Interfacial Dynamics for Stokes Flow

Pozrikidis, C.

doi:10.1006/jcph.2000.6582

Cited by 233 publications

(247 citation statements)

References 196 publications

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“…Pozrikidis [48] reviews the work on boundary integral formulations for particulate flows prior to 2000.…”

Section: Related Workmentioning

confidence: 99%

“…Several authors [6,7,16,17,35,57] have used direct integral equation formulation for simulating vesicle flows. This formulation results in a single-layer potential for flows with no viscosity contrast and a combination of a single-layer and a double-layer for flows with viscosity contrast [35,48,57,69]. A particular feature of vesicle flows is the local surface inextensibility constraint.…”

Section: Related Workmentioning

confidence: 99%

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A fast algorithm for simulating vesicle flows in three dimensions

Veerapaneni

Rahimian

Biros

et al. 2011

Journal of Computational Physics

136

143

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Vesicles are locally-inextensible fluid membranes that can sustain bending. In this paper, we extend "A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows", Veerapaneni et al. Journal of Computational Physics, 228(19), 2009 to general non-axisymmetric vesicle flows in three dimensions.Although the main components of the algorithm are similar in spirit to the axisymmetric case (spectral approximation in space, semi-implicit time-stepping scheme), important new elements need to be introduced for a full 3D method. In particular, spatial quantities are discretized using spherical harmonics, and quadrature rules for singular surface integrals need to be adapted to this case; an algorithm for surface reparameterization is neeed to ensure sufficient of the timestepping scheme, and spectral filtering is introduced to maintain reasonable accuracy while minimizing computational costs. To characterize the stability of the scheme and to construct preconditioners for the iterative linear system solvers used in the semi-implicit time-stepping scheme, we perform a spectral analysis of the evolution operator on the unit sphere.By introducing these algorithmic components, we obtain a time-stepping scheme that, in our numerical experiments, is unconditionally stable. We present results to analyze the cost and convergence rates of the overall scheme. To illustrate the applicability of the new method, we consider a few vesicle-flow interaction problems: a single vesicle in relaxation, sedimentation, shear flows, and many-vesicle flows.

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“…Pozrikidis [48] reviews the work on boundary integral formulations for particulate flows prior to 2000.…”

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

A fast algorithm for simulating vesicle flows in three dimensions

Veerapaneni

Rahimian

Biros

et al. 2011

Journal of Computational Physics

136

143

View full text Add to dashboard Cite

show abstract

“…To summarize, (21) and (22) give the update and incompressibility constraints, the forces f b and f σ are given by (15) and (16), and the single layer is given by (17). These equations form a closed system of equations for x(u) and σ(u).…”

Section: Axisymmetric Formulationmentioning

confidence: 99%

“…In [25] , we discussed vesicle-related algorithms. An excellent review of such methods can be found in [15] ( Table 1, pg. 289; for vesicles see the "liquid capsules" entry).…”

Section: Introductionmentioning

confidence: 99%

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

Veerapaneni

Gueyffier

Biros

et al. 2009

Journal of Computational Physics

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We extend "A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D", Veerapaneni et al. Journal of Computational Physics, 228(7), 2009 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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“…The principal value integral in (3.19) is computed using the method of singularity subtraction (Anselone 1981;Pozrikidis 2001) as in the case of Stokes flows…”

Section: Evaluation Of the Singular Integralsmentioning

confidence: 99%

Boundary integral formulation for flows containing an interface between two porous media

2017

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A system of boundary integral equations is derived for flows in domains composed of a porous medium of permeability k 1 , surrounded by another porous medium of different permeability, k 2 . The incompressible Brinkman equation is used to describe the flow in the porous media. We first apply a boundary integral representation of the Brinkman flow on each side of the dividing interface, and impose continuity of the velocity at the interface to derive the final formulation in terms of the interfacial velocity and surface forces. We discuss relations between the surface stresses based on the additional conditions imposed at the interface that depend on the porosity and permeability of the media and the structural composition of the interface. We present simulated results for test problems and different interface stress conditions. The results show significant sensitivity to the choice of the interface conditions, especially when the permeability is large. Since the Brinkman equation approaches the Stokes equation when the permeability approaches infinity, our boundary integral formulation can also be used to model the flow in sub-categories of Stokes-Stokes and Stokes-Brinkman configurations by considering infinite permeability in the Stokes fluid domain.

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Interfacial Dynamics for Stokes Flow

Cited by 233 publications

References 196 publications

A fast algorithm for simulating vesicle flows in three dimensions

A fast algorithm for simulating vesicle flows in three dimensions

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

Boundary integral formulation for flows containing an interface between two porous media

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