Boundary Path-integral Method for Direct Numerical Simulation of Fluid-particle Interaction

A new numerical model has been developed for simulating the dynamics of a large number of spherical particles within incompressible flows by computing the hydrodynamic forces and torques acting on the particles from the fully resolved fluid flow at sub-particle scales. The no-slip boundary condition is enforced on a geodesic (icosahedral) discretization of the particle surface, while the fluid equations are solved on fixed Cartesian grid nodes, exterior to the particles; the two grids exchange information through local Lagrange interpolation. High efficiency of the coupled Euler-Lagrange method was achieved by extending the pressure discontinuously across particle boundaries and using fast solvers for the pressure Poisson equation. No boundary integrals have to be solved for the pressure discontinuities on the boundaries since these are determined (to a constant) through path-integration of the known boundary pressure gradients. Particle- particle interactions are modeled with the discrete element method using linear springs and friction to represent normal and tangential forces, respectively, at particle-particle contact points (Walton Model). The multiphase solver is first tested against theoretical, experimental and numerical results for flows around a single sphere. The model was then applied to study the conditions for incipient motion of a bed of particles under both steady and oscillatory forcing. Quantitative comparisons for sediment entrainment are made with existing laboratory data.