Can anyone please enlighten me, why I get a larger Strouhal numbers, St, when a run test case of vortex shedding behind a circular cylinder with multigrid? The Reynolds numbers, Re is 200.0 and the St number for single grid is 0.19, whereas the St number I got for multigrid is 0.28.

Thank you very much

Regards, JonTai

(1). What code are you using? (2). Lower the Reynolds number such that the flow is steady-state, say Re=50, and then repeat the single grid and the multi-grid calculations. (3). Check the steady-state solutions to see if they are identical or not.

I'm using two-dimensional finite volume Navier-Stokes solver on unstructured grids using higher-order upwind scheme. The unsteady flows are calculated by using an implicit second-order real-time discretizations and a dual-time stepping scheme.

I have tried Re=41.0 for both single and multigrid. The results I got for both are comparable and the reduction of residual for MG is good.

What are possible reasons that make the St nos. different for single grid & MG ?

Thank you very much

JonTai

(1). Well, the next thing to do is to change the time step size to see how it affects the results. (2). You can also check your single grid case (RE=200) to see whether it is mesh independent or not.

Hi Jon,

you state that "the reduction of residual for the MG is good."

What about the single grid? If you don't shrink down the residuals to the same level, say 6 orders of magnitude with both methods then what do you have to compare? What is your single grid linear eq solver strategy for the single grid (Gauss Seidel)? and what is the convergence criteria? It really does take forever with the slow convergence of GS to squeeze down those residuals! Many people make this mistake! I heard a true story of a publication in a Numerical Heat Transfer that made a whole series of comparasons of convective heat transfer and conclusions about the physics behind it (all wrong). A reader then spotted a bunch of problems like isotherms not normal to sym boundaries etc. It was found that the authors used a single grid method and never got anywhere near convergence because they were monitoring the change in residual and it of course started to change very little but was nowhere near convergence when they stopped the computation.

If in doubt, read through the excellent discussion in Ferziger and Peric's text.

Regards, Duane