A particle method to solve the Navier-Stokes system. (English) Zbl 0707.76029

Summary: We extend to the case of the two-dimensional Navier-Stokes equations, a particle method introduced in a previous paper [the authors, C. R. Acad. Sci., Paris, Ser. I 297, 133-136 (1983; Zbl 0534.65077)] to solve linear convection-diffusion equations. The method is based on a viscous splitting of the operator. The particles move under the effect of the velocity field but are not affected by the diffusion which is taken into account by the weights. We prove the stability and the convergence of the method.


76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
76M25 Other numerical methods (fluid mechanics) (MSC2010)


Zbl 0534.65077
Full Text: DOI EuDML


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