# A simulation technique for slurries interacting with moving parts and deformable solids with applications

## TL;DR

This paper introduces a coupled numerical simulation method for particle-laden fluids interacting with deformable solids and moving parts, validated through piston-valve slurry flow applications.

## Contribution

It develops a unified coupling approach for lattice Boltzmann, discrete element, and Lagrangian mesh methods, including domain reduction techniques for efficient simulation.

## Key findings

- Validated the coupled simulation with separate component tests.
- Simulated slurry flows in piston-valve geometries.
- Analyzed valve and slurry dynamics across various parameters.

## Abstract

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.