Multiphase simulations of nonlinear fluids with SPH

A modified apparent viscosity approach has been implemented for a weakly compressible SPH scheme for two-phase flows where a nonlinear phase must yield under erosive dynamics but also maintain a pseudosolid behaviour under the right conditions. The final purpose is to provide a means to model both dam-break dynamics and erosive interactions between different phases simultaneously while also keeping smooth pressure fields in spite of discontinuities introduced by viscosity variations of a nonlinear phase along with significant differences in mean density. Key contributions include purposeful avoidance of nonphysical elastic behaviour and the integration of a specific particle shifting technique that allows for proper replication of erosion and scouring. In this work, the method is validated by applying it to model a silted-up dam that collapses over a static water bed, effectively including all main elements of interest. Although the formulation is inherently three dimensional, validation is done by direct comparison with data from physical experiments of a dominant two-dimensional nature, assuming variable yield stress of medium-grain quartz sand according to the Drucker–Prager equation. Overall results show most of the expected interface dynamics, such as erosion and transportation of the nonlinear phase, sustained piling of the non-yielded volume of silt, and good correspondence of both granular and water surface position with experimental data. Finally, a series of modelling assumptions and implications for future developments are explicitly stated because of their direct impact on stability and versatility for multiphase, nonlinear flows in general.