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Dynamic SGS model procedure in Large eddy simulation |
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October 14, 2013, 13:26 |
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#10 |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,783
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I have to distinguish between the test filtering procedure and its numerical implementation ...
If you want to use a top-hat filter, in a 2d plane say (x,y), you have to chose its width. Therefore, you write the continuous expression: f_test(x,y) = (1/Deltax/Deltay) * Int [y-Deltay/2,y+Deltay/2] dy' Int[x-Deltax/2,x+Deltax/2] f(x',y') dx' For example, you can choose Deltax=2*Dx and Deltay=2*Dy. Now you have to numerically compute the above integrals by using a proper discretization. For example, you can use a 2D Simpson rule. Therefore, centred at i,j you need of a stencil of 9 nodes going from i-1,j-1 up to i+1,j+1. The weights of the integration formula can be found in many textbooks. You can do that for any i,j nodes in the x,y plane. Then repeat for all the z planes. Finally, if you want to make the test filter three-dimensional, you have to average again the 2d filtered field using the 1d formula for the z direction. |
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