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A finite element approach to incompressible two-phase flow on manifolds

Published online by Cambridge University Press:  08 August 2012

I. Nitschke ,
A. Voigt  and
J. Wensch
I. Nitschke
Affiliation:
Institut für Wissenschaftliches Rechnen, Technische Universität Dresden, 01062 Dresden, Germany
A. Voigt*
Affiliation:
Institut für Wissenschaftliches Rechnen, Technische Universität Dresden, 01062 Dresden, Germany Center for Advanced Modeling and Simulation, Technische Universität Dresden, 01062 Dresden, Germany
J. Wensch
Affiliation:
Institut für Wissenschaftliches Rechnen, Technische Universität Dresden, 01062 Dresden, Germany
*
†Email address for correspondence: axel.voigt@tu-dresden.de
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Abstract

A two-phase Newtonian surface fluid is modelled as a surface Cahn–Hilliard–Navier–Stokes equation using a stream function formulation. This allows one to circumvent the subtleties in describing vectorial second-order partial differential equations on curved surfaces and allows for an efficient numerical treatment using parametric finite elements. The approach is validated for various test cases, including a vortex-trapping surface demonstrating the strong interplay of the surface morphology and the flow. Finally the approach is applied to a Rayleigh–Taylor instability and coarsening scenarios on various surfaces.

JFM classification

Biological Fluid Dynamics: Membranes Multiphase and Particle-laden Flows: Multiphase flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 708 , 10 October 2012 , pp. 418 - 438
Copyright
Copyright © Cambridge University Press 2012

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