ReALE: A reconnection-based arbitrary-Lagrangian-Eulerian method

  • Authors:

  • Raphaël Loubère;Pierre-Henri Maire;Mikhail Shashkov;Jérôme Breil;Stéphane Galera

  • Affiliations:

  • Institut de Mathématiques de Toulouse, CNRS, Université de Toulouse, 118 Route de Narbonne, 31062 Toulouse cedex 9, France;UMR CELIA, Université Bordeaux I 351, Cours de la Libération, 33405 Talence, France;Los Alamos National Laboratory, T-5, Los Alamos, NM 87545, USA;UMR CELIA, Université Bordeaux I 351, Cours de la Libération, 33405 Talence, France;UMR CELIA, Université Bordeaux I 351, Cours de la Libération, 33405 Talence, France

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2010

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Abstract

We present a new reconnection-based arbitrary-Lagrangian-Eulerian (ALE) method. The main elements in a standard ALE simulation are an explicit Lagrangian phase in which the solution and grid are updated, a rezoning phase in which a new grid is defined, and a remapping phase in which the Lagrangian solution is transferred (conservatively interpolated) onto the new grid. In standard ALE methods the new mesh from the rezone phase is obtained by moving grid nodes without changing connectivity of the mesh. Such rezone strategy has its limitation due to the fixed topology of the mesh. In our new method we allow connectivity of the mesh to change in rezone phase, which leads to general polygonal mesh and allows to follow Lagrangian features of the mesh much better than for standard ALE methods. Rezone strategy with reconnection is based on using Voronoi tessellation. We demonstrate performance of our new method on series of numerical examples and show it superiority in comparison with standard ALE methods without reconnection.