Originally Posted by HectorRedal (Post 795396)

Hi,


I would like to raise the following question from my side:
Does relaxation factor apply in transient problems?


I am currently studying the CBS algorithm for transient problem in fluids:
https://onlinelibrary.wiley.com/doi/...3E3.0.CO%3B2-7


The algorithm uses two factors: theta1 and theta2.
They are used in the follwoing manner:
Velocity: V(t=n+theta1) = V(t=n) * (1-theta1) + V(t=n+1) * theta1
Pressure: P(t=n+theta2) = P(t=n) * (1-theta2) + P(t=n+1) * theta2


Which value of theta1 and theta2 should I use for transient problems?
Is there any recommended value?
Can these parameters be considered "relaxation factors"?


Thanks for your kind support.


Best regards
Hector

Originally Posted by FMDenaro (Post 795409)

If I understand, this form is generally related to an implicit class of time integration, for theta=1/2 the well known Crank-Nicolson time integration resulting in the scheme. It is a second order accurate quadrature formula for the time integral.

Originally Posted by HectorRedal (Post 795632)

Hi,


One question from my side: If I understand it correctly, this means tha the error for the Crank-Nicolson scheme would be in the order of c * (delta T)^3.
How big is that c, constant? My understanding is that this c would be in the order of the third derivate, right?


Now, I would like to comment that I am using different schemes in my simulation (Backward Euler, forward Euler and Crank-Nicolson), but I do not see much difference in the simulation.


Additionally, I am reducing a lot the delta T for the simulation, and the results does not change.



This is puzzling me a bit.


Best regards,
Hector.