i.k i.k AxAz ^ R L yj ye ^ v ; 



td , , (1) 



where C^ |^is the first order (transported and diffused) concentration, f^ is 



computed according to Eq. (E-3). 



A higher order scheme, e.g., the central difference scheme, can be 

 , . . u. .- . ^, ^'2) ^(2) (2) . (2) 

 applied to compute higher order fluxes fp , fL , gj , and gg according to 



Eq. (E-9). Antidiffusive fluxes are then defined as: 

 (2) (1) 



(2) (1) 



At = gj - 97 

 (2) (1) 



Ab = 98 - 9b 

 It is these antidiffusive fluxes that are limited in the FCT scheme 

 (Zalesak, 1979) such that: 



(E-12) 



^J = ^1 ' Di,k+l/2 ^ Di^k+1/2 < 1 



Ab = Ag • Di^,,_i/2 0< Di^,,_i/2< 1 



Thus: 



Cn+1 = c^^ - -^ (An - a!^ + At - Ar) (E-13) 



i,k i.k AxAz ^ R L T B' 



The detailed of choosing the coefficients D's can be found in Zalesak (1979). 



c 



Ar = 



= Ar • 



^i+l/2.k 



^ Di+l/2,k ^ 1 



A^ 



-\ ' 



'^i-l/2,k 



^ Di-l/2,k " 1 



259 



