A numerical approach for fluid deformable surfaces

Reuther, Sebastian; Nitschke, Ingo; Voigt, Axel

doi:10.1017/jfm.2020.564

Cited by 31 publications

(39 citation statements)

References 42 publications

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“…Using the solution on the triangulation with 130k vertices as reference we obtain quadratic error convergence in the solution components v and q. This is in agreement with the obtained convergence results for the individual problems, the surface Navier-Stokes equations [40,39] and the surface Landau-de Gennes model [28,31] and the expected results for the coupled problem in flat space.…”

Section: Numerical Approachsupporting

confidence: 88%

“…Surface normals and curvature quantities are given by analytical results on the nodes of the triangulation. If these quantities are not available we refer to [34,39] for appropriate ways, how they can be computed. In the corrector step we evaluate p i+1 via a relaxation scheme l → l + 1…”

Section: Numerical Approachmentioning

confidence: 99%

“…In [43,37] it is based on a vorticity-stream function formulation and thus is restricted to surfaces which are topologically equivalent to a sphere [32]. More general numerical approaches have been proposed in [29,40,39]. We here combine such a general formulation with a numerical approach for a surface Landau-de Gennes model with intrinsic and extrinsic curvature contributions [28,31] and demonstrate the relation between flow, topological defects and geometric properties of the surface for surface active nematodynamics on surfaces with varying Gaussian curvature.…”

Section: Introductionmentioning

confidence: 99%

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Active nematodynamics on curved surfaces -- the influence of geometric forces on motion patterns of topological defects

Nestler,

Voigt

2021

Preprint

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We derive and numerically solve a surface active nematodynamics model. We validate the numerical approach on a sphere and analyse the influence of hydrodynamics on the oscillatory motion of topological defects. For ellipsoidal surfaces the influence of geometric forces on these motion patterns is addressed by taking into account the effects of intrinsic as well as extrinsic curvature contributions. The numerical experiments demonstrate the stronger coupling with geometric properties if extrinsic curvature contributions are present and provide a possibility to tune flow and defect motion by surface properties.

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Section: Numerical Approachsupporting

confidence: 88%

Section: Numerical Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Active nematodynamics on curved surfaces -- the influence of geometric forces on motion patterns of topological defects

Nestler,

Voigt

2021

Preprint

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“…For viscous membranes, a few numerical implementations have been recently proposed based either using finite element models [55,34] or discrete geometric approaches (computer graphics) [56,57]. Yet, no numerical work has been dedicated to implementing viscous thin shells to our best knowledge.…”

Section: Preliminariesmentioning

confidence: 99%

A viscous active shell theory of the cell cortex

da Rocha,

Bleyer,

Turlier

2021

Preprint

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The cell cortex is a thin layer beneath the plasma membrane that gives animal cells mechanical resistance and drives most of their shape changes, from migration, division to multicellular morphogenesis. Constantly stirred by molecular motors and under fast renewal, this material is well described by viscous and contractile active-gel theories.Here, we assume that the cortex is a thin viscous shell with non-negligible curvature and use asymptotic expansions to find the leading-order equations describing its shape dynamics, starting from constitutive equations for an incompressible viscous active gel. Reducing the three-dimensional equations leads to a Koiter-like shell theory, where both resistance to stretching and bending rates are present. Constitutive equations are completed by a kinematical equation describing the evolution of the cortex thickness with turnover. We show that tension and moment resultants depend not only on the shell deformation rate and motor activity but also on the active turnover of the material, which may also exert either contractile or extensile stress. Using the finite-element method, we implement our theory numerically to study two biological examples of drastic cell shape changes: cell division and osmotic shocks. Our work provides a numerical implementation of thin active viscous layers and a generic theoretical framework to develop shell theories for slender active biological structures.

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“…These equations constrain the velocity and pressure to a surface and, at least for stationary surfaces, enforce the velocity to be tangential to the surface, which leads to a tide coupling with geometric properties of the surface and new physical phenomena. Despite the apparent practical relevance, there has been only recently a strongly growing mathematical interest in modeling of surface fluids, e.g., [4,42,26,28,29,35,40,55,57,68,54] and their numerical simulation, e.g., [42,5,55,39,53,58,17,43,9,46,7,45,68,30,54,69]. Surface (Navier-)Stokes equations are also studied as an interesting mathematical problem on its own, e.g., [15,67,66,3,34,2].…”

mentioning

confidence: 99%

Finite element discretization methods for velocity-pressure and stream function formulations of surface Stokes equations

Brandner¹,

Jankuhn²,

Praetorius³

et al. 2021

Preprint

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In this paper we study parametric TraceFEM and parametric SurfaceFEM (SFEM) discretizations of a surface Stokes problem. These methods are applied both to the Stokes problem in velocity-pressure formulation and in stream function formulation. A class of higher order methods is presented in a unified framework. Numerical efficiency aspects of the two formulations are discussed and a systematic comparison of TraceFEM and SFEM is given. A benchmark problem is introduced in which a scalar reference quantity is defined and numerically determined.

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A numerical approach for fluid deformable surfaces

Abstract: Abstract

Cited by 31 publications

References 42 publications

Active nematodynamics on curved surfaces -- the influence of geometric forces on motion patterns of topological defects

Active nematodynamics on curved surfaces -- the influence of geometric forces on motion patterns of topological defects

A viscous active shell theory of the cell cortex

Finite element discretization methods for velocity-pressure and stream function formulations of surface Stokes equations

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