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QALE-FEM for modelling 3D overturning waves

Yan, S. & Ma, Q. (2010). QALE-FEM for modelling 3D overturning waves. International Journal for Numerical Methods in Fluids, 63(6), pp. 743-768. doi: 10.1002/fld.2100


A further development of the QALE-FEM (quasi-arbitrary Lagrangian–Eulerian finite element method) based on a fully nonlinear potential theory is presented in this paper. This development enables the QALE-FEM to deal with three-dimensional (3D) overturning waves over complex seabeds, which have not been considered since the method was devised by the authors of this paper in their previous works (J. Comput. Phys. 2006; 212:52–72; J. Numer. Meth. Engng 2009; 78:713–756). In order to tackle challenges associated with 3D overturning waves, two new numerical techniques are suggested. They are the techniques for moving the mesh and for calculating the fluid velocity near overturning jets, respectively. The developed method is validated by comparing its numerical results with experimental data and results from other numerical methods available in the literature. Good agreement is achieved. The computational efficiency of this method is also investigated for this kind of wave, which shows that the QALE-FEM can be many times faster than other methods based on the same theory. Furthermore, 3D overturning waves propagating over a non-symmetrical seabed or multiple reefs are simulated using the method. Some of these results have not been found elsewhere to the best of our knowledge.

Publication Type: Article
Additional Information: This is the peer reviewed version of the following article: Yan, S. and Ma, Q. W. (2010), QALE-FEM for modelling 3D overturning waves. Int. J. Numer. Meth. Fluids, 63: 743–768., which has been published in final form at This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving
Publisher Keywords: QALE-FEM, 3D overturning waves, Spring analogy method, Complex seabed, Fully nonlinear potential flow
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Departments: School of Science & Technology > Engineering
Related URLs:
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