# Computational Fluid Dynamics Questions and Answers – Large Eddy Simulation for Turbulent Models

This set of Computational Fluid Dynamics Multiple Choice Questions & Answers focuses on “Large Eddy Simulation for Turbulent Models”.

1. LES is preferred when _____________
a) the flow is compressible
b) the flow has a high Reynolds number
c) the flow is turbulent
d) the flow has heat transfers

Explanation: Large Eddy Simulation (LES) method is useful to capture the large turbulent eddies. It is not as accurate as the DNS method and not computationally demanding. As high Reynolds number will have large eddies, it is preferred when the flow has a high Reynolds number.

2. LES uses _____________
a) spatial filtering
b) time averaging
c) ensemble averaging
d) reynolds averaging

Explanation: Les captures large eddies only. So, spatial filtering is used to separate the large and small eddies. A filtering function and the cut-off width above which the flow will be solved are selected before solving the flow.

3. What does SGS stress stand for?
a) Sub-grid-scale stress
b) Suitable-grid-scale stress
c) Suitable-grey-scale stress
d) Sub-grey-scale stress

Explanation: During spatial filtering, the information about the small eddies will be lost. The interaction between large eddies and small eddies leads to this SGS stress. It stands for sub-grid-scale stress.

4. Which of these will not come under the types of filter functions used by the LES model?
a) Top-hat filter
b) Leonard filter
c) Gaussian filter
d) Spectral cut-off

Explanation: The LES method uses a filter function to spatially filter and get the larger eddies of interest. The most common three-dimensional filters are Top-hat filter, Gaussian filter and Spectral cut-off filters.

5. What is the other name of the top-hat filter?
a) Cross filter
b) Cube filter
c) Box filter
d) Square filter

Explanation: Top-hat filter is otherwise called as the box filter. It is the simplest filter function given by
$$G(\vec x,\vec{x’},\Delta) = \left\{\begin{array} (\frac{1}{\Delta^3} & \big|\vec x,\vec{x’}\big| \le \frac{\Delta}{2} \\ 0 & \big|\vec x,\vec{x’} \big|>\frac{\Delta}{2} \\ \end{array}\right\}$$
Where,
$$\vec{x}$$ → Spatial vector
$$\vec{x’}$$ → Derivative of spatial vector
Δ → Cut-off width
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6. 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) $$(\frac{\gamma}{\pi \Delta^2})^{\frac{3}{2}} exp(-\gamma \frac{\big|\vec x,\vec{x’}\big|^2}{\Delta^2})$$

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

7. Which of these is the spectral cut-off filter function?
a) $$\prod_{i=1}^3\frac{sin[(x_i-x_i^{‘})/\Delta]}{(x_i-x_i^{‘})}$$
b) $$\prod_{i=1}^3 sin[(x_i-x_i^{‘})/\Delta]$$
c) $$\prod_{i=1}^3\frac{sin[(x_i-x_i^{‘})]}{(x_i-x_i^{‘})}$$
d) $$\prod_{i=1}^3 sin[(x_i-x_i^{‘})/\Delta]$$

Explanation: The spectral cut-off filter is the product of $$\frac{sin[(x_i-x_i^{‘})]}{(x_i-x_i^{‘})}$$ for all three directions of the x-vector. This gives a sharp cut-off in the energy spectrum at a wavelength of Δ/π.

8. Which of these filters is commonly used in FVM models?
a) Gaussian filter
b) Top-hat filter
c) Spectral cut-off filter
d) Gaussian and spectral cut-off filter

Explanation: The top-hat or box filter is the one which is preferred for the finite volume methods in CFD packages. This is because of their simple elimination of small eddies. The Gaussian and spectral cut-off filter are used for research purposes.

9. In FVM methods, cut-off width depends on ____________
a) the PDE
b) the algebraic equation
c) the grid-size
d) the discretization method

Explanation: When we use the finite volume method, it is pointless to use a cut-off width which is smaller than the grid size. If such cut-off width is chosen, the accuracy of the method in capturing the eddies will be affected.

10. The cut-off width dependent on the finite volume grid size is equal to _____________
a) the square of the grid cell volume
b) the cube of the grid cell volume
c) the square root of the grid cell volume
d) the cube root of the grid cell volume

Explanation: If Δx, Δy and Δz are the grid sizes in the x, y and z-directions, the cut-off width should be the cube root of the cell volume ($$\sqrt[3]{\Delta x \Delta y \Delta z}$$). This is because the cut-off width is in a single direction.

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