[taalf]

Hi everybody,

I apology if this was already asked and answered but I didn't find any precise info about this here.

As everybody knows, the "Initial residuals" are those at which we should look to check convergence. I mean... of course it's not sufficient to check it but clients like to have somewhere a residual history plot.

For such charts, I always plot "Initial residuals". Now, the question is that when one uses correctors there can be several "Initial residuals" in a single "outer" iteration.

For example:

GAMG: Solving for p, Initial residual = 0.571166, Final residual = 0.011325, No Iterations 1
GAMG: Solving for p, Initial residual = 0.0176414, Final residual = 0.00164592, No Iterations 1
GAMG: Solving for p, Initial residual = 0.00263673, Final residual = 0.000137864, No Iterations 2

The question is: honestly, which value to plot? The first or the last one?

Of course, the last one looks better But I have some doubt if this is the most suitable to demonstrate convergence of the computation.

What do you think (or know) about that?

Thanks for replies!

Best regards,

[blais.bruno]

If you are looking to check if you have reached a converged steady solution, the first residual should be plotted. This residual means the "residual" when you begun solving this iteration. The other residual are only changed because of the updates in the pressure-correction scheme (PISO or whatever) and thus don't integrate the full non-linearity of the problem.

If you really wish to see if your problem has converged, the first residual should be as low as possible (1-e4 is a minimum IMO)

Originally Posted by taalf

Hi everybody,

I apology if this was already asked and answered but I didn't find any precise info about this here.

As everybody knows, the "Initial residuals" are those at which we should look to check convergence. I mean... of course it's not sufficient to check it but clients like to have somewhere a residual history plot.

For such charts, I always plot "Initial residuals". Now, the question is that when one uses correctors there can be several "Initial residuals" in a single "outer" iteration.

For example:

GAMG: Solving for p, Initial residual = 0.571166, Final residual = 0.011325, No Iterations 1
GAMG: Solving for p, Initial residual = 0.0176414, Final residual = 0.00164592, No Iterations 1
GAMG: Solving for p, Initial residual = 0.00263673, Final residual = 0.000137864, No Iterations 2

The question is: honestly, which value to plot? The first or the last one?

Of course, the last one looks better But I have some doubt if this is the most suitable to demonstrate convergence of the computation.

What do you think (or know) about that?

Thanks for replies!

Best regards,

[taalf]

Originally Posted by blais.bruno

If you are looking to check if you have reached a converged steady solution, the first residual should be plotted.

Hi Bruno,

Thank you for the answer.

I would like to take a more complex case now. I am running something using pimpleFoam and in my fvSolution file I have this:

PIMPLE
{
    nNonOrthogonalCorrectors 1;
    nCorrectors         2;
    nOuterCorrectors    15;
 
    residualControl
    {
        (...)
        p
        {
                tolerance  1e-3;
                relTol      0;
        }
     }
}

That is a max residual for p of 1e-3. Now, in the log file one can see that OpenFOAM considers it converged when the second iteration (due to nCorrectors = 2) gives an initial residual below 1e-3.

Time = 1

PIMPLE: iteration 1
(...)
PIMPLE: iteration 2
(...)
GAMG: Solving for p, Initial residual = 0.0326319, Final residual = 0.00230812, No Iterations 2
GAMG: Solving for p, Initial residual = 0.000288383, Final residual = 2.5225e-05, No Iterations 2
time step continuity errors : sum local = 9.08306e-08, global = 1.15651e-08, cumulative = 1.2079e-08
GAMG: Solving for p, Initial residual = 0.00081177, Final residual = 5.08786e-05, No Iterations 2
GAMG: Solving for p, Initial residual = 0.000189682, Final residual = 3.53319e-05, No Iterations 1
(...)
PIMPLE: converged in 2 iterations
ExecutionTime = 520.33 s ClockTime = 555 s

So, the conclusion is that:
- additional iterations due to nNonOrthogonalCorrectors > 0 should NOT be taken into account when looking at convergence
- when additional iterations due to nCorrectors > 1 should.

[blais.bruno]

The non-orthogonal correctors should not be taken into account when looking at the history of the residual. When you are doing non-orthogonal corrections in a way you are solving a different system of equation to correct for non-orthogonality and you are not really solving the Poisson equation for Pressure. Absolute tolerance gives you the lowest residual value you can reach before you stop solving (i.e if you put 1e-4, none of your equation will solve to a residual below approx. 1e-4). Generally, if are doing a steady-state simulation, it is best to put a very low absolute tolerance and a relative tolerance that can be higher IMO.

[AndreasPe]

Hi,

i have a similar question about the residual control of the PIMPLE algorithm.

I noticed, that the residual control for transient simulations takes the last initial residual of the PISO-Loop (inner iterations -> nCorrectors) as reference to stop the SIMPLE-Loop (outer iterations -> nOuterCorrectors).

So if for example six PISO-Iterations are done, the initial residual of the last PISO iteration is compared to the absolute tolerance of the residual control file. Wouldn't this mean, that the non-linearity of the problem is not taken into account?

I would assume that the nonlinear convergence of the pressure equation can only be assessed by looking at the first initial residual of every PISO-Loop.

Maybe this becomes more clear with an example:
In the attachement you can see the last two outer iterations of a simulation i was running with the PIMPLE Debug output. As we can see in the middle of the picture, the abs tol value of p refers to 2.92352087e-07.

So the solver compares this value to the absolute tolerance given in the dictionary (in this case 0) or it compares the initial residual of the first pimple loop (here refered to as ini res = 0.0128040077) devided by the abs tol value to the relative tolerance given in the dictionary (in this case 0.0001). Should'nt be the value of abs tol set to 1.00333041e-5 instead, to capture the whole nonlinearity of the problem? Or is there something, i am missing here, and the nonlinearity of the system is still inherent after doing several PISO-Corrector steps?