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 September 21, 2011, 03:04 Gauss Quadrature points #1 Member   supercommandodhruv Join Date: Sep 2011 Posts: 57 Rep Power: 8 Hi All, I am calculating volume flow in a channel, and want to use the Gauss quadrature to calculate the volume flow rate. I searched on the net, and found some tables that have the points ( abscissa) and the corresponding weighting functions. As far as i understood, I can select any of the points in my domain as a point corresponding to one of the Gauss point (say of 5X5 matrix points), and then can use co-ordinate transformation to select the other points. What happens however, if the other points are outside the domain? How can I select the points then? Is there some rule to fix the points according to my domain? Thanks, Dhruv

 September 21, 2011, 16:47 #2 Senior Member   Mirko Vukovic Join Date: Mar 2009 Posts: 159 Rep Power: 10 You can set those values to zero. But that might compromise the accuracy of the Gaussian quadrature: it is exact for a polynomial of degree 2n and below. How well is your data represented by a polynomial if some of it is identically zero? Probably not so good.

September 22, 2011, 02:42
#3
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supercommandodhruv
Join Date: Sep 2011
Posts: 57
Rep Power: 8
Quote:
 Originally Posted by mirko You can set those values to zero. But that might compromise the accuracy of the Gaussian quadrature: it is exact for a polynomial of degree 2n and below. How well is your data represented by a polynomial if some of it is identically zero? Probably not so good.
Hi Mirko,

Thanks for the reply. However, I did not fully understand your explanation. What do you mean when you say some of it is identically zero? I am attaching here the geometry, the cut and the region where I have the computation results. I want to set some points (say a 4 X 4 array) and find out the volume flow. How can I find a polynomial which can represent my data points?
Attached Images
 geometry.jpg (13.1 KB, 23 views) geometryslice.jpg (17.3 KB, 16 views) region.jpg (15.7 KB, 25 views)

September 22, 2011, 08:56
#4
Senior Member

Mirko Vukovic
Join Date: Mar 2009
Posts: 159
Rep Power: 10
Quote:
 Originally Posted by dhruv Hi Mirko, Thanks for the reply. However, I did not fully understand your explanation. What do you mean when you say some of it is identically zero? I am attaching here the geometry, the cut and the region where I have the computation results. I want to set some points (say a 4 X 4 array) and find out the volume flow. How can I find a polynomial which can represent my data points?
I misunderstood. I thought your region might be non-rectangular, and thus a 4x4 array of points would extend outside of it.

As for your problem, I have two suggestions:
- use an OF post-processing utility. I have never done this one, but search the forum for integrating fluxes over patches.
- Extract the points, and use a trapezoidal or a Romberg integration.

I don't think Gaussian quadratures are of much help here, as they require nodes at specific locations. That will force you to interpolate the flux to those locations, and then you face the question of how do you interpolate.

Finally, when I think about it, since this is a finite volume method, the flux is constant across a cell (at least in orthogonal meshes). Thus the self-consistent way of getting the total flux is to add the fluxes of all the cells on a patch.

Mirko

September 26, 2011, 04:59
Gau
#5
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supercommandodhruv
Join Date: Sep 2011
Posts: 57
Rep Power: 8
Quote:
 Originally Posted by mirko I misunderstood. I thought your region might be non-rectangular, and thus a 4x4 array of points would extend outside of it. As for your problem, I have two suggestions: - use an OF post-processing utility. I have never done this one, but search the forum for integrating fluxes over patches. - Extract the points, and use a trapezoidal or a Romberg integration. I don't think Gaussian quadratures are of much help here, as they require nodes at specific locations. That will force you to interpolate the flux to those locations, and then you face the question of how do you interpolate. Finally, when I think about it, since this is a finite volume method, the flux is constant across a cell (at least in orthogonal meshes). Thus the self-consistent way of getting the total flux is to add the fluxes of all the cells on a patch. Mirko
Thanks Mirko.. I got the required results by the OF post processing utility.