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

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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.

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Authors and Affiliations

  1. School of Computing, University of Leeds, Leeds, LS2 9JT, UK

    M. A. Walkley & P. K. Jimack

  2. School of Mechanical Engineering, University of Leeds, Leeds, LS2 9JT, UK

    P. H. Gaskell & J. L. Summers

  3. Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK

    M. A. Kelmanson

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  1. M. A. Walkley
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  2. P. H. Gaskell
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  3. P. K. Jimack
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  4. M. A. Kelmanson
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  5. J. L. Summers
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Correspondence to M. A. Walkley.

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Walkley, M.A., Gaskell, P.H., Jimack, P.K. et al. Finite Element Simulation of Three-Dimensional Free-Surface Flow Problems. J Sci Comput 24, 147–162 (2005). https://doi.org/10.1007/s10915-004-4611-0

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  • DOI: https://doi.org/10.1007/s10915-004-4611-0

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