where f|^ and f[^ are the mass flux across the right and left boundary of the 

 grid cell surrounding C^ |(, while gy and gg are mass flux across the top and 

 bottom boundary. 



Upwind Difference Scheme 



In the upwind scheme, the fluxes are defined according to the direction 

 of the flow along each boundary, e.g.. 



"i.k • Ci+l,k 



i^"i.k <0 



if u^.^k > 



Combined Upwind and Central Difference Scheme 



(E-3) 



Sheng (1975) combined the upwind and central difference schemes in the 

 following fashion: 



"i.k • Ci.k ^^ "i.k > «"d C^-.k < Ci+i.k 



"i.k • (Ci.k+Ci+i,k)/2 if u^^,, > and C^^^ ' ^i+Uk 



"i.k * ^i+l,k 



if u^.^,^ < and C^^,^ > Ci+i^i, 



, "i.k • (Ci.k ^ Ci+i^k)/2 ^^ "i.k < ^"d Ci^k ' Ci+i^k (E-4) 



This will reduce the strong numerical diffusion introduced by the upwind 

 scheme except when it is needed to avoid the possibility of generating 

 negative concentrations. 



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