Mesoscale fluid-particle interaction using two-way coupled SPH and the Discrete Element Method

We present a meshless simulation method for multiphase fluid-particle systems using Smoothed Particle Hydrodynamics (SPH) and the Discrete Element Method (DEM). Rather than fully resolving the interstitial fluid, which is often infeasible, we use an unresolved fluid model based on the locally averaged Navier Stokes equations. A variable-h SPH formulation is used to calculate the fluid phase, where the density of each particle is proportional to the local porosity. The SPH-DEM method is validated using simulations of single and multiple particle sedimentation in a 3D water column. The velocity and terminal velocity for the single particle compares well with the analytical solution, provided that the minimum resolution of the fluid phase is much larger than the solid particle diameter. In the multiple particle sedimentation simulation, the two-way coupling between the phases permits the growth of a Rayleigh-Taylor instability. The growth rate of the instability in the linear regime is calculated and compares well with theory.