In this paper, we quantify how the accuracy of ID and 2D smoothed particle hydrodynamics simulations of viscous diffusion depend upon (i) the mean inter-particle distance Ax, (ii) the smoothing length h and (iii) the randomness of the particle positions. In both the ID and 2D cases, the method converges only in the case where randomness is absent and for a few values of h/Ax including both integer (for ID) and non-integer values (both ID and 2D). For any other (fixed) value of h/Ax, the method does not converge. In most cases, increasing randomness decreases the accuracy of the results, as does the ability of particles to move. Simulations using larger values of h/Ax appear to be less influenced by particle randomness and ability to move.
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