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This paper is devoted to the presentation and the analysis of a new particle method for convection-diffusion equations. The method has been presented in detail in the first part of this paper for an isotropic diffusion operator. This part is concerned with the extension of the method to anisotropic diffusion operators. The consistency and the accuracy of the method require much more complex conditions on the cutoff functions than in the isotropic case. After detailing these conditions, we give several examples of cutoff functions which can be used for practical computations. A detailed error analysis is then performed.

The aim of this paper is to present and study a particle method for convection-diffusion equations based on the approximation of diffusion operators by integral operators and the use of a particle method to solve integro-differential equations described previously by the second author. The first part of the paper is concerned with isotropic diffusion operators, whereas the second part will consider the general case of a nonconstant matrix of diffusion. In the former case, the approximation of the diffusion operator is much simpler than in the general case. Furthermore, we get two possibilities of approximations, depending on whether or not the integral operator is positive.