Abstract
Arbitrary Lagrangian–Eulerian (ALE) finite element formulations based on segregated equal-order interpolation are presented with the aim of computing unsteady free surface flows time-accurately. A standing vortex problem is solved using both fixed and moving grids to design a solution method which is time-accurate in the sense that it conserves vortex kinetic energy. It turns out that the ‘Chorin type SIMPLE algorithm’ serves this purpose satisfactorily when it is used in conjunction with the Galerkin spatial discretization and the Crank–Nicolson temporal discretization. Then, a small amplitude sloshing problem is solved to assure that the Crank–Nicolson/central difference scheme among others used for discretizing the kinematic condition preserves the oscillating amplitude of the free surface. Lastly, the most time-accurate numerical technique thus designed is applied to solve a solitary wave propagation problem, which shows that the predicted maximum run-up heights for various initial heights are in good agreement with existing experiment.
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