Marangoni-Bénard convection with a deformable free surface
type: Item
instance of: scholarly article
title: Marangoni-Bénard convection with a deformable free surface
zbMATH Open document ID: 0924.76101
published in: Journal of Computational Physics
publication date: 1998-10-18T00:00:00Z
review text: We describe a finite element technique for calculating bifurcations that arise due to thermal gradients in a two-dimensional domain with a deformable free surface. The fluid is assumed to be Newtonian, to conform to the Boussinesq approximation, and to have a surface tension that varies linearly with temperature. An orthogonal mapping from the physical domain to a reference domain is employed, which is determined as the solution to a pair of elliptic partial differential equations. The mapping equations and the equilibrium equations for the velocity, pressure, and temperature fields and their appropriate nonlinear boundary conditions are discretized using the finite element method and solved simultaneously by Newton iteration. Contact angles other than 90 degrees are shown to disconnect the transcritical bifurcations to flows with an even number of cells in the expected manner. The loss of stability to single cell flows is associated with the breaking of a reflectional symmetry about the middle of the domain and therefore occurs at a pitchfork bifurcation point for contact angles both equal to, and less than, 90 degrees. \(\copyright\) Academic Press.
Mathematics Subject Classification ID: 76R05
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 76E15
Mathematics Subject Classification ID: 76D45
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 1212274
zbMATH Keywords: two-dimensional domain
zbMATH Keywords: Boussinesq approximation
zbMATH Keywords: orthogonal mapping
zbMATH Keywords: pair of elliptic partial differential equations
zbMATH Keywords: mapping equations
zbMATH Keywords: equilibrium equations
zbMATH Keywords: Newton iteration
zbMATH Keywords: transcritical bifurcations
zbMATH Keywords: pitchfork bifurcation point
author: K. A. Cliffe
author: S. J. Tavener
describes a project that uses: REDUCE
MaRDI profile type: Publication
full work available at URL: jcph.1998.5995
OpenAlex ID: W2042767410
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DOI: 10.1006/JCPH.1998.5995
description: scientific article; zbMATH DE number 1212274