# Calculation of Derivatives in Unstructured grids

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 May 18, 2003, 15:25 Calculation of Derivatives in Unstructured grids #1 Dayton Guest   Posts: n/a 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

 May 19, 2003, 01:55 Re: Calculation of Derivatives in Unstructured gri #2 Linfeng BI Guest   Posts: n/a 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

 May 20, 2003, 02:40 Re: Calculation of Derivatives in Unstructured gri #3 xing zhang Guest   Posts: n/a You can use Gauss-Green formula to calculate the gradient or you can use Least-Square method. From my experience, Least-Square is better!

 May 20, 2003, 07:45 Re: Calculation of Derivatives in Unstructured gri #4 Tom Guest   Posts: n/a 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

 May 20, 2003, 07:52 Re: Calculation of Derivatives in Unstructured gri #5 Praveen Guest   Posts: n/a 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 homepage.

 May 20, 2003, 13:03 Re: Calculation of Derivatives in Unstructured gri #6 Apurva Guest   Posts: n/a Hi, I have information about Least Square, but tell me where to find information about Gauss-Green method. Thanks

 May 20, 2003, 21:40 Re: Calculation of Derivatives in Unstructured gri #7 xing zhang Guest   Posts: n/a 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.

 June 20, 2003, 13:38 Re: Calculation of Derivatives in Unstructured gri #8 Ravi Guest   Posts: n/a 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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