Question

Consider the general discretized equation given by aP ΦP+∑F~NB(P)aF ΦF =0. According to the zero sum rule, which of these is correct?

(a) ∑F~NB(P)\(\frac{a_F}{a_P}\) = ∞

(b) ∑F~NB(P)\(\frac{a_F}{a_P}\) = 1

(c) ∑F~NB(P)\(\frac{a_F}{a_P}\) = -1

(d) ∑F~NB(P)\(\frac{a_F}{a_P}\) = -∞

This question was addressed to me in an online quiz.

I would like to ask this question from Diffusion Problem in chapter Diffusion Problem of Computational Fluid Dynamics

Answer 1

Right option is (c) ∑F~NB(P)\(\frac{a_F}{a_P}\) = -1

The best I can explain: From the zero sum rule,

\(a_P+\sum_{(F \sim NB(P))}a_F = 0\)

Divided by aP, the equation becomes

\(1+\frac{\sum_{F \sim NB(P)}a_F}{a_P} = 0 \)

\(\frac{\sum_{F \sim NB(P)}a_F}{a_P} =-1\)

This can be written as

\(\sum_{F \sim NB(P)}\frac{a_F}{a_P} =-1\).