  Deformable elastic bodies in viscous and viscoelastic media constitute a
large portion of synthetic and biological complex fluids. We present a
parallelized 3D-simulation methodology which fully resolves the momentum
balance in the solid and fluid domains. An immersed boundary algorithm is
exploited known as the immersed finite element method (IFEM) which accurately
determines the internal forces in the solid domain. The scheme utilized has the
advantages of requiring no costly re-meshing, handling finite Reynold's number,
as well as incorporating non-linear viscoelasticity in the fluid domain. Our
algorithm is designed for computationally efficient simulation of
multi-particle suspensions with mixed structure types. The internal force
calculation in the solid domain in the IFEM is coupled with a finite volume
based incompressible fluid solver, both of which are massively parallelized for
distributed memory architectures. We performed extensive case studies to ensure
the fidelity of our algorithm. Namely, a series of single particle simulations
for capsules, red blood cells, and elastic solid deformable particles were
conducted in viscous and viscoelastic media. All of our results are in
excellent quantitative agreement with the corresponding reported data in the
literature which are based on different simulation platforms. Furthermore, we
assess the accuracy of multi-particle simulation of blood suspensions (red
blood cells in plasma) with and without platelets. Finally, we present the
results of a novel simulation of multiple solid deformable objects in a
viscoelastic medium.
