A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D

JOURNAL OF COMPUTATIONAL PHYSICS

卷:228

Article

Veerapaneni, Shravan K.²  Gueyffier, Denis³  Zorin, Denis³  Biros, George¹ 

[1] Georgia Inst Technol, Coll Comp, Atlanta, GA 30332 USA

[2] Univ Penn, Sch Engn & Appl Sci, Philadelphia, PA 19104 USA

[3] NYU, Courant Inst Math Sci, New York, NY 10012 USA

关键词: Particulate flows;    Integral equations;    Numerical methods;    Fluid membranes;    Inextensible vesicles;    Fast summation methods;    Moving boundaries;   

DOI  :  10.1016/j.jcp.2008.11.036

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free