Grid independency in a Quasi-staedy flow
 

Hi guys
I deal with a quasi-staeady B.C in a microchannel.
What can I check my grid indepency???
This flow depend on time step size and this problem confuse me !!!

best regards
Kazem

What exactly do you mean with "quasi-steady boundary condition"?

Mesh dependency is usually checked by obtaining solutions on meshes with different cell sizes and comparing the results.

My B.C is V(t)=a sin (omega*t)

As you know, since this B.C depend on time, solution in addition to grid size, alter with different time step.

All right, now I see. To me, your boundary condition is transient. But lets not bother with definitions.

Since you have two factors influencing the accuracy of the solution (time step size and mesh size; of course there are others like covergence criteria...) i would study them individually.

First you choose a "reasonable" mesh size and obtain solutions with decreasing time step size. Plot a result of your computation (like wall shear or pressure drop, I don't know what you want to simulate) versus time step size and check for independency.

When finished, fix the time step size to a "reasonable" value (much easier to find now since you already have results for different time step sizes) and perform a normal grid dependency study.

This way, you cannot capture any cross-dependencies of the two influencing factors, but you still get an idea where the "independent" solution might be found.
There are better methods, especially when more than two influencing factors are to be considered, but these require some advanced statistics ("Design of experiments")

Dear flotus1.

Thanks for your comments.
Only one question.
My geometry is complex (various bifurcated and curved microchannel).
How do I determine the first "reasonable grid", for beginning ???
If I start with a coarse grid (that I think that is reasonable grid), then find the independence time step. afterwards, refine my grid to find the appropriate grid; Is there something problem???

Thanks

Yes, there is the problem that you don't know the cross-influence of the two factors.
On a fine grid, it is quite likely that details of the flow are resolved which have a smaller timescale and thus require an even smaller timestep for the solution to be considered as independent of the timestep size.
The "easy" way to determine this influence is by setting up a matrix with combinations of both parameters instead of changing them individually.
Of course this leads to a large number of simulations.

many Thanks,

If I act vice versa, i.e. I first solve the problem for critical boundary conditions (Vmax=a and -a) and determine the appropriate grid.
Then, I do time step independency, is it easier??

Regards

That sounds like quite a good idea. Damn, why didn't I come up with this one ;)