A continuous energy-based immersed boundary method for elastic shells
A continuous energy-based immersed boundary method for elastic shells
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DOI：
10.1016/j.jcp.2018.05.045
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发表时间：
2018-10-15
影响因子：
4.1
通讯作者：
Strychalski, Wanda
中科院分区：
文献类型：
--
作者：
Maxian, Ondrej;Kassen, Andrew T.;Strychalski, Wanda
浸入边界法是一种求解流固耦合问题的数学公式和数值方法。对于许多生物学问题，例如包括细胞膜的模型，浸没结构是浸没在不可压缩粘性流体中的二维无限薄弹性壳体。当壳体被建模为超弹性材料时，力可以通过取能量密度泛函的变分导数来计算。本文提出了一种计算壳体全表面连续力函数的新方法。新的方法相比，以前的配方中的表面和能量功能的离散力计算之前。对于Stokes流的情况，提供了一种用于计算正交权重的方法，以确保弹性扩展力密度的积分在整个动态模拟中保持为零。对该方法进行了测试，结果表明，它产生更准确的力计算比以前的配方，以及更准确的几何信息，如平均曲率。然后将该方法应用于毛细血管流动中的红细胞模型和细胞起泡的3D模型。(C)2018爱思唯尔公司All rights reserved.
The immersed boundary method is a mathematical formulation and numerical method for solving fluid-structure interaction problems. For many biological problems, such as models that include the cell membrane, the immersed structure is a two-dimensional infinitely thin elastic shell immersed in an incompressible viscous fluid. When the shell is modeled as a hyperelastic material, forces can be computed by taking the variational derivative of an energy density functional. A new method for computing a continuous force function on the entire surface of the shell is presented here. The new method is compared to a previous formulation where the surface and energy functional are discretized before forces are computed. For the case of Stokes flow, a method for computing quadrature weights is provided to ensure the integral of the elastic spread force density remains zero throughout a dynamic simulation. Tests on the method are conducted and show that it yields more accurate force computations than previous formulations as well as more accurate geometric information such as mean curvature. The method is then applied to a model of a red blood cell in capillary flow and a 3D model of cellular blebbing. (C) 2018 Elsevier Inc. All rights reserved.