Isogeometric FEM-BEM simulations of drop, capsule and vesicle dynamics in Stokes flow

We develop an algorithm for the three dimensional simulation of the dynamics of soft objects (drops, capsules, vesicles) under creeping flow conditions. Loop elements are used to describe the shape of the soft objects. This surface representation is used both for membrane solver based on finite element method (FEM) and for the fluid solver based on the boundary element method (BEM). This isogeometric analysis of the low Reynolds fluid-structure interaction problem is then coupled to high-order explicit time stepping or second-order implicit time stepping algorithm. For vesicles simulation, a preconditioner is designed for the resolution of the surface velocity incompressibility constraint, which is treated by the use of a local Lagrange multiplier. A mesh quality preserving algorithm is introduced to improve the control mesh quality over long simulation times. We test the proposed algorithm on capsule and vesicle dynamics in various flows, and study its convergence properties, showing a second-order convergence O(N−2) with mesh number of elements.