An Efficient 3-D FNPF Numerical Wave Tank for Virtual Large-Scale Wave Basin Experiment

Abstract

This paper presents an accurate and efficient threedimensional computational model (3D numerical wave tank), based on fully nonlinear potential flow (FNPF) theory, and its extension to incorporate the motion of a laboratory snake piston wavemaker, to simulate experiments in a large-scale 3D wave basin (i.e. to conduct "virtual" or numerical experiments). The code is based on a higher-order boundary element method combined with a Fast Multipole Algorithm (FMA). Particular efforts were devoted to make the code efficient for large-scale simulations using high-performance computing platforms to complement experimental 3D wave basins. The numerical simulation capability can serve as an optimization tool at the experimental planning and detailed design stages. To date, waves that can be generated in the NWT include solitary, Cnoidal, and Airy waves. In this paper, we detail the model, mathematical formulation, and wave generation. Experimental or analytical comparisons with NWT results are provided for several cases to assess the accuracy and applicability of the numerical model to practical engineering problems. INTRODUCTIONOver the past decade, as modern computing platforms gradually increased in power, accurate and efficient threedimensional (3D) computational wave-basins (called numerical wave tanks or simply NWTs in this paper) have been developed and refined, which simulate complex processes of ocean wave generation, propagation over arbitrary bottom topography, interaction with ocean structures, and dissipation over sloping beaches. These computational tools allow researchers to conduct "virtual" or numerical experiments. Until recently, fluid dynamic phenomena had been mostly investigated by performing laboratory experiments in large-scale 3D wave basins, which are both expensive and time consuming to operate. While not intended

Fully Nonlinear Potential Flow Simulations of Wave Shoaling Over Slopes: Spilling Breaker Model and Integral Wave Properties

“…Since the seminal work of Longuet-Higgins and Cokelet [75], increasingly efficient and generic numerical models were developed to simulate nonlinear ocean waves based on fully nonlinear potential flow (FNPF) equations, i.e., Euler equations for irrotational flows, in two-(2D), e.g., [2,13,19,21,22,35,37,38,40,43,44,46,47,58,65,66,81,84,88,111] or three-dimensions (3D), e.g., [5,11,25,26,34,55,82,83,94,114]. When simulating overturning waves in these models, as first proposed by [75], the free surface motion is typically described by an Eulerian-Lagrangian formulation.…”

“…Numerical models directly solving FNPF equations, which are the object of this paper, are often based on a boundary element method (BEM), but not always as for instance higher-order spectral or polynomial approximation methods have also been widely used when considering single-valued free surface elevations, e.g., [21,23,24,65,88,94] (see [32] for a review to date). Early 2D models were implemented in a space-periodic, conformally mapped, domain [19,22,75,81,111], but subsequent 2D and 3D models have been formulated in the physical space and gradually equipped with capabilities similar to those of physical wave tanks, such as various means of wave generation and absorption, e.g., [23,32,34,35,40,42,82]. In these so-called numerical wave tanks (NWTs; a termed coined by [39]), waves can be generated by internal sources, wavemakers, or other analytical/numerical solutions, e.g., [23,35,37,[42][43][44]46,47,82].…”

A stabilised nodal spectral element method for fully nonlinear water waves

“…State-of-the-art in finite element methods for fully nonlinear water waves Reviews on the state-of-the art of numerical models for freely propagating water waves are given in [37,62,11,59,53]. Our scope in the present work is restricted to FNPF solvers and FEM.…”

A heterogeneous flow model based on DD method for free surface fluid–structure interaction problems

“…A collocation BEM is used to solve Laplace's equation in Ω 2 . In particular, the BEM solver provides complete features of a numerical wave tank using a PF model, based on the work of Svendsen and Grilli , Grilli and Subramanya , Grilli et al , and Nimmala et al . In the BEM method, equation is converted into a BIE by applying Green's second identity, thus Here , with ϑ being the exterior solid angle at boundary point x .…”

“…A collocation BEM is used to solve Laplace's equation (1d) in 2 . In particular, the BEM solver provides complete features of a numerical wave tank using a PF model, based on the work of Svendsen and Grilli [42], Grilli and Subramanya [43], Grilli et al [44], and Nimmala et al [45]. In the BEM method, equation (1d) is converted into a BIE by applying Green's second identity, thus…”