PA。≥2, hybrid: ag = DeA(PAe+-F,0 ,A(PeD=[o,1-0.5|PAell=0 thus ae=0 remain the same, leading to the same numericalbut aw=D.A(PD+ F,osolutions for all cases with P, ≥2 Analytical solutions forgridPeclect number larger than 2PA=005P=10Numericalsolutions for gridPA=5Pecletnumberequal and largerthan 2x源项，X(X）Givensourceterm16/55
16/55 2, Pe hybrid： 2 Pe 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 ( ) ,0 W w w w a D A P F = + ( ) ,0 , E e e a D A P F = + − but
4.5.5Twofamousexamples1.Smith-Huttonproblems(1982)Solution for temp. distribution with a known flow fieldu= 2y(1- x2),Tv=-2x(1- y3)n7000-0.50Specified inlet distributionKnown flow fieldThe larger the coefficient CEq. of Tm : T,(x) = 1 + tanh[α(1 + 2x)]the sharper（更陡削）the profileSolved by 2-D D-C eq., convection term is discretizedby different schemes studied.17/55
17/55 4.5.5 Two famous examples 1. Smith-Hutton problems（1982） Solution for temp. distribution with a known flow field Known flow field 2 3 2 (1 ), 2 (1 ) u y x v x y = − = − − Solved by 2-D D-C eq., convection term is discretized by different schemes studied. Specified inlet distribution The larger the coefficient the sharper (更陡削） the profile. ( ) 1 tanh[ (1 2 )] Eq. of Tin ： T x x in = + +
TReferencesolutionSolutionbyQUICKwith20X10isclosetheonebyPowerlawwith 80×40REFREF80by40080by40-40by2040by2020by1020by10Power lawQUICKxSolution from QUICK by20X10grids has the same accuracyas thatfrompowerlawby80X40 grids.PLhas alargerfalsediffusionerror.18/55
18/55 Reference solution x T Solution from QUICK by 20X10 grids has the same accuracy as that from power law by 80X40 grids. PL has a larger false diffusion error. Power law QUICK Solution by QUICK with 20X10 is close the one by Power law with 80X40