A Robust volume conservative divergence-free ISPH framework for free-surface flow problems

- A volume conservative divergence free ISPH is proposed for modelling free-surface flow.
- A corrective displacement is added based on total incompressibility of continuity equation.
- The proposed method does not require parametric study for weighted PPE with source/sink terms.

This study presents a Volume Conservative approach for resolving volume conservation issue in divergence-free incompressible Smoothed Particle Hydrodynamics (ISPH). Irregular free surface deformation may introduce error in volume computation, which has a cascading effect over time. Proposed correction decreases this numerical compressibility to a minimal value. The correction is obtained directly by solving Navier-Stokes momentum equation. Consequently, the framework does not require any parametric study for mixed source/sink term or iterative solution of pressure Poisson equations. The correction is implemented on four different types of flow: (a) pressurized flow in a closed box, (b) dambreak flow, (c) flow through porous block, (d) lock-exchange flow of immiscible fluids (both free-surface and pressurized flow). All four scenarios are shown to have minimal error compared to pure divergence-free ISPH.