In this paper, we discuss the counting prob lem of an order n-group of set (A 1,A 2,…,A n) which satisfies ∪ni=1A i=｛a 1,a 2,…,a m｝ and one of the following: (1) ∩ni=1A i=Φ; (2) ∩ni=1A i=｛b 1,b 2,…,b k｝;(3)...In this paper, we discuss the counting prob lem of an order n-group of set (A 1,A 2,…,A n) which satisfies ∪ni=1A i=｛a 1,a 2,…,a m｝ and one of the following: (1) ∩ni=1A i=Φ; (2) ∩ni=1A i=｛b 1,b 2,…,b k｝;(3) ∩ni=1A 1｛b 1,b 2,…,b k｝; (4) A i≠Φ (i=1,2,…,k). We solve these problems by element analytical meth od.展开更多
We derive exact near-wall and centerline constraints and apply them to improve a recently proposed LPR model for finite Reynolds number(Re) turbulent channel flows.The analysis defines two constants which are invarian...We derive exact near-wall and centerline constraints and apply them to improve a recently proposed LPR model for finite Reynolds number(Re) turbulent channel flows.The analysis defines two constants which are invariant with Re and suggests two more layers for incorporating boundary effects in the prediction of the mean velocity profile in the turbulent channel.These results provide corrections for the LPR mixing length model and incorrect predictions near the wall and the centerline.Moreover,we show that the analysis,together with a set of well-defined sensitive indicators,is useful for assessment of numerical simulation data.展开更多
文摘In this paper, we discuss the counting prob lem of an order n-group of set (A 1,A 2,…,A n) which satisfies ∪ni=1A i=｛a 1,a 2,…,a m｝ and one of the following: (1) ∩ni=1A i=Φ; (2) ∩ni=1A i=｛b 1,b 2,…,b k｝;(3) ∩ni=1A 1｛b 1,b 2,…,b k｝; (4) A i≠Φ (i=1,2,…,k). We solve these problems by element analytical meth od.
基金supported by the National Natural Science Foundation of China (Grant Nos. 90716008 and 10921202)the National Basic Research Program of China (Grant No. 2009CB724100)
文摘We derive exact near-wall and centerline constraints and apply them to improve a recently proposed LPR model for finite Reynolds number(Re) turbulent channel flows.The analysis defines two constants which are invariant with Re and suggests two more layers for incorporating boundary effects in the prediction of the mean velocity profile in the turbulent channel.These results provide corrections for the LPR mixing length model and incorrect predictions near the wall and the centerline.Moreover,we show that the analysis,together with a set of well-defined sensitive indicators,is useful for assessment of numerical simulation data.
