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Sigma transformation and ALE formulation for three‐dimensional free surface flows
Authors:A Decoene  J F Gerbeau
Institution:1. MOX‐Modelling and Scientific Computing, Dipartimento di Matematica ‘F. Brioschi’, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy;2. Project‐Team REO, INRIA Paris‐Rocquencourt, BP 105, F‐78153 Le Chesnay Cedex, France
Abstract:In this paper we establish a link between the sigma transformation approach and the arbitrary Lagrangian–Eulerian (ALE) approach. For that purpose we introduce the ALE‐sigma (ALES) approach, which consists in an ALE interpretation of the sigma transformation. Taking advantage of this new approach, we propose a general ALES transformation, allowing for a great adaptability of the vertical discretization and therefore overcoming some drawbacks of the classical sigma transformation. Numerical results are presented, showing the advantages of this general coordinate system, as, for example, a better representation of horizontal stratifications. Copyright © 2008 John Wiley & Sons, Ltd.
Keywords:sigma transformation  ALE  free surface flows  horizontal pressure gradient error
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