QALE‐FEM for modelling 3D overturning waves

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. based on a fully nonlinear potential theory is presented in this paper. This development enables the QALE-FEM to deal with 3D (three dimensional) 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 [1][2]. In order to tackle challenges associated with 3D overturning waves, two new numerical techniques are suggested. Permanent repository linkThey 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, 3Doverturning 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.

A hybrid method for modelling two dimensional non-breaking and breaking waves

“…The notable papers based on particle methods for the topics related to wave-structure interactions include but are not limited to references [22][23][24] for using smoothed particle hydrodynamics (SPH), [25] for using moving particle semi-implicit method (MPS), [26][27] for using Meshless Local Petrov Galerkin with Rankine Source (MLPG_R). Some simplified test cases reported in the literature using these models showed a good agreement with the experimental measurements, see for example, [1][2][3][4][5][6][7][8][9][10]28] for the FNPT models and [22][23][24][25][29][30][31] for the NS models.…”

“…The FEM was used by Wu and Eatock Taylor [3] for the 2D cases and by Ma et al [4] for 3D cases, and it was further extended to handle complex objects and floating bodies simulations forming the QALE-FEM (Quasi-Arbitrary Lagrangian and Eulerian finite element method) by Ma et al [5,6], Yan et al [7,8,9] and SALE-FEM (SemiArbitrary Lagrangian and Eulerian finite element method) by Sriram [10], respectively. It has been shown that the FEM is more efficient for modelling strongly nonlinear waves while the BEM is more efficient for modelling linear or weak nonlinear problems [9]. The problems formulated by using the NS model are usually solved by employing a mesh-based method or a meshfree method.…”

“…(2) The FEM can be more than 10 times faster than the BEM for modelling large scale fully nonlinear waves [7,9]. (3) The FEM can provide solution at any points in the flow field, while the direct solution of the BEM is only given on boundaries.…”

Did the Draupner wave occur in a crossing sea?

“…More importantly, the QALE-FEM can model highly nonlinear free surfaces and three-dimensional overturning waves. The QALE-FEM method has been compared with experimental data and other numerical for wave breaking cases and found to be accurate 2010b). In all cases presented in this section, we use a water depth of 70 m. Average spatial discretization across the domain is 2.5 m, which reduced to approximately 0.8 m around the crest of the giant wave.…”

Numerical simulation of interaction between wind and 2D freak waves

“…In their approach, an in-house software package (QALE-FEM/FLOATMov) is combined with a commercial software, StarCD. The former is based on the FNPT model, which has been proven to be the fastest method for overturning waves [54,55]. The latter solves general ReynoldsAveraged Navier-Stokes (RANS) equations using the finite volume method.…”