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March 7, 2012, 09:58 
Convergence

#1 
New Member
Join Date: Mar 2011
Posts: 11
Rep Power: 7 
hi this may sound crazy. im dealing with modifying an equipment so have simulate more than 50 models to determine the most suitable geometry. some get converged and some models do not converge. the non converged model residuals reach nearly 0.002 and then remain in that value (i was expecting to get a tolerance of 0.001). Since the residual value reamain in a constant value, can i consider them as converged and accurate? do i have to change the cell size and obtain a lesser tolerance value?


March 8, 2012, 07:53 

#2 
Member

Instead of looking at residuals, better to monitor a quantity like mass flow rate or pressure at any point in the domain .. that would be more appropriate


March 8, 2012, 14:30 

#3 
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Join Date: Mar 2011
Posts: 11
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thanx Naren. you mean monitored values at reference location? well the graphs of moniterd values(u,v,w momentum, presure and temperature) will simply become a straight line after some iterations. does that mean it accurate? or other wise do we have to verify those values experimentally?


March 8, 2012, 23:24 

#4 
Member

If the curves become straight, (after running in second order also), we can say that the solution is converged and that is the final result.
As a second check check the mass balance also. It should be near to zero. 

March 13, 2012, 05:01 

#5 
Member

Hi,
If the residuals remian constant and don get close near the error u determined,then u are gonna have to refine your mesh, decrease the Y+ near walls or change the solver. If you are runing an unsteady simulation, then check the time step. high values of time steps could increas the CFL number and the residuals do not converge. best, 

March 13, 2012, 17:12 

#6 
Senior Member

There can be several reasons for a simulation not converging. As you are dealing with an optimization (i really hope you are not doing this by hand), the most probable issue is that the configurations not converging are determining some criticalities like the grid getting "weird" or the fluid dynamics becoming intrinsically unstable (i'm assuming you are doing a steady analysis).
In the general case is also possible that you need to relax the solver during its trip to convergence. However, i don't see the point in the difference between 1e3 and 2e3 in the residuals, they seem both high to me. As someone already did, i suggest you to check on the mass imbalance of your simulation. However, this is not conclusive. Visual inspection of the non converged solution could give additional details. In the very ending, i think that non converged solution shouldn't be used in numerical optimization routines and this usually requires a modification on the limits for the design variables 

March 14, 2012, 21:39 
About convergence...

#7 
Senior Member
Arjun
Join Date: Mar 2009
Location: Nurenberg, Germany
Posts: 501
Rep Power: 13 
Last 23 days I have been trying to understand sources of errors on unstructured grids and how to improve their accuracy. Not that it is something new or done for first time but I wish to make my code more accurate and so it was natural to try this.
Second reason for looking into this was that I had problems with calculations with very large viscosity. When I say problems I do not mean that it diverges but it seems to be converging to a solution which is not right. This behavior was noticed in some of the meshes but not all of them. So this is what I did. I took a pipe and created various grids on it. Same dimensions but various meshes of different size (few thousands to 1.6 million cells). Further tried all tetra, prisms and hexa meshes (with slight skew since it is pipe ). For this pipe using power law I know theoretical solution. Note that viscosity varies from say 100 till 1E12 in this case. I put theoritical velocity and pressure on cell centers and apply discretization and seek the errors. If someone to say that this solution is converged solution then there shall be no errors. After all this is theorical solution that is present on this grid cells. But it does not work quite this nice. If there is some skew then there exists errors. That is Left hand side NOT EQUAL to right hand side after descretization. If meshes have all well behaved hexa cells then error is very very low. The following are conclusions based on this excersize assuming that there exists some not so nice cells in mesh (which is usually the case): 1. If your solutions converged to machine precision ie 1E20 or so then it is very likely to be not the correct solution. Strange thing to say but you see when exact solution was descretised on that grid it showed errors so any solution that does not show those errors after discretization shall be other than the correct one. 2. If your solution converged to a state where there exists some errors and residual refuse to fall below certain values. Then it could be better solution than type 1. This is because theoritical solution does show some errors that refuse to go away. But it shall be noted that there is no guarantee of it to be the true solution. 

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