Dear Niki,

If my understanding is right. It seems that for dual-time AC method in 
pyFR, there are difficulties on the convergence of the diffusion term. 
Based on my simulations, the pressure residual of the pseudo convergence 
file increases with the intensity of the flow diffusion. Very low pressure 
residual (less than 1) only happens when the flow is only in convection 
dominance but not much diffusion, which makes the flow behave laminar. When 
the turbulence intensity of the flow occurs, the pressure residual is no 
longer small (around 10) and shows a strong stiffness (decreases linearly 
with very small slope). When the turbulence intensity of the flow increases 
the pressure residual increases (larger than 10) and still shows a very 
strong stiffness. So the pressure residual in pyFR is more like an 
indicator of diffusion intensity but not convergence.

So I don't quite understand how do you converge and meet the mass 
conservation (div u = 0) in AC method? It seems that pyFR has difficulties 
on holding mass conservation in turbulence.

Have you ever tested the AC solver on diffusion equations? Does it really 
show small residuals?  As you said "The pressure residual (div u), which is 
more stiff to converge than velocity residuals". According to you, "is kind 
of an indicator how far the pseudo waves which distribute the pressure have 
travelled". Actually, I don't know the connection between the pseudo waves 
and mass conservation.

In your cases shown above, you have really small pressure residual. How is 
the turbulence intensity in your cases? Is the flow behaving in chaos or 
more laminar flow?

Best regards,
Will

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