Vorticity‐stream function approaches are inappropriate to solve the surface Navier‐Stokes equation on a torus

Nitschke, Ingo; Reuther, Sebastian; Voigt, Axel

doi:10.1002/pamm.202000006

Cited by 5 publications

(1 citation statement)

References 12 publications

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“…Another critical issue is the considered numerical approach for the Navier-Stokes-like equations. 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].…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

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

Nestler,

Voigt

2021

Preprint

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A numerical approach for fluid deformable surfaces with conserved enclosed volume

Krause

Voigt

2023

Journal of Computational Physics

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Active flows on curved surfaces

Rank

Voigt

2021

Physics of Fluids

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We consider a numerical approach for a covariant generalized Navier–Stokes equation on general surfaces and study the influence of varying Gaussian curvature on anomalous vortex-network active turbulence. This regime is characterized by self-assembly of finite-size vortices into linked chains of anti-ferromagnet order, which percolate through the entire surface. The simulation results reveal an alignment of these chains with minimal curvature lines of the surface and indicate a dependency of this turbulence regime on the sign and the gradient in local Gaussian curvature. While these results remain qualitative and their explanations are still incomplete, several of the observed phenomena are in qualitative agreement with experiments on active nematic liquid crystals on toroidal surfaces and contribute to an understanding of the delicate interplay between geometrical properties of the surface and characteristics of the flow field, which has the potential to control active flows on surfaces via gradients in the spatial curvature of the surface.

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Vorticity‐stream function approaches are inappropriate to solve the surface Navier‐Stokes equation on a torus

Cited by 5 publications

References 12 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 numerical approach for fluid deformable surfaces with conserved enclosed volume

Active flows on curved surfaces

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