article

A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows

Authors:

Shravan K. Veerapaneni,

Denis Gueyffier,

Denis ZorinAuthors Info & Claims

Journal of Computational Physics, Volume 228, Issue 19

Pages 7233 - 7249

https://doi.org/10.1016/j.jcp.2009.06.020

Published: 01 October 2009 Publication History

Abstract

We extend [Shravan K. Veerapaneni, Denis Gueyffier, Denis Zorin, George Biros, A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D, Journal of Computational Physics 228(7) (2009) 2334-2353] to the case of three-dimensional axisymmetric vesicles of spherical or toroidal topology immersed in viscous flows. Although the main components of the algorithm are similar in spirit to the 2D case-spectral approximation in space, semi-implicit time-stepping scheme-the main differences are that the bending and viscous force require new analysis, the linearization for the semi-implicit schemes must be rederived, a fully implicit scheme must be used for the toroidal topology to eliminate a CFL-type restriction and a novel numerical scheme for the evaluation of the 3D Stokes single layer potential on an axisymmetric surface is necessary to speed up the calculations. By introducing these novel components, we obtain a time-scheme that experimentally is unconditionally stable, has low cost per time step, and is third-order accurate in time. We present numerical results to analyze the cost and convergence rates of the scheme. To verify the solver, we compare it to a constrained variational approach to compute equilibrium shapes that does not involve interactions with a viscous fluid. To illustrate the applicability of method, we consider a few vesicle-flow interaction problems: the sedimentation of a vesicle, interactions of one and three vesicles with a background Poiseuille flow.

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Malhotra DBarnett A(2024)Efficient convergent boundary integral methods for slender bodiesJournal of Computational Physics10.1016/j.jcp.2024.112855503:COnline publication date: 15-Apr-2024
https://dl.acm.org/doi/10.1016/j.jcp.2024.112855
Le Gia QLi MWang Y(2021)Algorithm 1018: FaVeST—Fast Vector Spherical Harmonic TransformsACM Transactions on Mathematical Software10.1145/345847047:4(1-24)Online publication date: 28-Sep-2021
https://dl.acm.org/doi/10.1145/3458470
Lu LMorse MRahimian AStadler GZorin DTaufer MBalaji PPeña A(2019)Scalable simulation of realistic volume fraction red blood cell flows through vascular networksProceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis10.1145/3295500.3356203(1-30)Online publication date: 17-Nov-2019
https://dl.acm.org/doi/10.1145/3295500.3356203
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A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
2. Theory of computation

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Published In

cover image Journal of Computational Physics

Journal of Computational Physics Volume 228, Issue 19

October, 2009

373 pages

ISSN:0021-9991

Issue’s Table of Contents

Copyright © Elsevier Inc. © 2009.

Publisher

Academic Press Professional, Inc.

United States

Publication History

Published: 01 October 2009

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Cited By

Malhotra DBarnett A(2024)Efficient convergent boundary integral methods for slender bodiesJournal of Computational Physics10.1016/j.jcp.2024.112855503:COnline publication date: 15-Apr-2024
https://dl.acm.org/doi/10.1016/j.jcp.2024.112855
Le Gia QLi MWang Y(2021)Algorithm 1018: FaVeST—Fast Vector Spherical Harmonic TransformsACM Transactions on Mathematical Software10.1145/345847047:4(1-24)Online publication date: 28-Sep-2021
https://dl.acm.org/doi/10.1145/3458470
Lu LMorse MRahimian AStadler GZorin DTaufer MBalaji PPeña A(2019)Scalable simulation of realistic volume fraction red blood cell flows through vascular networksProceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis10.1145/3295500.3356203(1-30)Online publication date: 17-Nov-2019
https://dl.acm.org/doi/10.1145/3295500.3356203
Barrett JGarcke HNürnberg R(2019)Variational discretization of axisymmetric curvature flowsNumerische Mathematik10.1007/s00211-018-1013-z141:3(791-837)Online publication date: 1-Mar-2019
https://dl.acm.org/doi/10.1007/s00211-018-1013-z
Seol YHu WKim YLai M(2016)An immersed boundary method for simulating vesicle dynamics in three dimensionsJournal of Computational Physics10.1016/j.jcp.2016.06.035322:C(125-141)Online publication date: 1-Oct-2016
https://dl.acm.org/doi/10.1016/j.jcp.2016.06.035
Trozzo RBoedec GLeonetti MJaeger M(2015)Axisymmetric Boundary Element Method for vesicles in a capillaryJournal of Computational Physics10.1016/j.jcp.2015.02.022289:C(62-82)Online publication date: 15-May-2015
https://dl.acm.org/doi/10.1016/j.jcp.2015.02.022
Heintz A(2015)A numerical method for simulation dynamics of incompressible lipid membranes in viscous fluidJournal of Computational and Applied Mathematics10.1016/j.cam.2015.03.011289:C(87-100)Online publication date: 1-Dec-2015
https://dl.acm.org/doi/10.1016/j.cam.2015.03.011
Hu WKim YLai M(2014)An immersed boundary method for simulating the dynamics of three-dimensional axisymmetric vesicles in Navier-Stokes flowsJournal of Computational Physics10.5555/2743142.2743717257:PA(670-686)Online publication date: 15-Jan-2014
https://dl.acm.org/doi/10.5555/2743142.2743717
Peco CRosolen AArroyo M(2013)An adaptive meshfree method for phase-field models of biomembranes. Part IIJournal of Computational Physics10.5555/2743138.2743485249:C(320-336)Online publication date: 15-Sep-2013
https://dl.acm.org/doi/10.5555/2743138.2743485
Salac DMiksis M(2011)A level set projection model of lipid vesicles in general flowsJournal of Computational Physics10.1016/j.jcp.2011.07.019230:22(8192-8215)Online publication date: 1-Sep-2011
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