Moving Unstructured Mesh Methods

Simulation of moving physical interfaces in 3-D is complicated by the need to (1) resolve complex realistic geometries with a spatial discretization, (2) accurately compute evolving physical fields on the discretization, and (3) evolve the discretization in response to moving physical geometry and interfaces. Unstructured mesh methods are inherently suited to this challenge; unstructured meshes have an unsurpassed capability of accurately representing physical geometry and aligning with anisotropies commonly present in physical fields. I will present two applications exploiting unstructured meshes that are current research topics at Pacific Northwest National Laboratory in Richland, Washington. In the first application, modeling of crystal growth, the moving finite element method is used to track a solid-liquid interface in 3-D. Triangles form the interface between solid and liquid, while moving tetrahedra, conformal to the triangles, "surf" with the evolving temperature field to keep elements concentrated where solution gradients require them most. In the second application, volumetric data from MRI imaging of animal lung geometries is rapidly transformed into a tetrahedral mesh suitable for computational fluid dynamics simulation. In both applications, the main emphasis is on placement and alignment of elements for optimum computational efficiency and accuracy.