Time-accurate computation of unsteady free surface flows using an ALE-segregated equal-order FEM

Arbitrary Lagrangian-Eulerian (ALE) finite element formulations based on se gregated equal-order interpolation are presented with the aim of computing unsteady free surface flows time-accurately. A standing vortex problem is s olved using both fixed and moving grids to design a solution method which i s time-accurate in the sense that it conserves vortex kinetic energy. It tu rns out that the 'Chorin type SIMPLE algorithm' serves this purpose satisfa ctorily when it is used in conjunction with the Galerkin spatial discretiza tion and the Crank-Nicolson temporal discretization. Then, a small amplitud e sloshing problem is solved to assure that the Crank Nicolson/central diff erence scheme among others used fur discretizing the kinematic condition pr eserves the oscillating amplitude of the free surface. Lastly, the most tim e-accurate numerical technique thus designed is applied to solve a solitary wave propagation problem, which shows that the predicted maximum run-up he ights for various initial heights are in good agreement with existing exper iment. (C) 2000 Elsevier Science S.A. All rights reserved.