Dear ,

I'm making a code for predicting lid-driven cavity flow using the conventional Lagrangian vortex method.

In my results, many particles go outside the box domain, especially near the upper two corners. I think the reason is that there are singular behaviours there. But except the moving wall vorticity and secondary vortex near two lower corners, overall flow patterns and the centerline velocity profiles are nealry same with Ghia's resutls after converging.

I think the wrong prediction of the moving wall vorticity profile is due to the outside particles. Am I right ?

And please let me know how can I reduce or eliminates the particles going outside ?

Thank you,

cf) dt = 0.01, Blob size = 1/64 for Re = 100

Are you using random walk for diffusion? This would explain so many particles outside the box. How are you dealing with the velocity boundary conditions and diffusion from the wall? A good/correct implementation would not lead to so many particles going out of the domain. And, anyway, particles that move outside should be removed from the computation, as keeping them will lead to incorrect flow field.

Adrin Gharakhani

Thank you for your kindness. I use PSE scheme for diffusion. And for no-slip condition at the wall, diffusion process is iterated. So, strengths of the particels are modified.

"Particles that move outside should be removed from the computation" means that outside particels must be eliminated from the computation even though they have large enough strength or they should be forced to have zero strength ?

Thank you.

Thank you,

I cured some mistakes in my program, so particles don't go outside. But, it is seen some wrong vectors in the region of the right bottom corner, very close to the corner. In the position direction of the velocity vector is north-west, so in the corner region streamline contours are slightly different from Ghia's solution. Please give me some advices.

Removing means removing particles from the computations. Setting the strengths to zero has essentially the same effect, but adds to your cost. A zero strength is equivalent to the case where no particles exist - of course when using PSE you will see some nearby particles gaining strength eventually, due to diffusion.

There is nothing wrong with removing the particles. What happens is that the loss of vorticity gets compensated for in the next timestep when you apply the no-slip BC. Essentially, you'll have a vortex sheet distribution at the walls with strength that accommodate the loss of particles. Nevertheless, if you are losing particles, then you may still have errors in implementation and/or your timestep size may be too large. A few particles here and there is not a problem, but an accurate solution should not lead to more losses.

Adrin Gharakhani

Well, since in one day you found problems that significantly improved your errors, I wonder if you will find other errors should you spend some more time!!

As for the vector going "in the wrong direction", I'm not so sure, because I don't have the vector field in front of me to make sense. However, barring you have additional errors (quite likely), I don't see a problem with the direction of the vector you described. You're supposed to have a very small secondary vortex there - it just makes physical sense - and the vector direction you mention, sort of, agrees with that. Try higher and lower resolution runs (_after_ you're sure you have no bugs) and see what happens. I won't be surprised one bit that you can capture small scales better than a finite-difference solution!

Adrin Gharakhani

I'm very appreciated in your kind answers. I'll try to do following your comments.

Thank you again.