Application of weakly compressible and truly incompressible SPH to 3-D water collapse in waterworks

Two algorithms of the SPH Lagrangian numerical method, the first weakly compressible, the second truly incompressible, are presented and applied to two free-surface three-dimensional flows. The first (schematic) case consists of a water column collapsing in a rectangular tank with a central rectangular obstacle, and allows the comparison and validation of both algorithms. It appears that the incompressible method is superior to predict the total strength experienced by the obstacle, while the weakly compressible method shows weaknesses under this criterion. The second application case, very close to an industrial study, represents a “ski-jump” spillway connecting the reservoir of a river dam to a valley with complex bottom shape. The global flow pattern is compared to laboratory observations from a physical model, leading to satisfactory conclusions which prove SPH has the potential to be a promising method for the design of complex waterworks.