A quadrature-free discontinuous Galerkin method for the level set equation

  • Authors:

  • Emilie Marchandise;Jean-François Remacle;Nicolas Chevaugeon

  • Affiliations:

  • Department of Civil Engineering, Université catholique de Louvain (UCL), Place du Levant 1, 1348 Louvain-la-Neuve, Belgium and Fonds National de la Recherche Scientifique, rue d'Egmont 5, 100 ...;Department of Civil Engineering, Université catholique de Louvain (UCL), Place du Levant 1, 1348 Louvain-la-Neuve, Belgium and Center for Systems Engineering and Applied Mechanics (CESAME), U ...;Department of Civil Engineering, Université catholique de Louvain (UCL), Place du Levant 1, 1348 Louvain-la-Neuve, Belgium

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2006

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Abstract

A quadrature free, Runge-Kutta discontinuous Galerkin method (QF-RK-DGM) is developed to solve the level set equation written in a conservative form on two- and tri-dimensional unstructured grids. We show that the DGM implementation of the level set approach brings a lot of additional benefits as compared to traditional ENO level set realizations. Some examples of computations are provided that demonstrate the high order of accuracy and the computational efficiency of the method.