The detail of the Fourth order, least squares scheme

ztdep · October 17, 2019, 02:00

Dear friends:
In OpenFOAM, there is a "Fourth order, least squares scheme" for the gradient computation.

Could you please give me some references about this.
Regards

hjasak · October 18, 2019, 12:45

Yes. If you take field values in cell neighbours, you can fit a second order function - either for gradient evaluation or interpolation.

If you take neighbouring values AND gradients, you can fit a fourth order function.

Hope this helps,

Hrv

P. S. The volume and surface integrals are still second order - life is not perfect...

ztdep · October 21, 2019, 08:26

Thank you very much! Could you please give me some reference paper or book. I still cann't get it. I have goolged it but nothing found.

October 17, 2019, 02:00	The detail of the Fourth order, least squares scheme	#1
ztdep Senior Member p ding Join Date: Mar 2009 Posts: 427 Rep Power: 19	Dear friends: In OpenFOAM, there is a "Fourth order, least squares scheme" for the gradient computation. Could you please give me some references about this. Regards

October 18, 2019, 12:45		#2
hjasak Senior Member Hrvoje Jasak Join Date: Mar 2009 Location: London, England Posts: 1,905 Rep Power: 33	Yes. If you take field values in cell neighbours, you can fit a second order function - either for gradient evaluation or interpolation. If you take neighbouring values AND gradients, you can fit a fourth order function. Hope this helps, Hrv P. S. The volume and surface integrals are still second order - life is not perfect... __________________ Hrvoje Jasak Providing commercial FOAM/OpenFOAM and CFD Consulting: http://wikki.co.uk

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October 21, 2019, 08:26		#3
ztdep Senior Member p ding Join Date: Mar 2009 Posts: 427 Rep Power: 19	Thank you very much! Could you please give me some reference paper or book. I still cann't get it. I have goolged it but nothing found.