An assessment of a parallel, finite element method for three-dimensional, moving-boundary flows driven by capillarity for simulation of viscous sintering

A parallel, finite element method is presented for the computation of three-dimensional, free-surface flows where surface tension effects are significant. The method employs an unstructured tetrahedral mesh, a front-tracking arbitrary Lagrangian - Eulerian formulation, and fully implicit time integration. Interior mesh motion is accomplished via pseudo-solid mesh deformation. Surface tension effects are incorporated directly into the momentum equation boundary conditions using surface identities that circumvent the need to compute second derivatives of the surface shape, resulting in a robust representation of capillary phenomena. Sample results are shown for the viscous sintering of glassy ceramic particles. The most serious performance issue is error arising from mesh distortion when boundary motion is significant. This effect can be severe enough to stop the calculations; some simple strategies for improving performance are tested.