On modification of pressure gradient operator in integrated ISPH for multifluid and porous media flow with free-surface

In Incompressible Smoothed Particle Hydrodynamics (ISPH) simulation, choice of pressure gradient operator plays an important role. Variations in effective porosity, fluid density, and free-surface conditions dictate the nature of the formulation. This study proposes an integrated ISPH framework with an implicit free-surface treatment. Pressure variation at the multi-fluid interface is maintained using a modified density-weighted pressure gradient with linear momentum conservation. Different pressure gradients with diffused interfaces for a porous domain as well as multifluid interface have been compared with the proposed operator. A unified form of Brinkman and Navier-Stokes equations are utilized to describe the flow-physics inside and outside the porous domain. Density variation in fluids is modelled by solving the scalar-transport equation. Effect of the porous domain is incorporated in terms of varying representative volume of the fluid particles. Porous media interface conditions are implicitly implemented using Darcy velocity and by introducing porosity into Pressure Poisson Equation (PPE). The present model is capable of minimizing error in velocity-divergence due to implicit free surface treatment combined with linear momentum conservation. Proposed framework is validated by using existing experimental data of density-dependent flow with very low-density ratio and flow through porous blocks. A result of density-current passing through porous domain demonstrates the capability of the developed model for complex scenarios.