The similarity with Eq. (38.6) for the U-equation, which has only some extra terms due to the presence of two derivatives in as opposed to one in

The above flux expressions can also be written as:

(39.6)

where is the surface vector defining the segment of surface η=constant bounded by nodes P and E (Fig. 37.1)

(39.7)

The underlined part of is often called as “cross-diffusion contribution”. The term vanishes if the grid is orthogonal, and is smaller than the remaining part if the grid non-orthogonality is not severe.

In a similar manner, for the north cell face we obtain:

	(39.8)

Usually, the source terms are integrated over the cell volume,

(39.9)

where is the volumetric unit source at the central node P. The source term can also be split into two parts, one of which being a function of :

(39.10)

This dependence on is artificially introduced (see Patankar, 1980) when a negative part of exists.