  In this paper, a three-dimensional numerical solver is developed for
suspensions of rigid and soft particles and droplets in viscoelastic and
elastoviscoplastic (EVP) fluids. The presented algorithm is designed to allow
for the first time three-dimensional simulations of inertial and turbulent EVP
fluids with a large number particles and droplets. This is achieved by
combining fast and highly scalable methods such as an FFT-based pressure
solver, with the evolution equation for non-Newtonian (including
elastoviscoplastic) stresses. In this flexible computational framework, the
fluid can be modelled by either Oldroyd-B, neo-Hookean, FENE-P, and Saramito
EVP models, and the additional equations for the non-Newtonian stresses are
fully coupled with the flow. The rigid particles are discretized on a moving
Lagrangian grid while the flow equations are solved on a fixed Eulerian grid.
The solid particles are represented by an Immersed Boundary method (IBM) with a
computationally efficient direct forcing method allowing simulations of a large
numbers of particles. The immersed boundary force is computed at the particle
surface and then included in the momentum equations as a body force. The
droplets and soft particles on the other hand are simulated in a fully Eulerian
framework, the former with a level-set method to capture the moving interface
and the latter with an indicator function. The solver is first validated for
various benchmark single-phase and two-phase elastoviscoplastic flow problems
through comparison with data from the literature. Finally, we present new
results on the dynamics of a buoyancy-driven drop in an elastoviscoplastic
fluid.
