热流科学与工程西步文源大堂E教育部重点实验室P。≥2, hybrid: A(|PeD=o,1-0.5|Pell= 0 thus ap=0and aw remain the same, leading to the same numerical solutionsfor all cases with Pa。 ≥ 2Analytical solutions for gridPeclectnumberlargerthan2PA=00虹-P=10Numericalsolutions for gridP=5Pecletnumberequal and larger=2Dthan 2x源项，X（X）Givensourceterm中CFD-NHT-I16/52CENTER
16/52 2, Pe hybrid： 2 Pe and aW remain the same, leading to the same numerical solutions for all cases with . Analytical solutions for grid Peclect number larger than 2 Numerical solutions for grid Peclet number equal and larger than 2 Given source term ( ) 0,1 0.5 = 0 A P P e e thus =0 E a
热流科学与工程亚步文源大堂G教育部重点实验室4.5.5Twofamousexamples1.Smith-Huttonproblems(1982)Solution for temp. distribution with a known flow fieldu= 2y(1-x),Tv=-2x(1-y3)2T000-0.50YSpecified inlet distributionKnown flow fieldThelargerthecoefficient T,(x) = 1+ tanh[α(1 + 2x)]the sharper the profileSolved by 2-D D-C eq., convection term is discretizedby the scheme studied.CFD-NHT-EHTΦ17/52CENTER
17/52 4.5.5 Two famous examples 1. Smith-Hutton problems（1982） Solution for temp. distribution with a known flow field Known flow field ( ) 1 tanh[ (1 2 )] T x x in 2 3 2 (1 ), 2 (1 ) u y x v x y Solved by 2-D D-C eq., convection term is discretized by the scheme studied. Specified inlet distribution The larger the coefficient the sharper the profile.
热流科学与工程西步文通大堂G教育部重点实验TReferencesolutionSolutionby QUICK with20X10isclosetheonebyPowerlawwith 80×40REFREF80by40a80by40P40by2040by2020by1020by10Power lawQUICKxSolutionfromQUICKby20X10gridshasthe sameaccuracyasthatfrompowerlawby 80X40gridsCFD-NHT-EHTG18/52CENTER
18/52 Reference solution x T Solution from QUICK by 20X10 grids has the same accuracy as that from power law by 80X40 grids. Power law QUICK Solution by QUICK with 20X10 is close the one by Power law with 80X40