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

Hugo Casquero, Carles Bona-Casas, Deepesh Toshniwal, Thomas J.R. Hughes, Hector Gomez, Yongjie Jessica Zhang

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

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 C2 inter-element continuity. In three-dimensional settings, we use analysis-suitable bi-cubic T-splines to obtain discretizations of closed surfaces with at least C1 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.

Original languageEnglish
Article number109872
Pages (from-to)1-26
Number of pages26
JournalJournal of Computational Physics
Volume425
DOIs
Publication statusPublished - 2021

Keywords

  • Capsules
  • Fluid-structure interaction
  • Immersed boundary method
  • Isogeometric analysis
  • Vesicles
  • Volume conservation

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