CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > OpenFOAM

Gauss Quadrature points

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Display Modes
Old   September 21, 2011, 03:04
Red face Gauss Quadrature points
  #1
Member
 
supercommandodhruv
Join Date: Sep 2011
Posts: 57
Rep Power: 5
dhruv is on a distinguished road
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
dhruv is offline   Reply With Quote

Old   September 21, 2011, 16:47
Default
  #2
Senior Member
 
Mirko Vukovic
Join Date: Mar 2009
Posts: 159
Rep Power: 8
mirko is on a distinguished road
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.
mirko is offline   Reply With Quote

Old   September 22, 2011, 02:42
Default Gaussian Quadrature
  #3
Member
 
supercommandodhruv
Join Date: Sep 2011
Posts: 57
Rep Power: 5
dhruv is on a distinguished road
Quote:
Originally Posted by mirko View Post
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
File Type: jpg geometry.jpg (13.1 KB, 19 views)
File Type: jpg geometryslice.jpg (17.3 KB, 14 views)
File Type: jpg region.jpg (15.7 KB, 19 views)
dhruv is offline   Reply With Quote

Old   September 22, 2011, 08:56
Default
  #4
Senior Member
 
Mirko Vukovic
Join Date: Mar 2009
Posts: 159
Rep Power: 8
mirko is on a distinguished road
Quote:
Originally Posted by dhruv View Post
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
mirko is offline   Reply With Quote

Old   September 26, 2011, 04:59
Default Gau
  #5
Member
 
supercommandodhruv
Join Date: Sep 2011
Posts: 57
Rep Power: 5
dhruv is on a distinguished road
Quote:
Originally Posted by mirko View Post
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.
dhruv is offline   Reply With Quote

Reply

Tags
gauss quadrature, weighting functions

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Problem in fvschemes divSchemes cannot use Gauss linearUpwind nico765 OpenFOAM Bugs 27 June 3, 2014 05:29
please help me which solver is better for my application Ger_US OpenFOAM 8 January 8, 2013 13:29
Submarine with SimpleFoam alex_rubel OpenFOAM 20 February 25, 2011 07:34
solution diverges when linear upwind interpolation scheme is used subash OpenFOAM 0 May 29, 2010 01:23
BlockMeshmergePatchPairs hjasak OpenFOAM Native Meshers: blockMesh 11 August 15, 2008 07:36


All times are GMT -4. The time now is 04:08.