Lattice Boltzmann scheme for diffusion on triangular grids

In this paper we present a Lattice Boltzmann scheme for diffusion on it unstructured triangular grids. In this formulation of a LB for irregular grids there is no need for interpolation, which is required in other LB schemes on irregular grids. At the end of the propagation step the lattice gas particles arrive exactly at neighbouring lattice sites, as is the case in LB schemes on Bravais lattices. The scheme is constructed using the constraints that the moments of the equilibrium distribution equals that of the Maxwell-Boltzmann distribution. For a special choice of the relaxation parameter (omega = 1) we show that our LB scheme is identical to a cell centered Finite Volume scheme on an unstructured triangular grid.