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Old   March 21, 2002, 23:31
Default how to calculate derivatives
  #1
Senthil
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Hi,

I need to get second derivative and fourth derivative of velocity and temperature. Are these quantities available directly from fluent macros. If not, then I have to use finite difference formula to calculate these derivatives. My problem is that I dont know in which order the cell variables are stored. How do I calculate these derivatives then?.

Thank you,

Senthil
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Old   March 22, 2002, 07:27
Default Re: how to calculate derivatives
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Greg Perkins
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You'll probably have to write udfs for this...

First derivatives are available as macros, eg. C_U_G(c,t)[d] gives the derivative of the U velocity in the dth co-ordinate direction.

You can apply these successively to obtain higher derivatives....by copying into a UDS.

However, I've never been too clear on exactly how these are calculated. In fact I found that when I wanted to calculate the face flux for diffusion, ie q = kdthi/dx using the above macros gave incorrect results and I ended up re-applying an upwind scheme to calculate the correct flux.

I think they are defined at the centre of the cell, which might be ok for your application, but you might need to be careful if accuracy is required...

Greg
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Old   March 22, 2002, 23:44
Default Re: how to calculate derivatives
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Senthil
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Hi Greg,

Thanks..

I assume UDS mean, user defined scalar. When I went through the fluent manual, I found out that if I define a UDS, it always try to solve a transport equation for that scalar. How can I make it calculate derivative. Could you tell me how you calculated dthi/dx. May be I could write udf by the same algorithm to calcualte higher derivatives.

Thank you Senthil
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Old   March 23, 2002, 00:32
Default Re: how to calculate derivatives
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Greg Perkins
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You can switch off solving a UDS in the solve/control panel.

I used a simple scheme (first-order) based on neighbouring cell data. You will need to loop over cell faces to get the neighbouring cells to calculate the derivative in this manner...

Greg
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Old   March 25, 2002, 11:53
Default Re: how to calculate derivatives
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keith
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Greg, I was wondering if you've calculated higher order derivatives (2nd and above) in the manner you describe. I used a similar approach to calculate 2nd derivatives of the velocity field, but I found the result to be very "noisy", especially on unstructured grids. With smoothing, I can get something usable, but still not great. Have you run into this and do you have any suggestions for improving it?

Regards,

Keith
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Old   March 26, 2002, 21:41
Default Re: how to calculate derivatives
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Greg Perkins
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I found even the C_UDSI_G etc derivatives weren't very good when compared to derivatives calculated at the faces using the approrpiate discretization scheme. I think this is partly because I'm not completely sure how these macros are defined. That's why I wasn't too keen on using them. The udf manual doesn't mention the definition, does it?

I haven't tried high-order schemes. I think increasing noise is common when taking derivatives - but I'm not up with what additional smoothing, adjustments etc are best to make. There's probably some literature on this, or see if Fluent can help....

Greg
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