The divergence-conforming immersed boundary method
| Autor: | Deepesh Toshniwal, Carles Bona-Casas, Hector Gomez, Yongjie Jessica Zhang, Thomas J. R. Hughes, Hugo Casquero |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Physics and Astronomy (miscellaneous) Discretization FOS: Physical sciences Capsules 010103 numerical & computational mathematics Isogeometric analysis 01 natural sciences Computational Engineering Finance and Science (cs.CE) symbols.namesake Fluid–structure interaction Fluid-structure interaction Vesicles 0101 mathematics Computer Science - Computational Engineering Finance and Science Mathematics Immersed boundary method Numerical Analysis Applied Mathematics Numerical analysis Mathematical analysis Fluid Dynamics (physics.flu-dyn) Eulerian path Physics - Fluid Dynamics Computer Science Applications Quadrature (mathematics) 010101 applied mathematics Computational Mathematics Volume conservation Modeling and Simulation symbols Knot (mathematics) |
| Zdroj: | Journal of Computational Physics, 425 |
| ISSN: | 0021-9991 |
| Popis: | 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 is 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. For supplementary movies go to https://www.andrew.cmu.edu/user/hugocp/research.html |
| Databáze: | OpenAIRE |
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