Using VEM for long time computations, I am concerned with the cost of calculation with such methods. I first thought using a fast O(N) method but I wonder if a VIC method is not cheaper. ( see the article from Cottet "3D vortex methods: achievements and challenges" ).

There is no such thing as free lunch in CFD (or in life in general ) You get what you pay for!

It all depends on what you wish to get out of the calculation and what level of accuracy you are willing to tolerate. Vortex-In-Cell (VIC) is definitely faster than Vortex-Element_Method (VEM), but you bring with it the bag of problems that VEM is used to eliminate - that is, (1) having to assign a grid distribution, (2) introducing numerical diffusion. If you have to introduce these difficulties you might as well stick with traditional finite volume methods.

Having said that I think a hybrid method is probably the best approach. For example, for simulating flow over a cylinder, you want to use VEM around the cylinder and for the near-wake, where its influence on vortex shedding characteristics is significant, and you'd probably want to use VIC further downstream because the dynamics of the far wake don't contribute significantly to near-cylinder processes.

Adrin Gharakhani