
[Sponsors] 
Convergence criteria for pressure correction method solving Unsteady NS equtions 

LinkBack  Thread Tools  Display Modes 
March 7, 2013, 03:24 
Convergence criteria for pressure correction method solving Unsteady NS equtions

#1 
Member
Osman
Join Date: Oct 2012
Location: Japan
Posts: 51
Rep Power: 4 
I am using a pressure correction method for solving Unsteady NavierStokes equations, i want to know what is the convergence criteria i have to use for every time step.


March 7, 2013, 04:49 

#2  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,642
Rep Power: 23 
Quote:
Convergence must imply that you fulfill the divergencefree constraint (at some tolerance). 

March 7, 2013, 04:57 

#3 
Member
Osman
Join Date: Oct 2012
Location: Japan
Posts: 51
Rep Power: 4 
So, for example, the maximum cell value in the Divergence matrix must be less than 1e6 for a time step!!!
what is the criteria for this value i.e 1e6 ?? what if the maximum cell value in the Divergence matrix is not satisfying this condition ?? which equations i have to iterate in the same time step?? 

March 8, 2013, 19:50 

#4 
Member
Osman
Join Date: Oct 2012
Location: Japan
Posts: 51
Rep Power: 4 
Any reply?


March 9, 2013, 13:15 

#5 
Senior Member
Lefteris
Join Date: Oct 2011
Location: UK, Greece
Posts: 187
Rep Power: 5 
What you ask is not very clear, at least to me. I will refer you again to Ferziger and Peric's book "computational methods for fluid dynamics", pages 124127.
__________________
Lefteris 

March 9, 2013, 20:24 

#6 
Member
Osman
Join Date: Oct 2012
Location: Japan
Posts: 51
Rep Power: 4 
I am not talking about the convergence criteria of poisson Eq. solver.
I am talking about the convergence criteria for one unsteady time step. I think the answer of Filippo Maria Denaro is correct. however, what i want to know if i am using a staggered grid, then: (for example) U matrix will be 100x99 cells V matrix will be 99x100 cells the Divergence matrix will be 100x100 So what i want to know: 1 Is the cell with with the maximum value in comparison with all other cells in the divergence matrix must be less than the tolerance we assume? 2 how can we decide the value of the tolerance? 3 Do I have to iterate all the equations i attach in the 1st post to reach to the required tolerance? 4 Isn't these iterations means that i am going forward in time although i am doing iteration for the same time step ? 

March 10, 2013, 06:46 

#7 
Senior Member
andy
Join Date: May 2009
Posts: 129
Rep Power: 8 
If you wish to iterate out the nonlinearity in the momentum equation I would suggest using a different scheme which includes an estimate of the u^n+1 value in the differencing of the convection terms. Including the diffusion terms implicitly in the momentum equation is normally done primarily for reasons of stability not accuracy. If the diffusion number remains stable it would be more efficient to use a fully explicit momentum equation. In practice a tight tolerance on the diffusion terms which are by definition small in high Reynolds number flows is unlikely to be worth the computational cost so long as the linear solver is one that gives reasonable values with a few steps.
The solution of the pressure related quantity is going to take most of the computational time and so one tends to use a larger tolerance during any settling down phase and tighten it during the accurate phase. Some have put forward the view that the residual errors from not fully solving the Poisson equation only need to be significantly less than the truncation error. Although one can see where this is coming from, small violations in continuity have a long history in destabilising flows and causing problems at boundaries (boundary conditions for schemes using pressure related quantities like your phi also need care). Perhaps the simplest thing to do is to perform a representative simulation with the Poisson equation solved into roundoff and then repeat with looser tolerances and look at what changes. 

Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Moving mesh  Niklas Wikstrom (Wikstrom)  OpenFOAM Running, Solving & CFD  122  June 15, 2014 06:20 
transsonic nozzle with rhoSimpleFoam  Unseen  OpenFOAM Running, Solving & CFD  7  April 16, 2014 03:38 
pisoFoam with kepsilon turb blows up  Some questions  Heroic  OpenFOAM Running, Solving & CFD  26  December 17, 2012 04:34 
High Courant Number @ icoFoam  Artex85  OpenFOAM Running, Solving & CFD  9  January 3, 2012 09:06 
Parallel rasInterFoam  openfoam_user  OpenFOAM Running, Solving & CFD  4  November 1, 2008 05:14 