CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > General Forums > Main CFD Forum

Solving Navier Stokes equations by projection method and predictor-corrector method.

Register Blogs Members List Search Today's Posts Mark Forums Read

Like Tree2Likes
  • 1 Post By zx-81
  • 1 Post By FMDenaro

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   February 9, 2017, 04:47
Default Solving Navier Stokes equations by projection method and predictor-corrector method.
  #1
Senior Member
 
Saideep
Join Date: Apr 2015
Location: INDIA
Posts: 203
Rep Power: 10
Saideep is on a distinguished road
Hi guys;

I am comparing two different CFD packages. OpenFoam and Gerris for studying two phase immiscible flow.

According to OpenFOAM, the Navier Stokes equations are solved using a "Predictor-Corrector" step using PISO loop.

In Gerris, the Navier Stokes equations are solved by a "time splitting Projection" method.

Though from my understanding the summary of both the methods are the same:
1. Using an initial guess of pressure find an intermediate velocity (which considers the viscous and convective terms of present time step) field that is not mass conservative;
2. Using the non-divergent velocity field, update the pressure field by solving "Poissons equation";
3. With known data on the correct pressure for present time step along with intermediate velocity field known update a mass conservative velocity field.

However, I am unable to catch the difference between Chorin's projection method and Issa's PISO loop.

Can anyone help me out?

Thanks;
SaiD
Saideep is offline   Reply With Quote

Old   February 9, 2017, 07:36
Default
  #2
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,041
Rep Power: 64
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Projection methods are based on the Hodge decomposition: in each time step, the intermediate velocity is projected onto the subspace of divergence-free velocity field by solving the Poisson equation. That is solved only once in each time step and is not iterated in "outer" iteration.
FMDenaro is offline   Reply With Quote

Old   February 9, 2017, 08:44
Default
  #3
Member
 
Kaya Onur Dag
Join Date: Apr 2013
Posts: 94
Rep Power: 11
kaya is on a distinguished road
Quote:
Originally Posted by Saideep View Post
Hi guys;

I am comparing two different CFD packages. OpenFoam and Gerris for studying two phase immiscible flow.

According to OpenFOAM, the Navier Stokes equations are solved using a "Predictor-Corrector" step using PISO loop.

In Gerris, the Navier Stokes equations are solved by a "time splitting Projection" method.

Though from my understanding the summary of both the methods are the same:
1. Using an initial guess of pressure find an intermediate velocity (which considers the viscous and convective terms of present time step) field that is not mass conservative;
2. Using the non-divergent velocity field, update the pressure field by solving "Poissons equation";
3. With known data on the correct pressure for present time step along with intermediate velocity field known update a mass conservative velocity field.

However, I am unable to catch the difference between Chorin's projection method and Issa's PISO loop.

Can anyone help me out?

Thanks;
SaiD



have a look at the red ferziger, this is covered in that book and explanations are very easy to get
kaya is offline   Reply With Quote

Old   February 9, 2017, 09:14
Default
  #4
Senior Member
 
Saideep
Join Date: Apr 2015
Location: INDIA
Posts: 203
Rep Power: 10
Saideep is on a distinguished road
Hi Denaro & Kaya;

Thanks for your reply.
PISO is an iterative approach (we specify number of pressure correction). The more corrections we make for Pressure the more accurate the divergence free flux we get.

Unlike, Projection is a single step method with pressure fixed upon reaching suitable specified tolerance limit. (I am not well versed by Hodge decomposition but I understand the velocity is decomposed into a divergence free term which we are interested in and a pressure term. What I understood from Wiki)

So, to conclude: Projection method = 1 PISO loop. Then, is PISO a more powerful approach to get a better conservative flux if both the methods have a fixed tolerance limit set by me.

Thanks Kaya I will have a look right now.

SaiD
Saideep is offline   Reply With Quote

Old   February 9, 2017, 11:39
Default
  #5
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,041
Rep Power: 64
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Well, more in details, we call Exact projection method when in a single step the divergence-free constraint is satisfied up to machine accuracy while the Approximate projection method is satisfied only up to the order of the local truncation error.
However, since the Hodge decomposition is well posed setting only one boundary condition, any projection method suffers from an approximation in the setting of the tangential condition.

