Three-dimensional algorithms for grid restructuring in Free-Lagrangian calculations

Abstract

Grid restructuring algorithms which lower the price of three-dimensional Free-Lagrange calculations are presented. The algorithms are first given for the case of planar triangulated surfaces embedded in and spanning a three-dimensional region. The tetrahedra generated by this technique form a Delaunay mesh if the interplane spacing is comparable to the resolution within the planes. The algorithm can therefore be used for efficient determinations of Voronoi connections for initial grids. Modifications of the algorithm for the case of closely spaced surfaces are demonstrated in the context of restructuring algorithms which can accommodate colliding surfaces. Then, the restriction to planar surfaces is removed and regular surfaces are examined. The basic algorithm is the same, with an additional operation to project the vertices of one surface onto another. Finally, vertices on the surface are allowed to migrate anywhere in space.