Convergence of the Random Vortex Method
This will be rather informal and imprecise. For precise statements and proofs, see the references. I will first explain my motives and goals in studying the particle system that is the random vortex method. Then I will outline the proof of the convergence theorem. For more basic discussion of vortex methods, see the book . Information on the practical success of vortex methods for computing viscous and inviscid flows can be found in . Despite many published demonstrations of the effectiveness of vortex methods, the methods still have many vocal opponents. I hope this confusion will be clarified over the next few years, but I will not comment on it here. Recently, Long  has announced a different proof that leads to a sharper convergence theorem than the one discussed here.
KeywordsVortex Core Pseudodifferential Operator Particle Simulation Inviscid Flow Monte Carlo Approximation
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- A.J. Chorin and J. Marsden, A Mathematical Introduction to Fluid Mechanics, Springer Verlag, New York, 1979Google Scholar
- J. Goodman, “Convergence of the random vortex method”, preprintGoogle Scholar
- A. Leonard, “Computing three-dimensional incompressible flows with vortex elements”, in Annual Review of Fluid Mechanics, ed. by M. van Dyke, J.V. Wehausen, and J.L. Lumley, vol. 17 (1985), pp. 523–559Google Scholar
- Long, PhD thesis, Princeton University, in preparationGoogle Scholar
- H. Osada, “Propagation of chaos for the two dimensional Navier-Stokes equation”, preprint. See also these proceedings.Google Scholar