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Sigma transformation and ALE formulation for three-dimensional free surface flows. (English) Zbl 1154.76031
Summary: 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.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76D33 Waves for incompressible viscous fluids
76D50 Stratification effects in viscous fluids
Software:
ROMS
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