On the other hand, PISO as well as other coupled method iterate continuity and momentum until the desired convergence is reached.
FMDenaro is offline   Reply With Quote

Old   February 10, 2017, 17:31
Default
  #6
Member
 
Bernd
Join Date: Jul 2012
Posts: 40
Rep Power: 11
zx-81 is on a distinguished road
Quote:
Originally Posted by FMDenaro View Post
while the Approximate projection method is satisfied only up to the order of the local truncation error.
As the OP mentioned the Gerris package it's worth noting that Gerris also uses an approximate pressure correction because approximate corrections can be stably used with co-located, i.e. non-staggered velocity grids which in turn allows for more efficient implementation of the adaptive, octree based grid structure.
FMDenaro likes this.
zx-81 is offline   Reply With Quote

Old   February 10, 2017, 17:43
Default
  #7
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,041
Rep Power: 64
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by zx-81 View Post
As the OP mentioned the Gerris package it's worth noting that Gerris also uses an approximate pressure correction because approximate corrections can be stably used with co-located, i.e. non-staggered velocity grids which in turn allows for more efficient implementation of the adaptive, octree based grid structure.
Yes, the original nature of the APM is for colocated grid with compact stencil for the pressure equation but it can be extended easily to general unstructured grids. However, an EPM can be implemented on non-staggered grids, too.
FMDenaro is offline   Reply With Quote

Old   February 10, 2017, 18:10
Default
  #8
Member
 
Bernd
Join Date: Jul 2012
Posts: 40
Rep Power: 11
zx-81 is on a distinguished road
Quote:
Originally Posted by FMDenaro View Post
However, an EPM can be implemented on non-staggered grids, too.
That sounds interesting as it was my impression that any non-staggered grid scheme is supposed to be vulnerable to pressure instabilities/oscillations when using the exact, i.e. non-compact stencil. The only 'work-arounds' I heard of so far are the approximate correction APM and "Rhie Chow"-like interpolation schemes ...

In my personal experience I have found that the APM is stable and only shows small divergence errors in the highest frequencies (wave numbers) of the solution but over all the computed flow is practically indistinguishable from the solution obtained via exact pressure projection.

However, severe pressure oscillations did appear with the APM derived pressure when used with the itarativ pressure correction method (i.e. when one solves the poisson equation not for the pressure but for a pressure increment )
zx-81 is offline   Reply With Quote

Old   February 10, 2017, 18:19
Default
  #9
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,041
Rep Power: 64
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by zx-81 View Post
That sounds interesting as it was my impression that any non-staggered grid scheme is supposed to be vulnerable to pressure instabilities/oscillations when using the exact, i.e. non-compact stencil. The only 'work-arounds' I heard of so far are the approximate correction APM and "Rhie Chow"-like interpolation schemes ...

In my personal experience I have found that the APM is stable and only shows small divergence errors in the highest frequencies (wave numbers) of the solution but over all the computed flow is practically indistinguishable from the solution obtained via exact pressure projection.

However, severe pressure oscillations did appear with the APM derived pressure when used with the itarativ pressure correction method (i.e. when one solves the poisson equation not for the pressure but for a pressure increment )

Yes, some years ago I worked a lot on this issue ... The APM produced some of these problems in my LES code and I wanted not to use the RC-interpolation to not introduce artificial dissipation. Thus, I developed an exact double-projection method that works on non-staggered grid. I had good and oscillation-free solutions without adding dissipation. The general idea can be implemented also on triangular (tetraedra in 3d) unstructured grids. If you are interested, you can find a couple of my published papers on IJNMF
mprinkey likes this.
FMDenaro is offline   Reply With Quote

Old   February 13, 2017, 08:16
Default
  #10
Senior Member
 
Michael Prinkey
Join Date: Mar 2009
Location: Pittsburgh PA
Posts: 363
Rep Power: 23
mprinkey will become famous soon enough
Quote:
Originally Posted by FMDenaro View Post
Yes, some years ago I worked a lot on this issue ... The APM produced some of these problems in my LES code and I wanted not to use the RC-interpolation to not introduce artificial dissipation. Thus, I developed an exact double-projection method that works on non-staggered grid. I had good and oscillation-free solutions without adding dissipation. The general idea can be implemented also on triangular (tetraedra in 3d) unstructured grids. If you are interested, you can find a couple of my published papers on IJNMF
I'm looking forward to reading those papers, Professor. I have never liked using RC for the reasons you cite.
mprinkey is offline   Reply With Quote

Old   February 13, 2017, 10:29
Default
  #11
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,041
Rep Power: 64
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by mprinkey View Post
I'm looking forward to reading those papers, Professor. I have never liked using RC for the reasons you cite.

we are discussing here:

double-projection method that works on non-staggered grid
FMDenaro is offline   Reply With Quote

Reply

Tags
navier stoke solver, piso, projection method

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Foam::error::PrintStack almir OpenFOAM Running, Solving & CFD 90 October 3, 2019 07:01
Projection method and mesh free Rime Main CFD Forum 7 June 15, 2015 14:43
New sixDoFRigidBody BC working with laplaceFaceDecomposition Ya_Squall2010 OpenFOAM Running, Solving & CFD 13 April 17, 2013 02:04
help: I am trying to solve Navier Stokes compressible and viscid flow Jose Choy Main CFD Forum 2 May 18, 2000 05:45
Laplace or Stokes equations solver by Boundary Elements Method Lemonnier Main CFD Forum 3 December 28, 1999 13:48


All times are GMT -4. The time now is 22:41.