Mixed miscible-immiscible fluid flow modelling with incompressible SPH framework

A divergence-free Incompressible Smoothed Particle Hydrodynamics (ISPH) framework is developed for modelling multifluid immiscible/miscible flows. The numerical model considers Navier-Stokes equation along with scalar-transport equation to represent flow characteristics. Pure divergence free ISPH algorithm is used to solve Navier-Stokes momentum equation. Scalar transport equation is solved based on the nature of the fluid particles represented in terms of colour indicator (ϕ). Fixed ghost particles are utilized for simulating slip boundary. Proposed model is validated against three analytical/experimental results: (a) immiscible Rayleigh-Taylor Instability (b) lock-exchange non-Boussinesq flow (c) miscible gravity current with low density ratio. The model can capture Kelvin-Helmholtz instabilities generated at the interface. the framework is capable of capturing density-dependent flow with low to high density ratio alike. The capability of the developed model in general multifluid system is demonstrated for two cases (a) miscible multimode Rayleigh-Taylor Instability and (b) mixed miscible-immiscible fluid flow simulation.