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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 |
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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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