Diffusive terms for the conservation of mass equation in SPH

Smoothed Particle Hydrodynamics Modeling with Advanced Boundary Conditions for Two-Dimensional Dam-Break Floods

“…When the computation water held under hydrostatic conditions is released, a downstream wave advances along a dry bed towards the downstream vertical wall and, finally, strikes this wall (i.e., primary wave). Later, two different successive high vertical run-up jets, due to the inviscid model used (as highlighted also in [32] and [34]), are created and fall by gravity onto the underlying fluid. The second jet initially disintegrates into droplets that splash onto and are reabsorbed by the main volume of the fluid flow.…”

“…They focused on the evolution of the water-water interface at various ratios of upstream to downstream flow depths along a long channel. In 2016, Cercos-Pita et al [32] treated the problem of anomalous pressure fluctuations during a dam-break event using a WCSPH approach and the introduction of diffusive terms in the conservation of mass equation. They demonstrated the method's greater reliability over other modified SPH schemes, based on an equivalence with Riemann solvers.…”

“…The results show the reliability of both the proposed boundary condition schemes in resolving violent wave breaking and impact events of this practical dam-break application, producing smooth pressure fields and accurately predicting pressure and water level peaks. In particular, the present SPH method is capable of numerically reconstructing time trends of the primary wave pressures acting on the solid vertical wall downstream and the primary and secondary wave heights at specific positions of the reference test case where both the experimental measurements and numerical results of [32,34] are available. This paper is organized as follows.…”

“…In addition, should a "weakly compressible" approach be adopted, the non-iterative SPH algorithms are simplified [8].The limits of SPH models are linked to slightly higher computational costs, complex procedures for the local refining of spatial resolution, and a relatively low accuracy for classical CFD applications where mesh-based models are well-validated (e.g., confined mono-phase flows [8]). However, they are effectively employed in several fields [9][10][11][12][13][14][15][16][17][18].Various flood propagation studies have focused on the use of the SPH method to investigate dam-break events [19][20][21][22][23][24][25][26][27][28][29][30][31][32]. Having implemented an SPH scheme to treat a dam-break problem in a two-phase approach, Colagrossi and Landrini [19] discussed the effects of density-ratio variations and air entrapment on loads.…”

“…Various flood propagation studies have focused on the use of the SPH method to investigate dam-break events [19][20][21][22][23][24][25][26][27][28][29][30][31][32]. Having implemented an SPH scheme to treat a dam-break problem in a two-phase approach, Colagrossi and Landrini [19] discussed the effects of density-ratio variations and air entrapment on loads.…”