Standard WCSPH for Free-Surface Multi-Phase Flows with a Large Density Ratio

Abstract

The standard weakly compressible Smoothed Particle Hydrodynamics (WCSPH) is successfully applied to multi-phase problems involving fluids with similar densities, but when density ratio increases at some order of magnitude, serious instability phenomena occur at the interface. Several remedies have been proposed based on numerical correctives that deviate from standard formulation, increasing the algorithm complexity and, sometimes, the computational cost. In this study, the standard SPH has been adapted to treat free-surface multi-phase flows with a large density ratio through a modified form of the governing equations which is based on the specific volume (i.e. the inverse of particle volume) instead of density: the former is continuous across the fluid interface while the latter is not and generates numerical instability. Interface sharpness is assured without cohesion forces; kernel truncation at the interface is avoided. The model, relatively simple to implement, is tested by simulating two-phase dam breaking for two configurations: kinematic and dynamic features are compared with reference data showing good agreement despite the reduced computational effort.

3D WCSPH modelling of the 1963 Vajont landslide

“…Since the density ratio between the solid and fluid phases (i.e. s/f) is small, there is no need for corrective terms that would be necessary to assure numerical stability in the case of large density ratio (Manenti 2018).…”

SPH Modeling of Water-Related Natural Hazards

“…A modified formulation of the standard weakly compressible SPH (WCSPH) governing equations were presented in [28] for modeling rapid free-surface multiphase flows with a high-density ratio involving violent impact against a rigid wall. This formulation, which is based on the coupled approach, allows for the numerical instability induced by the discontinuity of the fluid properties across the interface to be eliminated without excluding the heterogeneous particle during kernel interpolation.…”

Post-Failure Dynamics of Rainfall-Induced Landslide in Oltrepò Pavese

“…Meshless particle methods could be helpful for this purpose. Among the numerous types of meshless particle methods, the smoothed particle hydrodynamics (SPH) method [7] is successfully applied to simulate complex multiphase flows with impact and shock [8,9], involving fluids with high-density ratio [10] as well as non-Newtonian fluids [11][12][13][14]. These problems are of great concern in the applied engineering dealing with water related natural hazards [15], such as landslide induced tsunami in artificial reservoir [11] and intense rainfall-induced shallow landslides [16].…”