Dear Elmer group
I’m working on a FSI problem in which the solid part is vibrating with frequency of 2000 Hz (Displacement 2 = (0.3e-6)*sin(2*3.141593*2000*tx). Thus each period of vibration takes 5e-4 seconds. When I use time steps smaller than 1e-5 the Navier-Stokes equation doesn’t converge anymore while it converges normally in bigger time steps (contrary to the expectation that smaller time steps gives easier convergence). Do you any idea about it? Does it have anything to do with the computer time resolution or something in Navier-Stokes equation? I tried 1st and 2nd order BDF and Crank-Nicolson for time integration.
I guess I should use the dimensionless form of Navier-Stokes and nonlinear elasticity. I hope it doesn't need to manipulate the associated source codes.
Regards, Hamed
Convergence problem for smaller time steps!
Convergence problem for smaller time steps!
Last edited by hamed on 28 Apr 2010, 20:24, edited 1 time in total.
Re: Convergence problem for smaller time steps!
Hi,
There is a chance that this issue is related to a deficiency of standard stabilization strategies to cope with situations where the time step size is small in comparison with the spatial mesh size. A full discussion of this problem may be found at
P. B. Bochev, M. D. Gunzburger and R. B. Lehoucq,
On stabilized finite element methods for the Stokes problem in the small time-step limit, Internat. J. Numer. Methods Fluids, 53, 573-597 (2007).
You could check whether the situation remains the same if you omit the stabilization and use an (inf-sup) stable finite element. If the mesh consists of the lowest-order elements, I suppose one way for trying this is to set in the N-S section
Stabilize = False
Element = "p:1 b:1"
Bubbles in Global System = True
However, if the Reynolds number is high, difficulties may now arise due to instabilities caused by dominating convection.
- Mika
There is a chance that this issue is related to a deficiency of standard stabilization strategies to cope with situations where the time step size is small in comparison with the spatial mesh size. A full discussion of this problem may be found at
P. B. Bochev, M. D. Gunzburger and R. B. Lehoucq,
On stabilized finite element methods for the Stokes problem in the small time-step limit, Internat. J. Numer. Methods Fluids, 53, 573-597 (2007).
You could check whether the situation remains the same if you omit the stabilization and use an (inf-sup) stable finite element. If the mesh consists of the lowest-order elements, I suppose one way for trying this is to set in the N-S section
Stabilize = False
Element = "p:1 b:1"
Bubbles in Global System = True
However, if the Reynolds number is high, difficulties may now arise due to instabilities caused by dominating convection.
- Mika
Re: Convergence problem for smaller time steps!
Thanks Mika. Actually I didn't run my test case with the instructions given in this paper yet, but it seems that it can resolve my problem. Anyway it's a really interesting paper that gave some new insights to me. I really appreciate for your kind and useful comment.
Regards, Hamed
Regards, Hamed