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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 ΦfThe 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»

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.



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