Editing Computational fluid dynamics (section)

==== Vortex method ====

The vortex method, also Lagrangian Vortex Particle Method, is a [[Meshfree methods|meshfree]] technique for the simulation of incompressible turbulent flows. In it, [[vorticity]] is discretized onto [[Lagrangian and Eulerian specification of the flow field|Lagrangian]] particles, these computational elements being called vortices, vortons, or vortex particles.<ref>{{cite book |last1=Cottet |first1=Georges-Henri |last2=Koumoutsakos |first2=Petros D. |date=2000 |title=Vortex Methods: Theory and Practice |location=Cambridge, UK |publisher=Cambridge Univ. Press |isbn=0-521-62186-0
}}</ref> Vortex methods were developed as a grid-free methodology that would not be limited by the fundamental smoothing effects associated with grid-based methods. To be practical, however, vortex methods require means for rapidly computing velocities from the vortex elements – in other words they require the solution to a particular form of the [[N-body problem]] (in which the motion of N objects is tied to their mutual influences). This breakthrough came in the 1980s with the development of the [[Barnes–Hut simulation|Barnes-Hut]] and [[fast multipole method]] (FMM) algorithms. These paved the way to practical computation of the velocities from the vortex elements.

Software based on the vortex method offer a new means for solving tough fluid dynamics problems with minimal user intervention.{{Citation needed|date=November 2010}}  All that is required is specification of problem geometry and setting of boundary and initial conditions. Among the significant advantages of this modern technology;
* It is practically grid-free, thus eliminating numerous iterations associated with RANS and LES.
* All problems are treated identically. No modeling or calibration inputs are required.
* Time-series simulations, which are crucial for correct analysis of acoustics, are possible.
* The small scale and large scale are accurately simulated at the same time.