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Solute transport through heterogeneous porous media is governed by fuidadvection, molecular diffusion and anisotropic dispersion. The dispersion isassumed to obey Fick's law and the dispersion coefficient is defined as asecond rank tensor. However, this problem has revealed to be a very difficultone because independently of the numerical methods employed, the solutions areseen to exhibit artificial oscillations and negative concentrations when thedispersivity becomes anisotropic. Here we report consistent SPH simulations ofthe anisotropic dispersion of a Gaussian contaminant plume in porous mediausing the open source code DualSPHysics. Consistency of the SPH method isrestored by increasing the spatial resolution along with the number ofneighbours within the compact support of the interpolating kernel. The solutionshows that as the number of neighbours is increased with resolution, fullconvergence of the numerical solutions is guaranteed regardless of thedispersivity. However, despite the restored consistency, negativeconcentrations, albeit at a lower level, are still present. This suggests thata compromise between the number of neighbours and the size of the smoothinglength must be guaranteed such that sufficient implicit numerical diffusionremains to damp out unphysical oscillations.

Consistent SPH simulations of the anisotropic dispersion of a contaminant plume