The divergence-conforming immersed boundary method: Application to vesicle and capsule dynamics

We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. focus on capsules and vesicles, whose discretization is particularly challenging due higher-order derivatives that appear in their formulations. In two-dimensional settings, we employ cubic B-splines with periodic knot vectors obtain discretizations of curves C^2 inter-element continuity. three-dimensional use analysis-suitable bi-cubic T-splines surfaces at least C^1 Large spurious changes fluid volume inside solids a well-known issue for IB methods. The DCIB results orders magnitude lower than conventional This byproduct discretizing velocity-pressure pair B-splines, which lead negligible incompressibility errors Eulerian level. higher continuity also crucial avoid quadrature/interpolation methods becoming dominant error. Benchmark application vesicle capsule dynamics are solved, including mesh-independence studies comparisons other numerical