  A numerical method for particle-laden fluids interacting with a deformable
solid domain and mobile rigid parts is proposed and implemented in a full
engineering system. The fluid domain is modeled with a lattice Boltzmann
representation, the particles and rigid parts are modeled with a discrete
element representation, and the deformable solid domain is modeled using a
Lagrangian mesh. The main issue of this work, since separately each of these
methods is a mature tool, is to develop coupling and model-reduction approaches
in order to efficiently simulate coupled problems of this nature, as occur in
various geological and engineering applications. The lattice Boltzmann method
incorporates a large-eddy simulation technique using the Smagorinsky turbulence
model. The discrete element method incorporates spherical and polyhedral
particles for stiff contact interactions. A neo-Hookean hyperelastic model is
used for the deformable solid. We provide a detailed description of how to
couple the three solvers within a unified algorithm. The technique we propose
for rubber modeling/coupling exploits a simplification that prevents having to
solve a finite-element problem each time step. We also develop a technique to
reduce the domain size of the full system by replacing certain zones with
quasi-analytic solutions, which act as effective boundary conditions for the
lattice Boltzmann method. The major ingredients of the routine are are
separately validated. To demonstrate the coupled method in full, we simulate
slurry flows in two kinds of piston-valve geometries. The dynamics of the valve
and slurry are studied and reported over a large range of input parameters.
