A gradient-augmented level set method with an optimally local, coherent advection scheme
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Author(s)
Nave, Jean-Christophe
Rosales, Rodolfo R.
Seibold, Benjamin
Date Issued
February 2010
Journal
Journal of Computational Physics
Publisher
Elsevier
Citation
Nave, Jean-Christophe, Rodolfo Ruben Rosales, and Benjamin Seibold. “A Gradient-augmented Level Set Method with an Optimally Local, Coherent Advection Scheme.” Journal of Computational Physics 229.10 (2010): 3802–3827.
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Author's final manuscript
Abstract
The level set approach represents surfaces implicitly, and advects them by evolving a level set function, which is numerically defined on an Eulerian grid. Here we present an approach that augments the level set function values by gradient information, and evolves both quantities in a fully coupled fashion. This maintains the coherence between function values and derivatives, while exploiting the extra information carried by the derivatives. The method is of comparable quality to WENO schemes, but with optimally local stencils (performing updates in time by using information from only a single adjacent grid cell). In addition, structures smaller than the grid size can be located and tracked, and the extra derivative information can be employed to obtain simple and accurate approximations to the curvature. We analyze the accuracy and the stability of the new scheme, and perform benchmark tests.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1016/j.jcp.2010.01.029
