Adaptive Triangulation of Evolving, Closed, or Open Surfaces by the Advancing-Front Method

Kwak, Sehoon; Pozrikidis, C.

doi:10.1006/jcph.1998.6030

Cited by 43 publications

(31 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such computational work has been shown to be consistent with experimental results (Rumscheidt & Mason 1961;Kwak & Pozrikidis 1998). Many authors have also determined well known analytical results based on the main assumption of small deformation theory: (Taylor 1934;Chaffey & Brenner 1967;Cox 1969;Barthès-Biesel & Acrivos 1973;Rallison 1980;Vlahovska, Blawzdziewicz & Loewenberg 2005, 2009a.…”

Section: Clean Droplet In Shear Flowsupporting

confidence: 80%

“…The shape of a clean droplet (Bq = 0) in shear flow has been extensively studied numerically in the past using the boundary element method (Rallison 1981;Kennedy et al 1994), advancing front method (Kwak & Pozrikidis 1998) and volume-of-fluid method (Li et al 2000), among many others. Such computational work has been shown to be consistent with experimental results (Rumscheidt & Mason 1961;Kwak & Pozrikidis 1998).…”

Section: Clean Droplet In Shear Flowmentioning

confidence: 99%

See 1 more Smart Citation

Influence of surface viscosity on droplets in shear flow

et al. 2016

View full text Add to dashboard Cite

The behaviour of a single droplet in an immiscible external fluid, submitted to shear flow is investigated using numerical simulations. The surface of the droplet is modelled by a Boussinesq-Scriven constitutive law involving the interfacial viscosities and a constant surface tension. A numerical method using Loop subdivision surfaces to represent droplet interface is introduced. This method couples boundary element method for fluid flows and finite element method to take into account the stresses due to the surface dilational and shear viscosities and surface tension. Validation of the numerical scheme with respect to previous analytic and computational work is provided, with particular attention to the viscosity contrast and the shear and dilational viscosities characterized both by a Boussinesq number B q . Then, influence of equal surface viscosities on steady-state characteristics of a droplet in shear flow are studied, considering both small and large deformations and for a large range of bulk viscosity contrast. We find that small deformation analysis is surprisingly predictive at moderate and high surface viscosities. Equal surface viscosities decrease the Taylor deformation parameter and tank-treading angle and also strongly modify the dynamics of the droplet: when the Boussinesq number (surface viscosity) is large relative to the capillary number (surface tension), the droplet displays damped oscillations prior to steady-state tank-treading, reminiscent from the behaviour at large viscosity contrast. In the limit of infinite capillary number Ca, such oscillations are permanent. The influence of surface viscosities on breakup is also investigated, and results show that the critical capillary number is increased. A diagram (B q ; Ca) of breakup is established with the same inner and outer bulk viscosities. Additionally, the separate roles of shear and dilational surface viscosity are also elucidated, extending results from small deformation analysis. Indeed, shear (dilational) surface viscosity increases (decreases) the stability of drops to breakup under shear flow. The steady-state deformation (Taylor parameter) varies nonlinearly with each Boussinesq number or a linear combination of both Boussinesq numbers. Finally, the study shows that for certain combinations of shear and dilational viscosities, drop deformation for a given capillary number is the same as in the case of a clean surface while the inclination angle varies.

show abstract

Section: Clean Droplet In Shear Flowsupporting

confidence: 80%

Section: Clean Droplet In Shear Flowmentioning

confidence: 99%

Influence of surface viscosity on droplets in shear flow

et al. 2016

View full text Add to dashboard Cite

show abstract

“…An advancing-front method for remeshing of quadratic triangular elements (originally proposed in [39]) adapting triangle size to local criteria such as curvature is described in [36] and is extended in a number subsequent papers to surfaces, in particular in Lohner [42]. Tryggvason et al [60] briefly describe an algorithm for adapting a mesh to an evolving fluid interface, which uses edge length as a criterion for bisection and edge collapses to remove small elements.…”

Section: Related Workmentioning

confidence: 99%

“…In the context of deformable surfaces, the need and methods for maintaining grid quality is ubiquitous. All the resampling methods known to us in this context focus on mesh-based surface representations (primarily piecewise-linear, but also higher-order, e.g., [36]) and we are not aware of any methods designed for spectral discretizations.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

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

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.

show abstract

Curve linearization and discretization for meshing composite parametric surfaces

Laug

Borouchaki

2004

Commun. Numer. Meth. Engng.

View full text Add to dashboard Cite

SUMMARYIn the context of composite parametric surface meshing using a direct or an indirect (via the meshing of parametric domains) method, the discretization of interface curves joining patches plays a central part. In the case of an indirect method, the discretization of interface curves must be taken back to parametric spaces. This is usually done using root ÿnding techniques for generally non-linear parametric functions. This paper presents a new linearization technique to determine the above correspondence. In addition, this linearization of interface curves makes it possible to obtain their discretization without explicitly computing the arc length. This method has been implemented in a surface mesh generator and an example from Fluid Mechanics is given to illustrate the pertinence of the proposed approach.

show abstract

Adaptive Triangulation of Evolving, Closed, or Open Surfaces by the Advancing-Front Method

Cited by 43 publications

References 23 publications

Influence of surface viscosity on droplets in shear flow

Influence of surface viscosity on droplets in shear flow

A fast algorithm for simulating vesicle flows in three dimensions

Curve linearization and discretization for meshing composite parametric surfaces

Contact Info

Product

Resources

About