Finite Element Simulation of Three-Dimensional Free-Surface Flow Problems

Authors:
M. A. Walkley;P. H. Gaskell;P. K. Jimack;M. A. Kelmanson;J. L. Summers
Affiliations:
School of Computing, University of Leeds, Leeds, UK LS2 9JT;School of Mechanical Engineering, University of Leeds, Leeds, UK LS2 9JT;School of Computing, University of Leeds, Leeds, UK LS2 9JT;Department of Applied Mathematics, University of Leeds, Leeds, UK LS2 9JT;School of Mechanical Engineering, University of Leeds, Leeds, UK LS2 9JT
Venue:
Journal of Scientific Computing
Year:
2005

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Abstract

An adaptive finite element algorithm is described for the stable solution of three-dimensional free-surface-flow problems based primarily on the use of node movement. The algorithm also includes a discrete remeshing procedure which enhances its accuracy and robustness. The spatial discretisation allows an isoparametric piecewise-quadratic approximation of the domain geometry for accurate resolution of the curved free surface. The technique is illustrated through an implementation for surface-tension-dominated viscous flows modelled in terms of the Stokes equations with suitable boundary conditions on the deforming free surface. Two three-dimensional test problems are used to demonstrate the performance of the method: a liquid bridge problem and the formation of a fluid droplet.