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Which of these represent the Gaussian filter function?(a) \((\frac{\gamma}{\pi \Delta^2})^{\frac{3}{2}} exp(-\gamma \big|\vec x,\vec{x’}\big|)\)(b) \((\frac{\gamma}{\pi \Delta^2})^{\frac{3}{2}} exp(-\gamma \frac{\big|\vec x,\vec{x’}\big|}{\Delta})\)(c) \((\frac{\gamma}{\Delta^2})^{\frac{3}{2}} exp(-\gamma \frac{\big|\vec x,\vec{x’}\big|^2}{\Delta^2})\)(d) \((\frac{\gamma}{\pi \Delta^2})^{\frac{3}{2}} exp(-\gamma \frac{\big|\vec x,\vec{x’}\big|^2}{\Delta^2})\)This question was addressed to me in an online interview.This question is from Large Eddy Simulation for Turbulent Models topic in portion Turbulence Modelling of Computational Fluid Dynamics

Answer»

Right answer is (d) \((\FRAC{\gamma}{\PI \Delta^2})^{\frac{3}{2}} exp(-\gamma \frac{\big|\vec x,\vec{x’}\big|^2}{\Delta^2})\)

Easiest explanation: The filter function, in general, is a function of the spatial vector (\(\vec{x}\)), its derivative (\(\vec{x^{‘}}\)) and the cut-off width (Δ). The GAUSSIAN filter has an additional parameter (γ). The typical value of γ is 6. The function is given as

\(G(\vec{x},\vec{x’},\Delta)=(\frac{\gamma}{\pi \Delta^2})^{\frac{3}{2}} exp(-\gamma \frac{\big|\vec x,\vec{x’}\big|^2}{\Delta^2})\)



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