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Calculation of Derivatives in Unstructured grids

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Old   May 18, 2003, 15:25
Default Calculation of Derivatives in Unstructured grids
  #1
Dayton
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Hi,

I am looking for calculation of derivatives (du/dx, du/dy etc.) used for viscous flux calculation. Please provide insight on the methods used and literature.

Thanks and regards
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Old   May 19, 2003, 01:55
Default Re: Calculation of Derivatives in Unstructured gri
  #2
Linfeng BI
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There is a paper that may help.

J.C.Campbell et al, Mimetic finite difference operators for second-order tensors on unstructured grids, Computers and Mathematics with Applications 44 (2002) 157-173.

Linfeng
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Old   May 20, 2003, 02:40
Default Re: Calculation of Derivatives in Unstructured gri
  #3
xing zhang
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You can use Gauss-Green formula to calculate the gradient or you can use Least-Square method. From my experience, Least-Square is better!
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Old   May 20, 2003, 07:45
Default Re: Calculation of Derivatives in Unstructured gri
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Tom
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Hi there, can you explain the least square aproach please or provide references to its explanation. Why is it better than Gauss? Thank you Tom
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Old   May 20, 2003, 07:52
Default Re: Calculation of Derivatives in Unstructured gri
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Praveen
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I have used least squares extensively but not the Gauss technique. For least squares see the VKI lecture notes of TJ Barth. They are available for download on his <a href=http://people.nas.nasa.gov/~barth/home.html>homepage</a>.
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Old   May 20, 2003, 13:03
Default Re: Calculation of Derivatives in Unstructured gri
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Apurva
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Hi,

I have information about Least Square, but tell me where to find information about Gauss-Green method.

Thanks
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Old   May 20, 2003, 21:40
Default Re: Calculation of Derivatives in Unstructured gri
  #7
xing zhang
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These formulas can be found in VKI lectures. You can also read the papers by Demirdzic et al.: Comput. Methods Appl. Mech. Engrg. 125(1995) 235-255

or the book by Peric: Computational Methods for Fluid Dynamics.

I think the reason why Gauss method is worse since we can not approximate the value on the faces on the CV accurately. If you do it in an iterative manner, this method is equally good as the Least Square Method. I think the explanation is also written in Peric's book.

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Old   June 20, 2003, 13:38
Default Re: Calculation of Derivatives in Unstructured gri
  #8
Ravi
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Hi

Go to FUN2D/3D home page. I guess, a google search will take you there. Go to their publications page and download the paper "An Implicit Upwind Algorithm for Computing Turbulent Flows on unstructured grids" by W. Kyle Anderson and Daryl L. Bonhaus.

They explain how to evaluate the gradients for Least Squares and Gauss Gradients. I prefer a weighted Least Squares for viscous computations.

Ravi
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