Question

To get the gradient of the flow variable using the Green-Gauss Theorem, which of these theorems is used?

(a) Mean value theorem

(b) Stolarsky mean

(c) Racetrack principle

(d) Newmark-beta method

This question was addressed to me in an interview.

My question is based upon Diffusion Problem topic in portion Diffusion Problem of Computational Fluid Dynamics

Answer 1

Right choice is (a) Mean value theorem

Easy explanation: The Green-Gauss theorem states that for a closed volume V with the surrounding surface ∂V and outward pointing incremental surface vector d\(\vec{S}\),

∫V \(\nabla\Phi dV=∮_{∂V} \Phi d\vec{S}\)

Using the mean value theorem,

∫V ∇ΦdV=\(\overline{\nabla\Phi} V\)

Where, \(\overline{\nabla\Phi} V\) is the average gradient over the volume V.