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OVERVIEW APPLICATIONS INTERACTIVE APPLETS HISTORY OF THE METHODS/FLOW CHART PUBLICATIONS EDUCATIONAL MATERIAL ACKNOWLEDGEMENTS ABOUT THE AUTHOR/CV Copyright: 1996, 1999, 2006 J.A. Sethian 
Applications to Mesh Generation
The use of
level set methods to generate logically
rectangular bodyfitted 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.


AbstractWe describe a numerical technique to generate logically rectangular bodyfitted interior and exterior grids. The technique is based on solving a HamiltonJacobi 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.