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首页> 外文期刊>Journal of Computational Physics >A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D
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A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D

机译：边界积分法模拟二维粘性流体中不可膨胀囊泡的动力学

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We present a new method for the evolution of inextensible vesicles immersed in a Stokesian fluid. We use a boundary integral formulation for the fluid that results in a set of nonlinear integro-differential equations for the vesicle dynamics. The motion of the vesicles is determined by balancing the non-local hydrodynamic forces with the elastic forces due to bending and tension. Numerical simulations of such vesicle motions are quite challenging. On one hand, explicit time-stepping schemes suffer from a severe stability constraint due to the stiffness related to high-order spatial derivatives and a milder constraint due to a transport-like stability condition. On the other hand, an implicit scheme can be expensive because it requires the solution of a set of nonlinear equations at each time step. We present two semi-implicit schemes that circumvent the severe stability constraints on the time step and whose computational cost per time step is comparable to that of an explicit scheme. We discretize the equations by using a spectral method in space, and a multistep third-order accurate scheme in time. We use the fast multipole method (FMM) to efficiently compute vesicle-vesicle interaction forces in a suspension with a large number of vesicles. We report results from numerical experiments that demonstrate the convergence and algorithmic complexity properties of our scheme. (C) 2008 Elsevier Inc. All rights reserved.
机译：我们提出了一种浸入斯托克斯流体中的不可扩展囊泡演变的新方法。我们对流体使用边界积分公式，从而导致了囊泡动力学的一组非线性积分微分方程。囊泡的运动是通过平衡非局部流体动力与弯曲和拉伸产生的弹力来确定的。这种囊泡运动的数值模拟非常具有挑战性。一方面，由于与高阶空间导数相关的刚度，显式的时间步长方案遭受了严重的稳定性约束，而由于类似运输的稳定性条件，使得方案受到了较温和的约束。另一方面，隐式方案可能很昂贵，因为它需要在每个时间步求解一组非线性方程。我们提出了两个半隐式方案，它们在时间步长上规避了严格的稳定性约束，并且每个时间步长的计算成本与显式方案的计算成本相当。我们通过使用空间中的频谱方法和及时的多步三阶精确方案来离散化方程式。我们使用快速多极方法（FMM）来有效地计算具有大量囊泡的悬浮液中的囊泡-囊泡相互作用力。我们报告了数值实验的结果，这些结果证明了我们方案的收敛性和算法复杂性。 （C）2008 Elsevier Inc.保留所有权利。

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