Immersed-finite-element method for deformable particle suspensions in viscous and viscoelastic media

Deformable elastic bodies in viscous and viscoelastic media constitute a large portion of synthetic and biological complex fluids. We present a parallelized three-dimensional 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 remeshing, handling finite Reynolds number, as well as incorporating nonlinear viscoelasticity in the fluid domain. Our algorithm is designed for computationally efficient simulation of multiparticle 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 multiparticle simulation of blood suspensions (red blood cells in plasma) with and without platelets. Finally, we present the results of a simulation of multiple solid deformable objects in a viscoelastic medium.