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This work is centered on the safe usage of the Lattice Boltzmann Method (LBM) for two-dimensional pure diffusion. The basics of the LBM for pure diffusion are first elucidated using a new definition given in the paper. The oscillating behaviour and safe conditions of use are then explored in the case of homogeneous material as well as heterogeneous materials with circular and plane interfaces. As a conclusion, the range of valid relaxation factors is given for a correct use of the LBM.
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