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) aP+∑F~NB(P)aF = ∞

(b) aP+∑F~NB(P)aF = 0

(c) aP+∑F~NB(P)aF = 1

(d) aP+∑F~NB(P)aF = -1

The question was posed to me in final exam.

This intriguing question comes from Diffusion Problem in portion Diffusion Problem of Computational Fluid Dynamics

Answer 1

The correct choice is (b) aP+∑F~NB(P)aF = 0

The explanation is: A consistent discretization method should yield an equation which incorporates the property of the overall domain – conservation. To ensure this, the equation should satisfy the condition aP+∑F~NB(P)aF = 0.