Summary
We extend to the case of the two-dimensional Navier-Stokes equations, a particle method introduced in a previous paper 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.
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Cottet, G.H., Mas-Gallic, S. A particle method to solve the Navier-Stokes system. Numer. Math. 57, 805–827 (1990). https://doi.org/10.1007/BF01386445
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DOI: https://doi.org/10.1007/BF01386445