For an iterative solution algorithm it is usual to write Eg. (39.11) for the central point P (Cell center) as:

(39.12)

Where "nb" denotes the neighboring nodes.

The coefficients are in Eg. (39.11). For the stability of an iterative solution method it is sufficient to have Whether this condition is satisfied, depends on the interpolation practice used to evaluate the convection terms (U_e, U_n in Eqn (37.16)) and cross-derivative diffusion terms (U_ne, U_se in Eqn (37.5))

For faster convergence of the overall solution procedure, under- relaxation (Patankar, 1980) may be deployed. The change of the variable from one iteration to the next is multiplied by an under-relaxation factor

(39.13)

where superscript n+1 and n denote new and old iteration levels, and This can be arranged in a form equivalent with Eqn. (39.12) to yield:

(39.14)

where superscript n+1 has been omitted.

In the program, is simply taken to be and so that the structure of Eqn (39.12) is preserved.

The Coefficients and contain contributions of the convection and diffusion fluxes and . Their exact form depends on the interpolation method for evaluating the CV face values of the dependent variables.

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