
[Sponsors] 
October 16, 2015, 15:41 
Split the load of the Buoyancy Source term

#1 
New Member
Marcel
Join Date: Oct 2015
Posts: 7
Rep Power: 8 
I am testing currently a 2d incompressible code with natural convection in a square cavity. To include the natural convection part I implemented the Boussinesq approach, indicating the addition of the source in the NSy.
As of right now I am using the SIMPLE algorithm for pressurevelocity coupling and the code seems to be working fine, for lower Rayleigh numbers. On higher Rayleigh numbers however (Ra>1e5) the convergence is tediously slow, or not converging at all. I have some ideas to handle this, but they don't include any charming solutions, and I don't want to indefinitely underrelaxate my variables. I was thinking now, maybe it is possible to linearize the source term in such a way that I divide the load of the source term in my NSy, by solving it partly explicitly and implicitly, depending on linearization of the source term. As of right now, I handle Picard's method (S = Sc + SpTp), where Sc determines completely my natural convection and thus Sp=0 and thus solving the natural convection completely explicitly. Now I would like to find out if it is possible to reduce the load on Sc by incorporating a part of the load in Sp to come up with the same solution and by that solving partly implicitly. The idea behind is that I would like to obtain a more diagonal dominant system matrix, as the source term right now is pulling it out of balance. It should contribute to more stability, although it would probably not contribute to a faster convergence. Anyone knows if this even is possible? Or has any experience with it? I would really like to find out. Any literature on this would be welcome too. 

October 16, 2015, 16:03 

#2 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,041
Rep Power: 64 
high Ra number flows becomes transitional, the fact you don't get a steady solution is coherent to the physics of the problem.


October 16, 2015, 16:21 

#3 
New Member
Marcel
Join Date: Oct 2015
Posts: 7
Rep Power: 8 
although I understand that its not that black and white but the transition zone is usually close to Ra~1e9 and I run simulations up to a Rayleigh of 1e8, still in the 'laminar' regime.


October 16, 2015, 16:54 

#4  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,041
Rep Power: 64 
Quote:
yes, authors still consider laminar the flow at Ra=10^8, but also if the flow is laminar, the breakdown of the single flow structure happens at Ra=10^6 and if you run an unsteady simulation you will clearly see the onset of minor structures. Reaching an equilibrium state at such configuration need a very long time and small oscillations still are present in the small structures. A very refined grid is required to allow dissipation to act. Therefore, running a steady equation system and getting no convergence to steady solution, can be at high Ra number a physical indicator 

October 17, 2015, 19:27 

#5 
New Member
Marcel
Join Date: Oct 2015
Posts: 7
Rep Power: 8 
ok granted that it would be a physical problem, would I be able to 'cheat' by using a first order spatial interpolation scheme, like the first order upwind, to find a steadystate solution covered with artificial numerical diffusion and then use a higher order interpolation scheme to calculate a more reasonable solution?
and out of curiosity, still the question remains of splitting the load in the source term? Anyone knows if this is possible? And/or has some literature on it? 

October 18, 2015, 03:21 

#6  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,041
Rep Power: 64 
Quote:
well, if you use the trick of a strong dissipative scheme like firstorder scheme your steady solution will be simply not accurate and you cannot recover the accuracy by a successive interpolation... furthermore, the Bousinnesq model is already based on a linear expansion... 

October 18, 2015, 10:51 

#7 
New Member
Marcel
Join Date: Oct 2015
Posts: 7
Rep Power: 8 
ok thanks sir!
and my code is indeed converging for a finer grid, but yeah, i need a lot of patience to finally be able to postprocess Also, I am aware the source term is linearized... excuse me, perhaps I am slow in understanding but does that really answer the question? I simly want to try to incorporate a part of the buoyancy load directly into the discretized equations and by that reducing the impact of the explicit source term. I will probably try to incorporate it one of these days to see if it is possible, but I just wanted to read a little bit before starting doing it. 

Tags 
boussinesq approximation, cavity flow, code testing, picard's method, source term 
Thread Tools  Search this Thread 
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
[swak4Foam] difficulties installing swak4foam  newbie29  OpenFOAM Community Contributions  117  June 16, 2021 03:11 
centOS 5.6 : paraFoam not working  yossi  OpenFOAM Installation  2  October 9, 2013 01:41 
friction forces icoFoam  ofslcm  OpenFOAM  3  April 7, 2012 10:57 
pisoFoam compiling error with OF 1.7.1 on MAC OSX  Greg Givogue  OpenFOAM Programming & Development  3  March 4, 2011 17:18 
DxFoam reader update  hjasak  OpenFOAM PostProcessing  69  April 24, 2008 01:24 