热流科学与工程西步文源大堂G教育部重点实验室Thus when P is larger than 2, numerical solutionsare unrealistic: Φpis less than its two neighboring gridvalues, which is not possible for the case without source.The reason isP)<0, i.e. the east influencing-1-ae=coefficient is negative, which is physically meaningless4.2.3FUDofconvectionterm1. Definition in FDM-i+1Eadd-du<0AxAxaxOx2.Definition in FVM-interpolation of interface alwaystakes upstream grid valueΦCFD-NHT-EHT16/48CENTER
16/48 Thus when is larger than 2，numerical solutions are unrealistic： is less than its two neighboring grid values, which is not possible for the case without source. P P The reason is <0，i.e. the east influencing 1 1 (1 ) 2 2 E a P coefficient is negative，which is physically meaningless. 4.2.3 FUD of convection term 2. Definition in FVM－interpolation of interface always takes upstream grid value P 1. Definition in FDM－ 1 1 ) , 0; ) , 0 i i i i i i u u x x x x
热流科学与工程西老义毛大堂G教育部重点实验室dw,u,>0pp,ue >0.=Lm.u.20O(Ax) x =L1i+1i-1dp,u.<0WE2.Compactform（紧凑形式）For the convenience of discussion, combining interfacevalue Φ。with flow rate(pup)。= Fd。=Φ, max(F,O) - Φe max(-Fe, 0)Patankar proposed a special symbol as followsMAX: X, Y ,then:(pup)。=dp[F, O -Φ [-F,O(pup)w=dw [Fw,o-Φp -Fw,0Similarly :3.Discretized form of 1-D model equation with FUD forconvection term and CDfor diffusion term中CFD-NHT-EH17/48CENTER
17/48 2. Compact form (紧凑形式) ( )e e e P u F max( ,0) max( ,0) F e E F e Patankar proposed a special symbol as follows ,then： Similarly： 3. Discretized form of 1-D model equation with FUD for convection term and CD for diffusion term MAX： X Y, ( ) ,0 ,0 e P e E e u F F ( ) ,0 ,0 w W w P w u F F For the convenience of discussion, combining interface value e with flow rate e O x ( ) w , 0 P e u , 0 E e u , 0 W w u , 0 P w u P