An assessment of particle methods for approximating anisotropic dispersion

SUMMARY

We derive a smoothed particle hydrodynamics (SPH) approximation for anisotropic dispersion that only depends upon the first derivative of the kernel function and study its numerical properties. In addition, we compare the performance of the newly derived SPH approximation versus an implementation of the particle strength exchange (PSE) method and a standard finite volume method for simulating multiple scenarios defined by different combinations of physical and numerical parameters. We show that, for regularly spaced particles, given an adequate selection of numerical parameters such as kernel function and smoothing length, the new SPH approximation is comparable with the PSE method in terms of convergence and accuracy and similar to the finite volume method. On other hand, the performance of both particle methods (SPH and PSE) decreases as the degree of disorder of the particle increases. However, we demonstrate that in these situations the accuracy and convergence properties of both particle methods can be improved by an adequate choice of some numerical parameters such as kernel core size and kernel function. Copyright © 2012 John Wiley & Sons, Ltd.

We derive a smoothed particle hydrodynamics (SPH) approximation for anisotropic dispersion and compare it with the particle strength exchange (PSE) formulation and a standard finite volume formulation. We show that, given an appropriate selection of numerical parameters and regular particle distribution, the new SPH approximation is comparable with the PSE and the finite volume approximations. We also show that the performance of the SPH and PSE approximations decreases as the degree of disorder of the particle increases; however, the accuracy and convergence properties of both particle methods can be improved by an appropriate choice of some numerical parameters such as kernel core size and kernel function.