[alimea]

​Dear foamers

I have read a paper by the title of:
Method for time-dependent simulations of viscoelastic flows: vortex shedding behind cylinder
​I want to validate my research with this paper, but a problem have been occurred!
When I want to investigate time step independency, I will earn the attached results. it means that for dt=0.001 I can't get good in-dependency from time step in comparison with dt=0.0005. I'm working on viscoelastic fluid with these non-dimension numbers:
Re=100 - El=1 - Betta(etta_p/etta_0)=0.9 - epsilon=0.1 - zetta = 0.01 (EPTT model)
time derivative discretization scheme: CrankNicolson 0.9
I'm working with viscoelasticFluidFoam in openFoam code.

In addition I added the energy eqn to my equations (Is it possible that solving this eqn need a very small time step?)
I guess it may because of high betta(the ratio of polymeric viscosity to total viscosity).

Could you please give me your idea?


http://uupload.ir/files/s243_dt_study_cl.jpg

[FMDenaro]

What you are trying to do has some issues. Speaking in general, you can consider the local truncation error produced by your discretization. You are fixing the same mesh size and change the time step. As a consequence the CFL is not constant and therefore, for asymptotically vanishing time step, you still have an error that remains constant in the LTE. The only way to make this error disregardable is to use a very fine spatial grid, in such a way that the spatial terms of the LTE are of magnitude lower than the lowest dt you will use.

[alimea]

Originally Posted by FMDenaro

What you are trying to do has some issues. Speaking in general, you can consider the local truncation error produced by your discretization. You are fixing the same mesh size and change the time step. As a consequence the CFL is not constant and therefore, for asymptotically vanishing time step, you still have an error that remains constant in the LTE. The only way to make this error disregardable is to use a very fine spatial grid, in such a way that the spatial terms of the LTE are of magnitude lower than the lowest dt you will use.

dear Filippo
thanks for
I did grid study before and the grid is perfect.
by using dt=0.001 the CFL will be 0.1 !! you know that this is a very low courant number.
at first I used the Cr=0.3 to calculate dt, but when I want to investigate the independency of dt, I saw these results!
the did schemes are the best choices.