Accuracy Of Sph Viscous Flow Models

In this paper, we quantify how the accuracy of 1D and 2D smoothed particle hydrodynamics simulations of viscous diffusion depend upon (i) the mean inter-particle distance Delta x, (ii) the smoothing length h and (iii) the randomness of the particle positions. In both the 1D and 2D cases, the method converges only in the case where randomness is absent and for a few values of h/Delta x including both integer (for 1D) and non-integer values (both 1D and 2D). For any other (fixed) value of h/Delta x, 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/Delta x appear to be less influenced by particle randomness and ability to move. Copyright (C) 2007 John Wiley & Sons, Ltd.