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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 methodThis 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» 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.


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