Accuracy and efficiency of two numerical methods of solving the potential flow problem for highly nonlinear and dispersive water waves

J. Ocean Eng. Mar. Energy

Benoît

et al. 2019

Self Cite

The modeling of wave breaking dissipation in coastal areas is investigated with a fully nonlinear and dispersive wave model. The wave propagation model is based on potential flow theory, which initially assumes nonoverturning waves. Including the impacts of wave breaking dissipation is however possible by implementing a wave breaking initiation criterion and dissipation mechanism. Three criteria from the literature, including a geometric, kinematic, and dynamic-type criterion, are tested to determine the optimal criterion predicting the onset of wave breaking. Three wave breaking energy dissipation methods are also tested: the first two are based on the analogy of a breaking wave with a hydraulic jump, and the third one applies an eddy viscosity dissipative term. Numerical simulations are performed using combinations of the three breaking onset criteria and three dissipation methods. The simulation results are compared to observations from four laboratory experiments of regular and irregular waves breaking over a submerged bar, irregular waves breaking on a beach, and irregular waves breaking over a submerged slope. The different breaking approaches provide similar results after proper calibration. The wave transformation observed in the experiments is reproduced well, with better results for the case of regular waves than irregular waves. Moreover, the wave statistics and wave spectra are predicted well in general, and in particular for regular waves. Some differences are observed for irregular wave cases, in particular in the low-frequency range. This is attributed to incomplete absorption of the long waves in the numerical model. Otherwise, the wave spectra in the range [0.5fp, 5fp] are reproduced well, before, inside, and after the breaking zone for the three irregular wave experiments.

Section: Numerical Solution Of the Dtn Problem With A Spectral Methodsmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 96%

Comparing methods of modeling depth-induced breaking of irregular waves with a fully nonlinear potential flow approach

Simon

J. Ocean Eng. Mar. Energy

Benoît

et al. 2019

Self Cite

“…The resulting equations retain the dimensionally-reduced Hamiltonian structure of the water wave system (Zakharov, 1968;Craig and Sulem, 1993) and give accurate predictions of fully nonlinear and strongly dispersive waves over variable bathymetry up to breaking (Athanassoulis and Papoutsellis, 2015;Papoutsellis and Athanassoulis, 2017;Papoutsellis et al, 2018). Wave models with similar mathematical structure and capabilities have also been developed using Chebyshev series representations of the potential in the vertical direction (Tian and Sato, 2008;Yates and Benoit, 2015;Raoult et al, 2016Raoult et al, , 2019. The purpose of this paper is to extend the domain of application of fully nonlinear potential flow models by incorporating wave-breaking effects.…”

Section: Introductionmentioning

confidence: 99%

Modelling of depth-induced wave breaking in a fully nonlinear free-surface potential flow model

Yates

Simon

et al. 2019

Coastal Engineering

Self Cite

Two methods to treat wave breaking in the framework of the Hamiltonian formulation of free-surface potential flow are presented, tested, and validated. The first is an extension of Kennedy et al. (2000)'s eddyviscosity approach originally developed for Boussinesq-type wave models. In this approach, an extra term, constructed to conserve the horizontal momentum for waves propagating over a flat bottom, is added in the dynamic free-surface condition. In the second method, a pressure distribution is introduced at the free surface that dissipates wave energy by analogy to a hydraulic jump (Guignard and Grilli, 2001). The modified Hamiltonian systems are implemented using the Hamiltonian Coupled-Mode Theory, in which the velocity potential is represented by a rapidly convergent vertical series expansion. Wave energy dissipation and conservation of horizontal momentum are verified numerically. Comparisons with experimental measurements are presented for the propagation of a breaking dispersive shock wave following a dam break, and then incident regular waves breaking on a mildly sloping beach and over a submerged bar.Keywords: wave breaking, Hamiltonian formulation of water waves, eddyviscosity, fully nonlinear water waves Highlights• Two wave breaking techniques are tested in a fully nonlinear model. • Breaking is implemented by extending the Hamiltonian Coupled-Mode

“…No additional assumptions concerning the slope or the deformation of the free-surface elevation and the seabed are invoked, which ensures that HCMS accounts for fully non-linear and dispersive waves over variable bathymetry. Wave models of similar structure can also be obtained by approximating the wave potential in the vertical direction by means of Chebyshev polynomials, in conjunction with a transformation of the fluid domain to a flat strip [51], [52], [53].…”

Section: Introductionmentioning

confidence: 99%

Implementation of a fully nonlinear Hamiltonian Coupled-Mode Theory, and application to solitary wave problems over bathymetry

European Journal of Mechanics - B/Fluids

Charalampopoulos

Athanassoulis

2018

1. Introduction 2. Formulation of the problem 2.1 Classical formulation of the problem 2.2 The Hamiltonian Coupled-Mode Theory 2.2.1.. Exact vertical series expansion of the wave potential 2.2.2 The Hamiltonian coupled-mode system 2 6. Interaction of solitary waves with bathymetry and vertical walls 6.1 Reflection of solitary waves on a vertical wall 6.2 Shoaling of solitary waves over a plane beach 6.3 Reflection of shoaling solitary waves on a vertical wall at the end of a sloping beach 6.4 Propagation of a solitary wave over a sinusoidal patch 6.5 Transformation of a solitary wave over a 3D bathymetry with banks and trenches 7. Discussion and conclusions Acknowledgments Appendix A: An outline of the derivation of the Hamiltonian Coupled Mode System Appendix B: Calculation of the basic vertical integrals (a) Vertical integrals of the form ( ; ) m J s Z and ( ; ) m J s W (b) Vertical integrals of the form ( ; ) n m J s Z Z for 0 ,1, 2 s = (c) Vertical integrals of the form ( ; ) n m J s W Z for 0 ,1 s = Appendix C. Fast and accurate calculation of local wavenumbers ( , ) n k t x Appendix D: Finite-difference linear system for the substrate problem Eqs. (17a,b) Appendix E. Description of the 3D bathymetry References List of abbreviationsBEM boundary element method CMS coupled-mode system DNM direct numerical methods DtN Dirichlet-to-Neumann (operator) FD finite difference FDM finite difference method FEM finite element method HCMS Hamiltonian coupled-mode system HCMT Hamiltonian Coupled-Mode Theory NLPF nonlinear potential flow NR Newton-Raphson (method) RK Runge-Kutta (method) SGN Serre-Green-Nagdhi (equations) AbstractThis paper deals with the implementation of a new, efficient, non-perturbative, Hamiltonian coupled-mode theory (HCMT) for the fully nonlinear, potential flow (NLPF) model of water waves over arbitrary bathymetry Papoutsellis and Athanassoulis (2017) (arxiv.org/abs/1704.03276). Applications considered herein concern the interaction of solitary waves with bottom topographies and vertical walls both in two-and three-dimensional environments. The essential novelty of HCMT is a new representation of the Dirichlet-to-Neumann operator, which is needed to close the Hamiltonian evolution equations. This new representation emerges from the treatment of the substrate kinematical problem by means of exact semi-separation of variables in the instantaneous, irregular, fluid domain, established recently by Athanassoulis & Papoutsellis (2017) (https://doi.org/10.1098/rspa.2017.0017). The HCMT ensures an efficient dimensional reduction of the exact NLFP, being able to treat an arbitrary bathymetry as simply as the flat-bottom case, without domain transformation. A key point for the efficient implementation of the method is the fast and accurate evaluation of the space-time varying coefficients appearing in some of its equations. In this paper, all varying coefficients are calculated analytically, resulting in a refined version of the theory, characterized by improved accuracy at significantly reduced computationa...