Linear algebraic(1)Iteration for solvingABEqs.-InneriterationInneriteration。可下一层次This is the solutionUpdateprocedure for ABEqs. withOuterspecified coefficients andsource term. Discussed inChapter 5L(2) Iteration for non-linearcerationproblem-OuteriterationThis is the process inwhichthecoefficientsandsource term are updated16/43
16/43 (1) Iteration for solving ABEqs.－ Inner iteration (2) Iteration for non-linear problem－Outer iteration This is the solution procedure for ABEqs. with specified coefficients and source term. Discussed in Chapter 5 This is the process in which the coefficients and source term are updated. Linear algebraic
2. Criteria for terminating inner iteration of flow field solutionThe major solution work for flow field is in the p 'eqs. .Terminatingtoo earlyisnot infavor of(不利于)massconservation,whiletoolateisnoteconomicThree criteria may be used :(1) Specify the number of iteration cycles: One cycle meansthat the dependent variables at all nodes have been updated----Simplebut not rational(合理的);(2）Specifyathreshold（阈值）forthe norm（范数)of residual(余量)ofp’eqsZ[(apPp -ZanbPnb -b)())/2= R(k)Resumeto（回复到）originalZero if convergedR(k)<dimensionResidual may beL17/43negative
17/43 2. Criteria for terminating inner iteration of flow field solution The major solution work for flow field is in the p ’eqs. . Terminating too early is not in favor of (不利于)mass conservation ,while too late is not economic. Three criteria may be used： (1) Specify the number of iteration cycles：One cycle means that the dependent variables at all nodes have been updated. -Simple but not rational(合理的)； (2) Specify a threshold (阈值）for the norm (范数) of residual (余量) of p’ eqs. ' ' ( ) 2 1/ 2 ( ) { [( ) ] } k k P P nb nb p a p a p b R − − = Zero if converged Residual may be negative Resume to (回复到)original dimension ( ) k R p