Un modello SPH per flussi multi-fase a superficie libera con forti differenze di densità

This paper illustrates the theoretical aspects of an alternative SPH formulation for handling free-surface multiphase flows involving slightly compressible fluids with large density difference (i.e. water and air). The standard form of the governing equations in the SPH approximation allows to treat hydrodynamic problems with relatively small density difference between the fluids (Manenti et al., 2012a); when this gap increases approaching a ratio of some order of magnitude, instability phenomena occurs leading to a crash of the computation. Even if some strategies have been proposed for handling these problems (Monaghan, 2011), in this study is proposed a relatively simple formulation based on the standard SPH approximation introducing the specific particle volume instead of the density: while the former is continuous across the fluid interface, the latter is not, thus introducing fictitious forces in the momentum balance equation causing local instabilities. The proposed strategy allows avoiding corrective expedients which are incoherent with respect to the SPH principles. In some cases, for example, the physical properties of an interface particle are computed by excluding the contribution of those neighbors belonging to a different medium (Colagrossi & Landrini, 2003). This can produce a numerical noise that affects the density calculation and forces to adopt cumbersome corrections that increase the computational effort. Furthermore there is no needs for an additional surface tension term in the momentum balance equation to control interface sharpness (Nugent & Posch, 2000). The main aim of this work is to set up an efficient and simple numerical tool for obtaining accurate reproduction of the physical behavior with reduced computational cost. The proposed method is tested on some significant problems, such as dam breaking on wet and dry bottom and the rise of an air bubble in a fluid. The final objective is the simulation of the impulsive dynamics of a multiphase system composed by water and saturated non-cohesive sediments at rest: a finite volume of cold CO2 is instantaneously injected through a nozzle at the tank bottom and propagates toward the free surface. Some experimental data are available to compare with numerical results (Manenti et al., 2012b).