Implicit Filtering concept in LES

selig5576 · August 21, 2018, 14:24

I have one question regarding $\hat{\Delta}$ . Early it was established that $\hat{\Delta} x = 4 \Delta x$ . So to calculate $\hat{\Delta}$ (like in the Dynamic Smagorinsky) we have $\hat{\Delta} = \left(\hat{\Delta } x \hat{\Delta} y \hat{\Delta} z\right)^{1/3} = \left(4\Delta x \cdot 4 \Delta y \cdot 4 \Delta z\right)^{1/3}$ . The specific term I am interested in is

$M_{ij} = \hat{\Delta}^{2} |\hat{S}| \hat{S}_{ij} + \Delta^{2} \hat{|S| S_{ij}}$

FMDenaro · August 21, 2018, 15:42

Quote:

Originally Posted by selig5576

I have one question regarding $\hat{\Delta}$ . Early it was established that $\hat{\Delta} x = 4 \Delta x$ . So to calculate $\hat{\Delta}$ (like in the Dynamic Smagorinsky) we have $\hat{\Delta} = \left(\hat{\Delta } x \hat{\Delta} y \hat{\Delta} z\right)^{1/3} = \left(4\Delta x \cdot 4 \Delta y \cdot 4 \Delta z\right)^{1/3}$ . The specific term I am interested in is

$M_{ij} = \hat{\Delta}^{2} |\hat{S}| \hat{S}_{ij} + \Delta^{2} \hat{|S| S_{ij}}$

That depends on your choice, if you perform the test filtering over a 2D plane, the test filter width is computed accordingly, by taking into account the two grid steps

selig5576 · August 21, 2018, 15:51

I am performing a 3D filtering procedure, i.e. I am computing a 3D integral. to obtain $\hat{f}$ . I am defining new filter such that the width $\hat{\Delta}$ is equal to twice the grid filter width of $\Delta$ .

FMDenaro · August 21, 2018, 15:59

Delta_tilde=2*Delta = 2* (8*dx*dy*dz)^1/3

that is quite correct for a Delta value evaluated for a second order central discretization.

Moreza7 · January 19, 2021, 04:26

Please delete this post

August 21, 2018, 14:24	Follow up question	#21
selig5576 Senior Member Selig Join Date: Jul 2016 Posts: 213 Rep Power: 11	I have one question regarding $\hat{\Delta}$ . Early it was established that $\hat{\Delta} x = 4 \Delta x$ . So to calculate $\hat{\Delta}$ (like in the Dynamic Smagorinsky) we have $\hat{\Delta} = \left(\hat{\Delta } x \hat{\Delta} y \hat{\Delta} z\right)^{1/3} = \left(4\Delta x \cdot 4 \Delta y \cdot 4 \Delta z\right)^{1/3}$ . The specific term I am interested in is $M_{ij} = \hat{\Delta}^{2} \|\hat{S}\| \hat{S}_{ij} + \Delta^{2} \hat{\|S\| S_{ij}}$

August 21, 2018, 15:51	Filtering	#23
selig5576 Senior Member Selig Join Date: Jul 2016 Posts: 213 Rep Power: 11	I am performing a 3D filtering procedure, i.e. I am computing a 3D integral. to obtain $\hat{f}$ . I am defining new filter such that the width $\hat{\Delta}$ is equal to twice the grid filter width of $\Delta$ .

August 21, 2018, 15:59		#24
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,896 Rep Power: 73	Delta_tilde=2Delta = 2 (8dxdy*dz)^1/3 that is quite correct for a Delta value evaluated for a second order central discretization. selig5576 likes this.

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