High order relaxation

Techies · August 3, 2022, 11:35

Hi guys,
I'm reading about high order relaxation but i don't understand how it works. Can anyone explain me what is phi intermediate and what is the term which the high order relaxation is applied ? Thanks

sbaffini · August 3, 2022, 12:33

phi_intermediate is the value that phi would have taken if relaxation was not present.

The explanation in the manual is not extra clear, but the idea is that the factor f multiplies the so called "deferred-correction" terms, which are those that switch a first order scheme to a high order one.

They appear as source terms on the RHS in the equations. When f is 0 the scheme stays first order, when f is 1 it is high order (trough deferred correction), values inbetween imply some relaxation of the high order part, as we have a factor f between 0 and 1 that multiplies a typically non benign source term.

arjun · August 3, 2022, 13:03

it just saying that the change is slowly added. This is very old way of doing things (For example older version of fluent did this). Nowadays we directly put the higher order values and under-relax the linear system so that the change is under control.

Techies · August 3, 2022, 21:31

So it's like a fraction of new gradient term inside high order scheme, right ?
phi face = phi cell + anpha*gradient(phi)*x with anpha=old gradient+f( calc gradient-old gradient)

sbaffini · August 4, 2022, 07:59

I haven't coded it myself, nor I use deferred correction in the form typically presented (I use a density based solver in delta form), but the overall effect is indeed similar to the gradient limiting.

But I wouldn't make too much similarities nor mix things up in the programming. Especially in the classical deferred correction approach, the term multiplies a cell term on the RHS, which happens to be just the high order part of the flux.

August 3, 2022, 12:33		#2
sbaffini Senior Member Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,151 Blog Entries: 29 Rep Power: 39	phi_intermediate is the value that phi would have taken if relaxation was not present. The explanation in the manual is not extra clear, but the idea is that the factor f multiplies the so called "deferred-correction" terms, which are those that switch a first order scheme to a high order one. They appear as source terms on the RHS in the equations. When f is 0 the scheme stays first order, when f is 1 it is high order (trough deferred correction), values inbetween imply some relaxation of the high order part, as we have a factor f between 0 and 1 that multiplies a typically non benign source term. Techies and JasmineFeng like this.

August 3, 2022, 13:03		#3
arjun Senior Member Arjun Join Date: Mar 2009 Location: Nurenberg, Germany Posts: 1,272 Rep Power: 34	it just saying that the change is slowly added. This is very old way of doing things (For example older version of fluent did this). Nowadays we directly put the higher order values and under-relax the linear system so that the change is under control. Techies likes this.

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Why use high order schemes?	aerosayan	Main CFD Forum	18	January 11, 2021 09:48
SimpleFoam high order schemes	vcvedant	OpenFOAM Running, Solving & CFD	2	September 19, 2017 11:38
Software to mesh using high order element with unevenly spaced interpolation node	lzhaok6	Mesh Generation & Pre-Processing	4	August 14, 2016 00:01
lduMatrix problem in High order scheme	rxgrch	OpenFOAM Programming & Development	3	April 2, 2013 10:30
High order difference scheme for KIVA3v2???	LiQiang	Main CFD Forum	1	May 9, 2005 13:50

August 3, 2022, 21:31		#4
Techies Member Mercurial Join Date: Mar 2021 Posts: 72 Rep Power: 5	So it's like a fraction of new gradient term inside high order scheme, right ? phi face = phi cell + anphagradient(phi)x with anpha=old gradient+f( calc gradient-old gradient)

August 4, 2022, 07:59		#5
sbaffini Senior Member Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,151 Blog Entries: 29 Rep Power: 39	I haven't coded it myself, nor I use deferred correction in the form typically presented (I use a density based solver in delta form), but the overall effect is indeed similar to the gradient limiting. But I wouldn't make too much similarities nor mix things up in the programming. Especially in the classical deferred correction approach, the term multiplies a cell term on the RHS, which happens to be just the high order part of the flux.