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

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.