In this paper, we present an isogeometric analysis for studying the dynamical behavior of inextensible vesicles under an external fluid flow with inertial forces. We consider a phase-field model Aland, et al. (2014) for the coupled fluid–vesicle problem which enforces global area and volume constraints using a Lagrange multiplier method and employs an extra equation for enforcing local inextensibility condition. Full Navier–Stokes equations are considered and their finite element formulation is presented based on a residual-based variational multiscale method while a standard Galerkin finite element framework is employed for the rest of partial differential equations in the model. We solve the system of PDEs using an implicit, monolithic scheme based on the generalized-$\alpha$ time integration method. Compared to the system of equations considered in Aland, et al. (2014), we reduce the number of equations to be solved by leveraging high continuity of NURBS functions. We also extend the algorithm of the phase-field method to three-dimensional problems. A number of two-dimensional numerical examples which model the dynamics of a vesicle in a quiescent fluid, in a shear flow, and in plane Poiseuille flow with and without obstructions are studied. The resistive immersed surface method is employed for dealing with obstructions. We also consider a 3D example where we study the dynamics of a vesicle in a constricted channel which resembles the situation that a vesicle experiences in a stenosed microchannel.

在本文中，我们提出了一种等几何分析，用于研究在具有惯性力的外部流体流动下不可伸展囊泡的动力学行为。我们考虑 Aland 等人的相场模型。(2014) 用于耦合流体 - 囊泡问题，该问题使用拉格朗日乘数方法强制执行全局面积和体积约束，并使用额外的方程来强制执行局部不可扩展条件。考虑了完整的 Navier-Stokes 方程，它们的有限元公式是基于基于残差的变分多尺度方法提出的，而模型中其余的偏微分方程采用标准 Galerkin 有限元框架。我们使用基于广义的隐式整体方案求解 PDE 系统$\alpha$时间积分法。与 Aland 等人考虑的方程组相比。(2014)，我们通过利用 NURBS 函数的高度连续性来减少要求解的方程的数量。我们还将相场法的算法扩展到三维问题。研究了许多二维数值示例，这些示例模拟了在有障碍物和无障碍物的情况下囊泡在静止流体、剪切流和平面 Poiseuille 流中的动力学。采用电阻浸入面法处理障碍物。我们还考虑了一个 3D 示例，在该示例中，我们研究了狭窄通道中囊泡的动力学，类似于囊泡在狭窄微通道中经历的情况。