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: 434 Rep Power: 20	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: 1,907 Rep Power: 34	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

Thread Tools	Search this Thread
Show Printable Version Email this Page	Search this Thread: Advanced Search
Display Modes
Linear Mode Switch to Hybrid Mode Switch to Threaded Mode

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
2nd order Upwind Scheme (FDM)	jd87	Main CFD Forum	5	March 20, 2019 12:01
2nd order TVD scheme	Wenjun	Main CFD Forum	8	March 14, 2013 12:31
Do we really have a fourth order scheme?	ville	Main CFD Forum	13	November 5, 2012 06:31
Error with higher order (2nd, GAMMA) upwind scheme	quarkz	Main CFD Forum	0	September 24, 2012 03:02
How to compute UDS fourth order gradient	Emma66	FLUENT	1	April 27, 2010 05:44

October 21, 2019, 08:26		#3
ztdep Senior Member p ding Join Date: Mar 2009 Posts: 434 Rep Power: 20	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.