Viscous flow with large free surface motion

Abstract

An arbitrary Lagrangian-Eulerian (ALE) Petrov-Galerkin finite element technique is developed to study nonlinear viscous fluids under large free surface wave motion. A review of the kinematics and field equations from an arbitrary reference is presented and since the major challenge of the ALE description lies in the mesh rezoning algorithm, various methods, including a new mixed formulation, are developed to update the mesh and map the moving domain in a more rational manner. Moreover, the streamline-upwind/Petrov-Galerkin formulation is implemented to accurately describe highly convective free surface flows. The effectiveness of the algorithm is demonstrated on a tsunami problem, the dam-break problem where the Reynolds number is taken as high as 3000, and a large-amplitude sloshing problem.