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Geometric integration over irregular domains with application to level-set methods

✍ Scribed by Chohong Min; Frédéric Gibou

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 603 KB
Volume: 226
Category: Article
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2007.05.032

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✦ Synopsis

We present a geometric approach for calculating integrals over irregular domains described by a level-set function. This procedure can be used to evaluate integrals over a lower dimensional interface and may be used to evaluate the contribution of singular source terms. This approach produces results that are second-order accurate and robust to the perturbation of the interface location on the grid. Moreover, since we use a cell-wise approach, this procedure can be easily extended to quadtree and octree grids. We demonstrate the second-order accuracy and the robustness of the method in two and three spatial dimensions.

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