection term4.1.1Importanceofdiscretizationscheme（离散格式）Mathematically convective term is only of 1st orderderivative, while its physical meaning (strong directional)makes its discretization one of the hot spots (热点) ofnumerical simulation:1.Itaffectsthe numerical accuracy(精确性）Whenaschemeoftheconvectiontermwith1st-orderisused the solution involves severe numerical error.2.It affects the numerical stability(稳定性）The schemes ofCD，TUD(三阶迎风) and QUICK areonly conditionally stable.3.It affects numerical economics(经济性)5/49
5/49 4.1 Two ways of discretization of convection term 4.1.1 Importance of discretization scheme (离散格式) Mathematically convective term is only of 1st order derivative, while its physical meaning ( strong directional) makes its discretization one of the hot spots (热点) of numerical simulation： 1. It affects the numerical accuracy(精确性). When a scheme of the convection term with 1st -order is used the solution involves severe numerical error. 2. It affects the numerical stability(稳定性). The schemes of CD，TUD(三阶迎风) and QUICK are only conditionally stable. 3. It affects numerical economics (经济性)