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

Shravan K. Veerapaneni, Denis Gueyffier, George Biros, Denis Zorin

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)7233-7249
Number of pages17
JournalJournal of Computational Physics
Volume228
Issue number19
DOIs
StatePublished - Oct 20 2009

Fingerprint

viscous flow
Viscous flow
Numerical methods
Topology
Flow interactions
Fluids
viscous fluids
Sedimentation
Linearization
Costs
topology
Physics
boundary integral method
interactions
linearization
laminar flow
constrictions
costs
physics
evaluation

Keywords

  • Axisymmetric flows
  • Fluid membranes
  • Inextensible vesicles
  • Integral equations
  • Moving boundaries
  • Numerical methods
  • Particulate flows

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy (miscellaneous)

Cite this

A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows. / Veerapaneni, Shravan K.; Gueyffier, Denis; Biros, George; Zorin, Denis.

In: Journal of Computational Physics, Vol. 228, No. 19, 20.10.2009, p. 7233-7249.

Research output: Contribution to journalArticle

Veerapaneni, Shravan K. ; Gueyffier, Denis ; Biros, George ; Zorin, Denis. / A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows. In: Journal of Computational Physics. 2009 ; Vol. 228, No. 19. pp. 7233-7249.
@article{7d9295524f5446bb93c6f1758cb6d792,
title = "A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows",
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.",
keywords = "Axisymmetric flows, Fluid membranes, Inextensible vesicles, Integral equations, Moving boundaries, Numerical methods, Particulate flows",
author = "Veerapaneni, {Shravan K.} and Denis Gueyffier and George Biros and Denis Zorin",
year = "2009",
month = "10",
day = "20",
doi = "10.1016/j.jcp.2009.06.020",
language = "English (US)",
volume = "228",
pages = "7233--7249",
journal = "Journal of Computational Physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",
number = "19",

}

TY - JOUR

T1 - A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows

AU - Veerapaneni, Shravan K.

AU - Gueyffier, Denis

AU - Biros, George

AU - Zorin, Denis

PY - 2009/10/20

Y1 - 2009/10/20

N2 - 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.

AB - 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.

KW - Axisymmetric flows

KW - Fluid membranes

KW - Inextensible vesicles

KW - Integral equations

KW - Moving boundaries

KW - Numerical methods

KW - Particulate flows

UR - http://www.scopus.com/inward/record.url?scp=68549103443&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=68549103443&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2009.06.020

DO - 10.1016/j.jcp.2009.06.020

M3 - Article

AN - SCOPUS:68549103443

VL - 228

SP - 7233

EP - 7249

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 19

ER -