Modeling free-surface flow in porous media with modified incompressible SPH

This paper presents a modified incompressible smoothed particle hydrodynamics (MISPH) method for fluid-porous media interaction problems. Navier–Stokes and Brinkman Equations are considered for modeling the fluid flow outside and inside porous media. The MISPH method utilizes a truly incompressible divergence free velocity formulation. The equations are solved by using a robust two-step semi-implicit exact projection method. Turbulence stresses are evaluated by using an semi-analytical Smagorinsky model. The representative volume of the particles changes with the porosity. Interface conditions are imposed implicitly by using Darcy velocity and modified Pressure Poisson Equation (PPE) with porosity in the source/sink term. Impermeable boundary conditions are simulated with fixed ghost particles. The model is validated by using existing experimental results of dambreak flow through a homogeneous porous block in a wet bed. Simulation results show good agreement with experimental data. An application to heterogeneous porous media demonstrates the applicability and adaptability of the proposed framework. The numerical model is capable of efficiently capturing the interaction of fluid in porous and nonporous media.