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Quasi ALE finite element method for nonlinear water waves

Ma, Q. & Yan, S. (2006). Quasi ALE finite element method for nonlinear water waves. Journal of Computational Physics, 212(1), pp. 52-72. doi: 10.1016/


This paper presents a newly developed quasi arbitrary Lagrangian-Eulerian finite element method (QALE-FEM) for simulating water waves based on fully nonlinear potential theory. The main difference of this method from the conventional finite element method developed by one of authors of this paper and others (see, e.g., [11] and [22]) is that the complex mesh is generated only once at the beginning and is moved at all other time steps in order to conform to the motion of the free surface and structures. This feature allows one to use an unstructured mesh with any degree of complexity without the need of regenerating it every time step, which is generally inevitable and very costly. Due to this feature, the QALE-FEM has high potential in enhancing computational efficiency when applied to problems associated with the complex interaction between large steep waves and structures since the use of an unstructured mesh in such a case is likely to be necessary. To achieve overall high efficiency, the numerical techniques involved in the QALE-FEM are developed, including the method to move interior nodes, technique to re-distribute the nodes on the free surface, scheme to calculate velocities and so on. The model is validated by water waves generated by a wavemaker in a tank and the interaction between water waves and periodic bars on the bed of tank. Satisfactory agreement is achieved with analytical solutions, experimental data and numerical results from other methods.

Publication Type: Article
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational Physics, Volume 212, Issue 1, 10 February 2006, Pages 52–72,
Publisher Keywords: QALE-FEM, Nonlinear water waves, Spring analogy, Periodic bars, Free surface
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Departments: School of Science & Technology > Engineering
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