A reliable SPH(2) formulation for Darcy–Forchheimer–Brinkman equation using a density-based particle shifting in the ALE description

This paper proposes a numerical framework to perform highly accurate simulations of seepage flow through porous media with the incompressible smoothed particle hydrodynamics (ISPH). Our approach follows the arbitrary Lagrangian–Eulerian description, which can introduce an arbitrary advection velocity for particle shifting techniques (PSTs) independently of the physical fluid velocity. The Darcy–Forchheimer–Brinkman equation is applied to deal with free surface flow and seepage flow simultaneously instead of the Navier–Stokes equation. There are three main improvements to solving this problem using ISPH. The first is replacing the SPH(2) with a highly accurate derivative operator. The second is modifying a volume-conserving particle shifting for seepage flow problems to maintain the apparent fluid density consistent with the spatially distributed porosity. Finally, we propose a newly geometric porosity estimation method automatically estimating numerical porosity referenced in the proposed PST from the soil particle distributions. Through simple convergence tests, we verify the convergence of truncation errors and the applicability limits of SPH(2) to simulate seepage flow problems. We also performed numerical simulations of hydrostatic pressure problems and dam-break experiments involving porous layers to demonstrate the proposed method’s excellent computational stability and volume conservation performance.