Anisotropic dispersion with a consistent smoothed particle hydrodynamics scheme

Consistent SPH simulations of the anisotropic dispersion of a contaminant plume

“…Thus the higher the number of neighbours, the lower the discretization errors. Working with a million particles and 31590 neighbours, Alvarado-Rodríguez et al [18] found convergence rates and magnitudes of the negative concentrations comparable to those reported by Avesani et al [13] with their MWSPH method. These calculations showed that while first-order consistency was achieved at the maximum employed resolution, this was not enough to ensure a positive concentration everywhere.…”

“…Although this scheme conserves the main diffusing directions, it is rather sen-sitive to particle disorder and reduces the degree of anisotropy due to the SPH smoothing. Results using a consistent SPH approach were further reported by Alvarado-Rodríguez et al [18]. In this case, consistency is restored by means of scaling relations that define the number of neighbours (n) and the smoothing length (h) in terms of the total number of particles (N ) and comply with the asymptotic limits n → ∞ and h → 0 when N → ∞ for complete SPH consistency [19,20,21,22,23].…”

“…The choice of these parameters allows direct comparison with the standard SPH results of Herrera and Beckie [12], the MWSPH simulations of Avesani et al [13] and the lower resolution calculations of Alvarado-Rodríguez et al [18]. The calculations were performed with two and four million irregularly distributed particles and in all cases they were terminated after 300 days.…”

“…In particular, when standard SPH is applied to anisotropic dispersive transport, the occurrence of negative concentrations accompanied by large errors and slow convergence rates is a common result. Since for isotropic dispersion, the results are free from spurious oscillations that cause negative values of the concentration regardless of the degree of disorder of the particles [10,12,13,18], it has been inferred that the problem arises when the off-diagonal terms of the tensor dispersion coefficient are nonzero, which is the case of anisotropic dispersion.…”

“…In addition to the work of Herrera and collaborators [10,11,12], efforts to minimize and eventually remove unphysical oscillations and negative concentrations in SPH simulations of anisotropic dispersion have been made by Avesani et al [13], Tran-Duc et al [14], and more recently by Alvarado-Rodríguez et al [18]. In particular, Avesani et al [13] proposed a modified version of standard SPH based on a Moving-Least-Squares Weighted-Essentially-Non-Oscillatory (MWSPH) reconstruction technique on moving points.…”