Journal of Scientific Computing

, Volume 35, Issue 2–3, pp 114–131

Second-Order Accurate Computation of Curvatures in a Level Set Framework Using Novel High-Order Reinitialization Schemes

  • Antoine du Chéné
  • Chohong Min
  • Frédéric Gibou
SI Level Set Method

DOI: 10.1007/s10915-007-9177-1

Cite this article as:
du Chéné, A., Min, C. & Gibou, F. J Sci Comput (2008) 35: 114. doi:10.1007/s10915-007-9177-1

Abstract

We present a high-order accurate scheme for the reinitialization equation of Sussman et al.(J. Comput. Phys. 114:146–159, [1994]) that guarantees accurate computation of the interface’s curvatures in the context of level set methods. This scheme is an extension of the work of Russo and Smereka (J. Comput. Phys. 163:51–67, [2000]). We present numerical results in two and three spatial dimensions to demonstrate fourth-order accuracy for the reinitialized level set function, third-order accuracy for the normals and second-order accuracy for the interface’s mean curvature in the L1- and L-norms. We also exploit the work of Min and Gibou (UCLA CAM Report (06-22), [2006]) to show second-order accurate scheme for the computation of the mean curvature on non-graded adaptive grids.

Keywords

Level set method Second-order accurate curvature Reinitialization equation Adaptive mesh refinement 

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Antoine du Chéné
    • 1
    • 2
  • Chohong Min
    • 3
  • Frédéric Gibou
    • 4
  1. 1.Mechanical Engineering DepartmentUniversity of CaliforniaSanta BarbaraUSA
  2. 2.École PolytechniquePalaiseauFrance
  3. 3.Mathematics Department and Research Institute for Basic SciencesKyung Hee UniversitySeoulKorea
  4. 4.Mechanical Engineering Department & Computer Science DepartmentUniversity of CaliforniaSanta BarbaraUSA

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