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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. [ABSTRACT FROM AUTHOR]

We present and study a conservative particle method of approximation of linear hyperbolic and parabolic systems. This method is based on an extensive use of cut-off functions. We prove its convergence in L at the order $$\varepsilon ^2 + \frac{{h^m }}{{\varepsilon ^{m + 1} }}$$ as soon as the cut-off function belongs to W. [ABSTRACT FROM AUTHOR]