ADAPTIVE UNSTRUCTURED GRID FOR THREE-DIMENSIONAL INTERFACE REPRESENTATION

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Abstract
Moving-boundary problems arise in numerous important physical phenomena, and often form complex shapes during their evolution. The ability to track the interface in such cases in two dimensions is well established. However, modifying the grid representing the interface as it evolves in three-dimensional space introduces additional issues. In the current work, three-dimensional interfaces are represented by adaptive unstructured grids. The grids are restructured and refined based on the shape and size of the triangular elements in the grid that forms the interfaces. As the interface deforms, points are automatically added to ensure that the accuracy of interface representation remains consistent. Results are presented to show how complex interface features, including surface curvatures and normals, can be captured by modifying an existing method that uses an approximation to the Dupin indicatrix.