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-   -   How to compute second derivatives accurarately? (http://www.cfd-online.com/Forums/main/2566-how-compute-second-derivatives-accurarately.html)

 keith September 5, 2000 18:47

How to compute second derivatives accurarately?

Hello Gurus,

I am trying to implement a CFD simulation on an unstructured mesh (FVM) that requires the explicit calculation of a second-derivative to be used in a source term. This is not the second order diffusion term, but I actually need to calculate a number at each cell. The straightforward approach is to use Gauss divergence theorem and some type of technique for interpolating to the cell boundaries, and computing the first derivative for the cell. Then to repeat the process and calculate the second derivative. But this ends up being far too noisy.

Does anyone have any experience with this, or know of some literature about it? Any help is greatly appreciated.

Keith

 Zhou September 7, 2000 04:38

Re: How to compute second derivatives accurarately

You may use the DSC method to get the highly precise value. (see J.Phys, A 33,2000)

 z.zeng September 12, 2000 08:59

Re: How to compute second derivatives accurarately

Hi, Zhou,

It seems very difficult to find your mentioned paper on DSC method by following your supported information. Could you please give more detailed information (e.g. page number) on this paper?

Thanks

 Thomas Wolfanger September 13, 2000 11:25

Re: How to compute second derivatives accurarately

Keith,

I had the same problem with second order derivatives (I needed the velocity for implementing an oldroyd derivative) but I used structured FVM. Applying Gauss two times worked for me, no noise disturbation...

sincerely,

Thomas

 Guoping Xia September 25, 2000 01:43

Re: How to compute second derivatives accurarately

Hi,

I have compared two methods to evaluate the second derivative, one is the Green-Gauss type approach, another is by T. Barth(in an AIAA paper, around 1994). My conclusion is that the later one results in better solution on highly streched grids. It appreas that there is more diffusion like effects in the Green-Gauss approach.

Guoping

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