A Smoothed Particle Hydrodynamics scheme for arbitrarily shaped rigid bodies within highly viscous fluids

We present a Smoothed Particle Hydrodynamics (SPH) scheme suitable to model spatially resolved flow of arbitrarily shaped rigid bodies within highly viscous fluids. Coupling to other methods is avoided by representing both fluid and solid phase by SPH particles. The scheme consists of two elements, an implicit viscosity solver and a rigid body solver, both of which are adapted from existing literature. We present how both methods can be coupled with ease and little modification. The scheme presented in this paper can be used for simulations of a representative volume element in which the motion of rigid bodies can be studied in defined velocity gradients composed of elongation and/or shear conditions. The scheme only requires stabilization by particle shifting. However, this causes the loss of exact momentum and energy conservation at the boundary between fluid and rigid bodies. Results are shown for both 2-dimensional and 3-dimensional simulations including academic cases with existing analytical solutions and industrially relevant cases of semi-dilute suspensions of rigid bodies of various shapes.