A natural element updated Lagrangian strategy for free-surface fluid dynamics

  • Authors:

  • D. González;E. Cueto;F. Chinesta;M. Doblaré

  • Affiliations:

  • Aragón Institute of Engineering Research., University of Zaragoza, Edificio Betancourt, Campus Rio Ebro. María de Luna, s.n. E-50018 Zaragoza, Spain;Aragón Institute of Engineering Research., University of Zaragoza, Edificio Betancourt, Campus Rio Ebro. María de Luna, s.n. E-50018 Zaragoza, Spain;Laboratoire de Mécanique des Systémes et des Procédés, LMSP UMR 8106, CNRS-ENSAM-ESEM, 105, Bvd. de l'Hôpital, F-75013 Paris, France;Aragón Institute of Engineering Research., University of Zaragoza, Edificio Betancourt, Campus Rio Ebro. María de Luna, s.n. E-50018 Zaragoza, Spain

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

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Abstract

We present a novel algorithm to simulate free-surface fluid dynamics phenomena at low Reynolds numbers in an updated Lagrangian framework. It is based on the use of one of the most recent meshless methods, the so-called natural element method. Free-surface tracking is performed by employing a particular instance of ''shape constructors'' called @a-shapes. This means that at each time step the geometry of the domain is extracted by employing a particular member of the finite set of shapes described by the nodal cloud. The Lagrangian framework allows us to integrate the inertial terms of the Navier-Stokes equations by employing the method of characteristics which are, precisely, the nodal pathlines. A theoretical description of the method is included together with some examples showing its performance.