Pacific Institute for the Mathematical Sciences - PIMS

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.