The divergence-conforming immersed boundary method: Application to vesicle and capsule dynamics
The divergence-conforming immersed boundary method: Application to vesicle and capsule dynamics
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DOI：
10.1016/j.jcp.2020.109872
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发表时间：
2021-01-15
影响因子：
4.1
通讯作者：
Zhang, Yongjie Jessica
中科院分区：
文献类型：
--
作者：
Casquero, Hugo;Bona-Casas, Carles;Zhang, Yongjie Jessica
我们将最近引入的散度一致浸入边界 (DCIB) 方法 [1] 扩展到涉及闭余维一固体的流固耦合 (FSI) 问题。我们专注于胶囊和囊泡，由于其配方中出现高阶导数，其离散化特别具有挑战性。在二维设置中，我们采用具有周期性结向量的三次 B 样条来获得具有 C-2 元素间连续性的闭合曲线的离散化。在三维设置中，我们使用适合分析的双三次 T 样条来获得具有至少 C-1 元素间连续性的闭合曲面的离散化。封闭共维一固体内流体体积的巨大虚假变化是 IB 方法的一个众所周知的问题。 DCIB 方法导致体积变化比传统 IB 方法低几个数量级。这是使用符合散度的 B 样条曲线离散化速度-压力对的副产品，这会导致欧拉水平上的不可压缩性误差可以忽略不计。符合散度的 B 样条的较高元素间连续性对于避免 IB 方法的求积/插值误差成为主要离散化误差也至关重要。解决了囊泡和胶囊动力学的基准和应用问题，包括网格无关性研究以及与其他数值方法的比较。 (C) 2020 作者。由爱思唯尔公司出版
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.