Question

What is the final form of the Green-Gauss gradient method for finding the gradient of Φ over element C?

(a) ∇ΦC=∑f~nb(c)Φf \(\vec{S_f}\)

(b) ∇ΦC=1/VC  ∑f~nb(c)Φf \(\vec{S_f}\)

(c) ∇ΦC=1/VC  ∑f~nb(c)Φf

(d) ∇ΦC=1/VC  ∑f~nb(c)af Φf

The question was posed to me by my college professor while I was bunking the class.

My question is taken from Diffusion Problem in division Diffusion Problem of Computational Fluid Dynamics

Answer 1

The correct choice is (b) ∇ΦC=1/VC  ∑f~nb(c)Φf \(\vec{S_f}\)

Easy explanation: The final form of the Green-Gauss gradient method is given by

∇ΦC=1/VC  ∑f~nb(c)Φf \(\vec{S_f}\)

Where,

\(\vec{S_f}\) is known from the geometry of the grids.

Φf for all the faces should be known to compute ∇ΦC.