文档介绍:Chapter5NumericalMethodsinHeatConduction15-1WhyNumericalMethods?5-2FiniteDifferenceFormulationofDifferentialEquations5-3One-dimensionalSteadyHeatConduction5-4SolutionMethodsforSystemsofAlgebraicEquations5-5Two-dimensionalSteadyHeatConduction5-6TransientHeatConduction5-7ControllingtheNumericalError5-8SummaryChapter5NumericalMethodsinHeatConductionContents2Chapter5NumericalMethodsinHeatConduction5-1WhyNumericalMethods?Afullmathematicaldescriptionofaconductionproblem:Conductionequation+Conditionsforuniquesolution=concretetemperaturefieldBoundaryCondition+InitialConditionTheoretically:Ananalyticalsolutionisdifficulttofind!+ConditionsforuniquesolutionAlternative?3Chapter5NumericalMethodsinHeatConduction5-parisonofanalyticalandnumericalmethodsAnalyticalMethodNumericalMethoddifferentialequationAsetofnalgebraicequationssolution:DiscreteValues(finite):ContinuousFunction(infinite)+.+?notemeshT(x)xxT(x)4Chapter5NumericalMethodsinHeatConduction5-1WhyNumericalMethods?FiniteDifferenceMethod-FDMFiniteElementMethod-FEMBoundaryElementMethod-BEMThewaysofobtainingthenumericalformulationFiniteAnalyticMethod-FAMFiniteVolumeMethod–FVMControlVolumeMethod-CVMEnergyBalanceMethod-EBM5Chapter5NumericalMethodsinHeatConduction5-2FiniteDifferenceFormulationofDifferentialEquationsdifferentialdx,dTdifferencex, TdifferentialquotientdT/dxdifferencequotientT/xFDM2notes!3notes!One-dimensionalProblem:ForwarddifferencebackwarddifferenceDifferentialEquation:6Forallinternalnotes!Chapter5NumericalMethodsinHeatConduction5-2FiniteDifferenceFormulationofDifferentialEquationsOne-dimensionalProblem:m=0,m=M:BoundaryAsetofM+1algebraicequations:Solution:7Chapter5NumericalMethodsinHeatConduction5-2FiniteDifferenceFormulationofDifferentialEquationsTwo-dimensionalProblem:8Chapter5NumericalMethodsinHeatConduction5-3One-dimensionalSteadyHeatConductionProblem:One-dimensionalconductioninaplanewallofthicknessLwithandconstantkEnergyBalanceMethodStep1:Discretization(M+1)nodes,Mequalsections ofx=