Parallel simulation of three-dimensional free-surface fluid flow problems

We describe parallel simulations of viscous, incompressible, free surface, Newtonian fluid flow problems that include dynamic contact, lines. The Galerkin finite element method was used to discretize the fully-coupled governing conservation equations and a "pseudo-solid" mesh mapping approach was used to determine the shape of the free surface. In this approach, the finite element mesh is allowed to deform to satisfy quasi-static solid mechanics equations subject to geometric or kinematic constraints on the boundaries. As a result, nodal displacements must be included in the set of problem unknowns. Issues concerning the proper constraints along the solid-fluid dynamic contact line in three dimensions are discussed. Parallel computations are carried out for an example taken from the coating flow industry, flow in the vicinity of a slot coater edge. This is a three-dimensional free-surface problem possessing a contact line that advances at the web speed in one region but transitions to static behavior in another part of the flow domain. Discussion focuses on parallel speedups for fixed problem size, a class' of problems of immediate practical importance.