A finite element method for free surface flows of incompressible fluids inthree dimensions. Part I. Boundary fitted mesh motion

Computational fluid mechanics techniques for examining free surface problem s in two-dimensional form are now well established. Extending these methods to three dimensions requires a reconsideration of some of the difficult is sues from two-dimensional problems as well as developing new formulations t o handle added geometric complexity. This paper presents a new finite eleme nt formulation for handling three-dimensional free surface problems with a boundary-fitted mesh and full Newton iteration, which solves for velocity, pressure, and mesh variables simultaneously. A boundary-fitted, pseudo-soli d approach is used for moving the mesh, which treats the interior of the me sh as a fictitious elastic solid that deforms in response to boundary motio n. To minimize mesh distortion near free boundary under large deformations, the mesh motion equations are rotated into normal and tangential component s prior to applying boundary conditions. The Navier-Stokes equations are di scretized using a Galerkin-least square/pressure stabilization formulation, which provides good convergence properties with iterative solvers. The res ult is a method that can track large deformations and rotations of free sur face boundaries in three dimensions. The method is applied to two sample pr oblems: solid body rotation of a fluid and extrusion from a nozzle with a r ectangular cross-section. The extrusion example exhibits a variety of free surface shapes that arise from changing processing conditions. Copyright (C ) 2000 John Wiley & Sons, Ltd.