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. We focus on capsules and vesicles, whose discretization is particularly challenging due to the higher-order derivatives that appear in their formulations. In two-dimensional settings, we employ cubic B-splines with periodic knot vectors to obtain discretizations of closed curves with C-2 inter-element continuity. In three-dimensional settings, we use analysis-suitable bi-cubic T-splines to obtain discretizations of closed surfaces with at least C-1 inter-element continuity. Large spurious changes of the fluid volume inside closed co-dimension one solids are a well-known issue for IB methods. The DCIB method results in volume changes orders of magnitude lower than conventional IB methods. This is a byproduct of discretizing the velocity-pressure pair with divergence-conforming B-splines, which lead to negligible incompressibility errors at the Eulerian level. The higher inter-element continuity of divergence-conforming B-splines is also crucial to avoid the quadrature/interpolation errors of IB methods becoming the dominant discretization error. Benchmark and application problems of vesicle and capsule dynamics are solved, including mesh-independence studies and comparisons with other numerical methods. (C) 2020 The Authors. Published by Elsevier Inc.

Automated summary

The paper introduces a new divergence-conforming immersed boundary (DCIB) method for fluid-structure interaction problems involving closed co-dimension one solids, focusing on capsules and vesicles. By discretizing the velocity-pressure pair with divergence-conforming B-splines, the method significantly reduces the large spurious changes of fluid volume inside closed co-dimension one solids, resulting in higher discretization accuracy.