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From Navier–Stokes to Stokes by means of particle methods. (English) Zbl 1088.76054
Summary: The viscous flow around a circular cylinder was investigated by means of a particle method over a wide Reynolds number range, from 0.0001 to 1000. A special care was devoted to the satisfaction of the no-slip condition which was expressed through a fourth-order partial differential equation for the stream function according to the method initially proposed by Y. Achdou and O. Pironneau [SIAM J. Numer. Anal. 32, No. 4, 985–1016 (1995; Zbl 0833.76032)]. This equation was solved by a boundary integral method which simultaneously satisfied a Dirichlet and a Neumann condition. The algorithm was immersed within a particle method framework and results in a versatile method which can deal with relatively high Reynolds numbers as well as Stokes flows. The numerical results were analysed and compared to those obtained by others numerically, experimentally and even theoretically for the low Reynolds number limit. The behaviour of the method for two extreme cases was specially investigated.

MSC:
76M28 Particle methods and lattice-gas methods
76D05 Navier-Stokes equations for incompressible viscous fluids
76D07 Stokes and related (Oseen, etc.) flows
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