Implicitly-coupled finite difference schemes for fictitious domain simulation of solid-liquid flow; marker, volumetric, and hybrid forcing

摘要

We propose fictitious domain algorithms for accurately and economically capturing the momentum exchange between dispersed solids and a liquid carrier phase. Instead of solving separately the momentum equations for each phase, we model the solid-fluid system as a variable density fluid mixture with artificial body forces applied inside particles to recover rigid motion. These rigidity constraint forces can be evaluated volumetrically within grid cells [1] and/or at Lagrangian markers forming a rigid template [2]. We present three variants: volumetric, marker and hybrid forcing schemes, and test them in the context of a freely moving disk in 2D Couette flow and a sphere dropped in a 3D bath. The new hybrid scheme appears to combine the strengths of the basic methods well.