A Dynamical System Describing Evolution of the Implicit Surfaces in Incompressible Viscous Liquids

Petr Klouček (), Michel V. Romerio () and Jennifer L. Wightman ()
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Petr Klouček: Rice University, Department of Computational and Applied Mathematics
Michel V. Romerio: École Polytechnique Fédérale de Lausanne, Institut d’Analyse et Calcul Scientifique
Jennifer L. Wightman: Rice University, Department of Computational and Applied Mathematics

A chapter in Numerical Mathematics and Advanced Applications, 2004, pp 569-579 from Springer

Abstract: Summary We present an equation capable of describing the evolution of implicit surfaces (boundaries of gas bubbles) in liquids. The equation does not contain any convective term and thus it is independent of the velocity and pressure fields, given by e.g. Navier-Stokes equations. The equation itself is obtained by a series of variational problems. First, by interpreting the Euler implicit time-stepping scheme for the update of Lagrangian flow maps as a Monge-Kantorovich transference problem. This approach provides then a variational principle for the updates of an Eulerian phase Indicatrix in terms of the Wasserstein metric. The Euler-Lagrange equations corresponding to the later variational principle provide the thought after evolution equation for the implicit surfaces.

Keywords: Variational Principle; Euler Equation; Implicit Surface; Incompressible Euler Equation; Incompressible Viscous Liquid (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-3-642-18775-9_54

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