Residual converged, solution not, theory behind?

CellZone · May 17, 2022, 08:48

Hello cfd experts,

can someone explain me, that for RANS steady simulation more or less all of the residuals are really low (below 10-6) but for example the drag coefficient still changes strongly from iteration to iteration (let us say still after 1000 iterations)?

What is the theory behind it?

Actually a low residual tells me, that the numeric solution is really close to the exact solution - so where is this change still coming?

Do I need to be more specific (turbulence model , solver settings , ...) or is this enough to explain me the numerical theory behind it why the characteristical values can still change while it seems to be converged for momentum, mass conservation, ...

Thank you
Cellzone

FMDenaro · May 17, 2022, 11:56

Quote:

Originally Posted by CellZone

Hello cfd experts,

can someone explain me, that for RANS steady simulation more or less all of the residuals are really low (below 10-6) but for example the drag coefficient still changes strongly from iteration to iteration (let us say still after 1000 iterations)?

What is the theory behind it?

Actually a low residual tells me, that the numeric solution is really close to the exact solution - so where is this change still coming?

Do I need to be more specific (turbulence model , solver settings , ...) or is this enough to explain me the numerical theory behind it why the characteristical values can still change while it seems to be converged for momentum, mass conservation, ...

Thank you
Cellzone

There is no theory in you case. You have solved the equations, if your residuals are correctly computed and are driven to vanish, your solution reached a convergence (but not necessarily the exact one).

There is no solved equation and no residual for the drag, it is computed from your converged solution by computing the normal derivative of the streamwise velocity. If you see relevant oscillations in the value, you can suppose an error in the computation of the drag. Otherwise, your residuals are wrongly computed and you have a false convergence.
By the way, the drag can be computed only if you have a resolved boundary layer, that is at least 3-4 nodes belove y+=1.

agd · May 17, 2022, 16:12

Another way to put is - you have solved a set of equations. But how does that set of equations compare to what you think you are solving? You need to make sure that the discrete equations you are solving faithfully represent the differential equations being modeled and capture the physics of the problem at hand.

sbaffini · May 17, 2022, 16:35

I bet on the false convergence.

1e-6 is not at convergence unless you are using single precision (and even in that case it might not be).

It doesn't mean that 1e-6 is always not at convergence, but when you stop there you actually use other monitors like forces to assess convergence. If you want the drag and it flattens when residual are at 1e-6, then you might be ok, but not orherwise.

This is especially so if, say, the force is still varying monotonically (as opposed to a force that instead oscillates around a mean, which opens to another set of issues, depending from the amount of oscillation)

May 17, 2022, 08:48	Residual converged, solution not, theory behind?	#1
CellZone Member Join Date: Apr 2016 Posts: 91 Rep Power: 10	Hello cfd experts, can someone explain me, that for RANS steady simulation more or less all of the residuals are really low (below 10-6) but for example the drag coefficient still changes strongly from iteration to iteration (let us say still after 1000 iterations)? What is the theory behind it? Actually a low residual tells me, that the numeric solution is really close to the exact solution - so where is this change still coming? Do I need to be more specific (turbulence model , solver settings , ...) or is this enough to explain me the numerical theory behind it why the characteristical values can still change while it seems to be converged for momentum, mass conservation, ... Thank you Cellzone

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May 17, 2022, 16:12		#3
agd Senior Member Join Date: Jul 2009 Posts: 358 Rep Power: 19	Another way to put is - you have solved a set of equations. But how does that set of equations compare to what you think you are solving? You need to make sure that the discrete equations you are solving faithfully represent the differential equations being modeled and capture the physics of the problem at hand.

May 17, 2022, 16:35		#4
sbaffini Senior Member Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,195 Blog Entries: 29 Rep Power: 39	I bet on the false convergence. 1e-6 is not at convergence unless you are using single precision (and even in that case it might not be). It doesn't mean that 1e-6 is always not at convergence, but when you stop there you actually use other monitors like forces to assess convergence. If you want the drag and it flattens when residual are at 1e-6, then you might be ok, but not orherwise. This is especially so if, say, the force is still varying monotonically (as opposed to a force that instead oscillates around a mean, which opens to another set of issues, depending from the amount of oscillation)