Tsunami-like solitary waves impinging and overtopping an impermeable seawall: Experiment and RANS modeling

Hsiao, Shih Chun; Lin, Ting Hsiang

doi:10.1016/j.coastaleng.2009.08.004

Cited by 155 publications

(101 citation statements)

References 40 publications

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“…17). We can note a very good agreement, similar to those exhibited in [36] with a obtained with a Volume Of Fluid (VOF) method for the Reynolds averaged Navier-Stokes equations and [68] with a hybrid FVM discretization of the original GN equations. Note that a similar level of agreement can be obtained with a regular mesh of 500 elements.…”

Section: Cox's Experiments ( [16])supporting

confidence: 66%

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Discontinuous-Galerkin Discretization of a New Class of Green-Naghdi Equations

Duran

Marche

2015

Commun. Comput. Phys.

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Abstract. We describe in this work a discontinuous-Galerkin Finite-Element method to approximate the solutions of a new family of 1d Green-Naghdi models. These new models are shown to be more computationally efficient, while being asymptotically equivalent to the initial formulation with regard to the shallowness parameter. Using the free surface instead of the water height as a conservative variable, the models are recasted under a pre-balanced formulation and discretized using an expansion basis of arbitrary order. Independently from the polynomial degree in the approximation space, the preservation of the motionless steady-states is automatically ensured, and the water height positivity is enforced. A simple numerical procedure devoted to handle broken waves is also described. The validity of the resulting model is assessed through extensive numerical validations.. . IntroductionDepth-averaged equations are widely used in coastal engineering for the simulation of nonlinear waves propagation and transformations in nearshore areas. The full description of surface water waves in an incompressible, homogeneous, inviscid fluid, is provided by the free surface Euler (or water waves) equations but this problem remains mathematically and numerically challenging. As a consequence, the use of depth averaged equations helps to reduce the three-dimensional problem to a two-dimensional problem, while keeping a good level of accuracy in many configurations. Many Boussinesq-like models are used nowadays and a detailed review can be found in [42] and the recent monograph [41]. Denoting by λ the typical horizontal scale of the flow and h 0 the typical depth, the shallow water regime usually corresponds to the configuration where µ := [52,54,57] for instance, an additional smallness amplitude assumption on the typical wave amplitude a is classically performed: ε := a h0 = O(µ). This assumption often appears as too restrictive for many applications in coastal oceanography. Removing the small amplitude assumption while still keeping all the O(µ) terms, we obtain the so-called Green-Naghdi equations (GN equations in the following) [34], also referred to as Serre equations [62] or fully non-linear Boussinesq equations [76]. A large number of numerical methods have been developed in the past few years for the BT equations. Let us mention for instance some Finite-Difference (FDM in the following) approaches [49,54,65,75] As far as flexibility is concerned, the use of discontinuous-Galerkin methods (dG methods in the following) would appear as a natural choice. Indeed, this class of method provides several appealing features, like compact discretization stencils and hp-adaptivity, flexibility with a natural handling of unstructured meshes, easy parallel computation and local conservation properties in the approximation of conservation laws. A general review of dG methods for convection dominated problems is performed in [14]. Concerning the approximation of more general problems, involving higher-order derivatives, several methods a...

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Section: Cox's Experiments ( [16])supporting

confidence: 66%

“…A cross-section of the 22 m flume is described in Fig. 15, together with the location of several gauges where measurements of the free surface are available (see [36] for more details). We consider an initial water depth of 0.2 m, and an incoming wave with a relative amplitude a/h 0 = 0.35.…”

Section: Cox's Experiments ( [16])mentioning

confidence: 99%

Discontinuous-Galerkin Discretization of a New Class of Green-Naghdi Equations

Duran

Marche

2015

Commun. Comput. Phys.

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“…The hybrid method is further validated for the case with a solitary wave overtopping a seawall. Its results are compared with the experimental results from Hsiao and Lin [52].…”

Section: Validation Against Experimental Resultsmentioning

confidence: 96%

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

Sriram

Schlurmann

2014

Journal of Computational Physics

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractThis is the first paper to present a hybrid method coupling a Improved Meshless Local Petrov Galerkin method with Rankine source solution (IMLPG_R) based on the Navier Stokes (NS) equations, with a finite element method (FEM) based on the fully nonlinear potential flow theory (FNPT) in order to efficiently simulate the violent waves and their interaction with marine structures. The two models are strongly coupled in space and time domains using a moving overlapping zone, wherein the information from both the solvers is exchanged. In the time domain, the Runge-Kutta 2 nd order method is nested with a predictor-corrector scheme. In the space domain, numerical techniques including 'Feeding Particles' and two-layer particle interpolation with relaxation coefficients are introduced to achieve the robust coupling of the two models. The properties and behaviours of the new hybrid model are tested by modelling a regular wave, solitary wave and Cnoidal wave including breaking and overtopping. It is validated by comparing the results of the method with analytical solutions, results from other methods and experimental data. The paper demonstrates that the method can produce satisfactory results but uses much less computational time compared with a method based on the full NS model.

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“…Hu et al (2000), Hubbard and Dodd (2002)), Boussinesq-type equations (see for example Fuhrman and Madsen (2008) or review documents by Dingemans (1997), Kirby (1997), Madsen and Schäffer (1999), Kirby (2003), Brocchini (2013)), hybrid Boussinesq-shallow flow equations (Watson et al (1994), Borthwick et al (2006a), Tonelli and Petti (2009), Tissier et al (2011), Orszaghova et al (2012), McCabe et al (2013)), potential flow theory (Fructus and Grue (2007)), and the NavierStokes equations (see e.g. Hsiao and Lin (2010) for volume-of-fluid method, Ingram et al (2009) for free surface tracking implementation, and Rogers and Dalrymple (2008) for a smoothed particle hydrodynamics solver).…”

Section: Introductionmentioning

confidence: 99%

Importance of second-order wave generation for focused wave group run-up and overtopping

Orszaghova

Taylor

Borthwick

et al. 2014

Coastal Engineering

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Focused wave groups offer a means for coastal engineers to determine extreme run-up and overtopping events. Numerical predictions and laboratory measurements are presented for NewWave-type focused wave groups generated by a piston-type paddle generator, and interacting with a plane beach and a seawall in a wave basin. The numerical wave tank is based on the Boussinesq equations for non-breaking waves, and the non-linear shallow water equations for broken waves. Good agreement is achieved between the numerical predictions and laboratory measurements of free surface elevation, run-up distances and overtopping volumes for the test cases driven by linear paddle signals. Errors in run-up distance and overtopping volume are then assessed by repeating the test cases using second-order accurate wave generation signals. Focused wave groups generated using first-order wave-maker theory are found to be substantially contaminated by a preceding long error wave, resulting in erroneously enhanced run-up distances and overtopping volumes. Thus, the use of secondorder wave-maker theory for wave group run-up and overtopping experiments is instead recommended.

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Tsunami-like solitary waves impinging and overtopping an impermeable seawall: Experiment and RANS modeling

Cited by 155 publications

References 40 publications

Discontinuous-Galerkin Discretization of a New Class of Green-Naghdi Equations

Discontinuous-Galerkin Discretization of a New Class of Green-Naghdi Equations

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

Importance of second-order wave generation for focused wave group run-up and overtopping

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