The paper reports a progress on the development of a hybrid approach coupling the Meshless Local Petrov-Galerkin Method based on Rankine Solution (MLPG-R) and the Quasi Arbitrary Langangian-Eulerian Finite Element Method (QALE-FEM) for modelling nonlinear water waves. The former is to solve the one-phase incompressible Naiver-Stokes model using a fractional step method (projection method), whereas the latter is to solve the Fully Nonlinear Potential Theory (FNPT) using a time-marching procedure. They are fully coupled using a zonal approach. The hybrid approach takes the advantage of the QALE-FEM on modelling fully nonlinear water waves with relatively higher computational efficiency and that of the MLPG-R on its capacity on dealing with viscous effects and breaking waves. The model is validated by comparing the numerical prediction with the experimental data for a unidirectional focusing wave. A good agreement has been achieved.


Wave-structure interaction has been a focus for the researches on offshore, coastal and ocean engineering for many years. For safety and survivability of the structures, extreme wave condition must be considered. Accurately modelling such extreme wave condition usually requires a large-scale (~ 10s km) and long-duration (e.g. 3-hour sea state) numerical simulation to capture the spatial-temporal propagation of the ocean wave. On the other hand, the response of the structure in extreme condition is considerably influenced by small-to micro-scale physics, such as the viscous/turbulent effect, hydro elasticity and so on. This implies that an effective numerical model shall be able to deal with both large-scale oceans wave and small-scale near-field physics simultaneously. The presence of the extreme waves invalids the routine wave diffraction analysis based on linear and second-order potential theory in frequency domain and a fully nonlinear analysis shall be considered using time domain analysis.

Advances have been made on the development of fully nonlinear potential theory (FNPT) on modelling highly nonlinear wave waves in large scale and for long duration, e.g. 3-hour sea state. Various numerical models based on the FNPT, e.g. the quasi-arbitrary Lagrange-Euler finite element method (QALE-FEM, Ma and Yan, 2006; Yan and Ma, 2010a) and Spectral Boundary Integral methods (e.g. Wang and Ma, 2015; Wang et al, 2016), have been developed and proven to be robust and highly efficient for modelling extreme water waves without breaking. The FNPT assumes that the flow is inviscid and irrotational, therefore, it cannot deal with breaking waves, slamming and other small-scale physics near structures.

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