Explicit filtering in LES

callahance · November 30, 2016, 04:21

How can I do this ? If I have the field only on the fine 128 grid, how can I map this field on the 64 grid without smoothing ? Each coarse cell on the 64 grid has to get a value from 8 fine cells. Averaging all 8 cells is the logical method to me.

FMDenaro · November 30, 2016, 04:26

Just select one node each two somehow similar to the multi grid procedure

callahance · November 30, 2016, 04:39

lets take a simple 2D example. How would you calculate the value in the bigger cell based on the values of the fine cells (1,2,3,4) ?

FMDenaro · November 30, 2016, 04:48

No You should consider Nyquist theorem and the simplest 2D example requires a 4x4 grid to be sampled on a 2x2 grid

callahance · November 30, 2016, 05:11

which would look like this ...

FMDenaro · November 30, 2016, 05:22

well, I was thinking about a 4x4 mesh of size h with values at grid intersection (5x5 values) not at the center of the cells but we can work also on this figure you have done.
Consider the nodes structured as i=1:5 and j=1:5 at step h. You select the node (2,2), (4,2), (2,4),(4,4) and you have the coarser grid represented by a 2x2 mesh of size 2h. Periodicity completes the construction of the coarse grid.

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November 30, 2016, 04:21		#81
callahance Member Join Date: Mar 2012 Posts: 51 Rep Power: 14	How can I do this ? If I have the field only on the fine 128 grid, how can I map this field on the 64 grid without smoothing ? Each coarse cell on the 64 grid has to get a value from 8 fine cells. Averaging all 8 cells is the logical method to me.

November 30, 2016, 04:26		#82
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	Just select one node each two somehow similar to the multi grid procedure

November 30, 2016, 04:48		#84
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	No You should consider Nyquist theorem and the simplest 2D example requires a 4x4 grid to be sampled on a 2x2 grid

November 30, 2016, 05:22		#86
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	well, I was thinking about a 4x4 mesh of size h with values at grid intersection (5x5 values) not at the center of the cells but we can work also on this figure you have done. Consider the nodes structured as i=1:5 and j=1:5 at step h. You select the node (2,2), (4,2), (2,4),(4,4) and you have the coarser grid represented by a 2x2 mesh of size 2h. Periodicity completes the construction of the coarse grid.