[alimea]

Originally Posted by FMDenaro

For an explicit time-marching scheme, the numerical stability region is determined by the curve (in the 1D case) cfl=f(Re_h), being Re_h the cell Reynolds number. Only for Re_h >>1 you can recover the constraint due to only the cfl value.
In your case, at Re=100 I suppose you are working at Re_h=O(1) so that the max cfl value for the stability is much lower than it would be for the inviscid case.

yes, my Re_h is in O(1). that's almost 0.85.
please introduce me a reference to see this curve (cfl=f(Re_h)) and how to obtain that.
Also, what's the meaning of "recovering the constraint due to only the cfl value" ?

[FMDenaro]

That is a classical issue in CFD and numerical analysis and requires the use of the von Neumann analysis. Many texbooks give details about that.
An example for a 2D case is shown in https://www.researchgate.net/publica...y-driven_flows

[alimea]

Originally Posted by FMDenaro

That is a classical issue in CFD and numerical analysis and requires the use of the von Neumann analysis. Many texbooks give details about that.
An example for a 2D case is shown in https://www.researchgate.net/publica...y-driven_flows

Thank you for participating in this discussion and sharing your valuable experiences.

[arjun]

Originally Posted by alimea

Thanks for your nice answer. because it will force me to learn some new concept. could you please explain about these concepts, or give me link or reference to read about them:
1- dissipation (physical or numerical?). especially what is Rhie Chow dissipation?
2- what are implicit and explicit under relaxations? what is the difference between them?

why did you think that in my problem, viscosity becomes dominant term?

I am really short on time to explain these two things. Also you would have to do some search on it. For now just take it as a hint and try to investigate.

About the Rhie and Chow term, which is difficult to find from books as to what my comment was talking about here is very short hint.

Rhie and chow term is inversely propertional to diagonal of momentum matrix. Diagonal of momentum matrix is inversely propertional to time step size. For euler time stepping it would be ( density * volume / delta_T ).

So when delta goes to 0, it shall go to infinity and 1/Ap goes to 0.

So basically as delta_T reduces the Rhie and Chow term becomes weaker and weaker. After certain value, it could be too small at some parts of simulation that solution can diverge.

[alimea]

Hi all
I want to solve the flow around the cylinder in viscoelastic fluid. At first I did it for Newtonian fluid in Re= 10 , 40 , 100 and for viscoelastic fluid in Re= 10 , 100 and obtained exact results. But when I change the Re to 40 for viscoelastic fluid, it became diverged!
I changed many parameters of solution:
urf = from 0.1 to 0.9 --> diverged!
corunt Nu. = from 0.1 to 0.9 --> diverged!
changing the kind and size of mesh --> diverged!
changing the kind and size of mesh --> diverged!
increasing the number of solving pressure correction Eqn from 2 to 20 --> diverged!
decreasing the min residuals to 1e-8 --> diverged!
changing discretization schemes of div terms: Gauss linear (central), Gauss upwind(1st), Gauss upwind(2nd), limitedLinear , QUICK --> diverged!

But I have done some ways to solve that:
1- I saw in this page that sb proposed to the other that decrease the residuals to 1e-19 !! I did it and my solution became converged! I can't analyze that! Is it possible?
2- In the other way I increased the number of solving pressure correction Eqn to 20, decreasing the min residuals to 1e-8
3- setting the time step to 0.001 instead of setting Cr=0.3

Now I don't know that my results are reliable or not!
Could you please tell me what happend that these solutions are appropriate for solve it?

Thanks