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.
| Original language | English |
|---|---|
| Pages (from-to) | 1425-1440 |
| Number of pages | 16 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 190 |
| Issue number | 11-12 |
| DOIs | |
| State | Published - 8 Dec 2000 |