A hybrid variational front tracking-level set mesh generator for problems exhibiting large deformations and topological changes

  • Authors:

  • Ricardo H. Nochetto;Shawn W. Walker

  • Affiliations:

  • University of Maryland, Department of Mathematics, Mathematics Building, College Park, MD 20742-4015, USA;New York University, Mathematics, Courant Inst., 251 Mercer Street, New York, NY 10012-1185, United States

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

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Abstract

We present a method for generating 2-D unstructured triangular meshes that undergo large deformations and topological changes in an automatic way. We employ a method for detecting when topological changes are imminent via distance functions and shape skeletons. When a change occurs, we use a level set method to guide the change of topology of the domain mesh. This is followed by an optimization procedure, using a variational formulation of active contours, that seeks to improve boundary mesh conformity to the zero level contour of the level set function. Our method is advantageous for Arbitrary-Lagrangian-Eulerian (ALE) type methods and directly allows for using a variational formulation of the physics being modeled and simulated, including the ability to account for important geometric information in the model (such as for surface tension driven flow). Furthermore, the meshing procedure is not required at every time-step and the level set update is only needed during a topological change. Hence, our method does not significantly affect computational cost.