nonlinear nature of many of the conservation equations and of the coupling between the boundary or interface An implicit, pseudo-solid domain mapping technique is described that facilitates finite element analysis of free and moving boundary shapes and the internal field variables.
problems. The technique is based on an implicit, full-Newton strat-Among the several computational approaches available egy, free of restrictions on mesh structure; this leads to many advanfor FB or MB problems, the best choice depends on the tages over existing domain mapping techniques. The fully coupled particular set of field equations, boundary conditions, paapproach using Newton's method is particularly effective for probrameter ranges of interest, and the range of domain topololems with strong coupling between the internal bulk physics and the governing physics at unknown free boundary locations. It is gies that need to be simulated. Each computational techalso useful when the distinguishing conditions which constrain the nique offers its own balance between efficiency, accuracy, free boundary shape provide only an implicit dependence on the and robustness, all of which are desirable objectives for boundary location. Unstructured meshes allow for efficient resoluany computational approach to analyzing FB or MB probtion of internal and boundary layers and other regions of strong
local variations in the solution and they also reduce the amount of user interaction required to define a problem since the meshes may
The most accurate techniques parameterize the free or be generated automatically. The technique is readily applied to moving boundary as a mathematical curve (two dimensteady or transient problems in complex geometries of two and sions) or surface (three dimensions) in space, i.e., boundary three dimensions. Examples are shown that include free and moving parameterization techniques, so that the boundary condiboundary problems from solidification and capillary hydrodynamtions may be applied precisely at an interface with a wellics.