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Copyright:
1996, 1999, 2006
J.A. Sethian

Applications to Mesh Generation
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The use of level set methods to generate logically rectangular body-fitted meshes around irregular objects was introduced in Ref. 1 below. The idea is to view the given body as the initially position of the front, and then interpret this as the zero level set of a higher dimensional function. A suitably chosen speed law carries the front outwards; the position of the evolving zero contour at any time gives one set of grid lines; tracing back normal to the level set function, similar to as is done in robotic navigation and constructing shortest paths geodesics gives the other grid lines.

The method is able to produce logically rectangular interior and exterior meshes around highly irregular objects, including those with sharp corners and inward cusps.




Examples:
Grids generated using interface propagation; see Reference 1 below.


New Book and Resource on Level Set and Fast Marching Methods




References:

  1. Curvature Flow and Entropy Conditions Applied to Grid Generation : Sethian, J.A., Curvature Flow and Entropy Conditions Applied to Grid Generation, Journal of Computational Physics, 115, pp. 440-454, 1994.
    Abstract

    We describe a numerical technique to generate logically rectangular body-fitted interior and exterior grids. The technique is based on solving a Hamilton-Jacobi type equation for a propagating level set function, using techniques borrowed from hyperbolic conservation laws. Coordinate grid lines are kept smooth through curvature terms which regularize the equation of motion, and upwind difference schemes which satisfy the correct entropy conditions of front propagation. The resulting algorithm can be used to generate two and three dimensional interior and exterior grids around reasonably complex bodies which may contain sharp corners and significant variations in curvature. The technique may also be easily extended to problems of boundary fitted moving grids.

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