Exact semi-separation of variables in waveguides with non-planar boundaries

Athanassoulis, G. A.; Papoutsellis, Christos E.

doi:10.1098/rspa.2017.0017

Cited by 14 publications

(34 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This approach resolves the potential flow problem by advancing in time free surface quantities only. Several approaches can be considered to solve the Zakharov equations, such as the Hamiltonian Coupled-Mode Theory (or HCMT) method (Athanassoulis and Papoutsellis, 2017;Papoutsellis et al, 2018a), the extension of the high-order spectral (or HOS) method to variable bottom cases (Gouin et al, 2016), or the direct use of finite difference schemes (Bingham and Zhang, 2007). Other commonly applied approaches for solving the fully nonlinear potential flow problems are, for example, the Boundary Element Method (Longuet-Higgins and Cokelet, 1976;Dold and Peregrine, 1986;Grilli et al, 1989;Dold, 1992), the Finite Element Method (Wu and Eatock Taylor, 1994), the Quasi-Arbitrary Lagrangian Eulerian Finite Element Method (Ma and Yan, 2006), the Spectral Element Method (Engsig-Karup et al, 2016) and the Spectral Boundary Integral Method (Fructus et al, 2005;Wang and Ma, 2015).…”

Section: Introductionmentioning

confidence: 99%

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

Simon

Papoutsellis

Benoît

et al. 2019

J. Ocean Eng. Mar. Energy

View full text Add to dashboard 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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

Simon

Papoutsellis

Benoît

et al. 2019

J. Ocean Eng. Mar. Energy

View full text Add to dashboard Cite

show abstract

“…They form an elliptic problem which should be supplemented by appropriate lateral boundary conditions, dependent on the specific problem considered. A detailed description of the lateral boundary conditions for various specific problems, both in 2D and in 3D configurations, can be found in the Supplementary Material (Appendix C) of the paper [56], and in [57], available online through the link https://arxiv.org/abs/1710.10847 . In the above formulation, Eqs.…”

Section: The Hcmtmentioning

confidence: 99%

“…(12), in terms of the roots κ n of Eq. (16). The whole numerical scheme is implemented as explained in Subection.…”

Section: Evolution Of Steady Travelling Waves Over Flat Bottommentioning

confidence: 99%

“…Recently, [1], see also [15], proposed a new formulation of the exact waterwave problem over arbitrary (smooth) bathymetry, providing both dimensional reduction and high accuracy, comparable with that ensured by DNM. This formulation is based on the exact semi-separation of variables in the instantaneous (non-canonical) fluid domain, established in [16], referred subsequently as AP17. The wave potential Φ = Φ(x, z, t), where x = (x 1 , x 2 ) is the horizontal position in the fluid domain, is expanded in a rapidly convergent series of the form Φ = ϕ n (x, t)Z n ( z ; η, h), where the local vertical functions Z n are defined in the varying interval [− h(x), η(x, t)], delimited by the local depth h(x) and the local, instantaneous free-surface elevation η(x, t).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Semi-explicit solutions to the water-wave dispersion relation and their role in the non-linear Hamiltonian coupled-mode theory

Papathanasiou¹,

Papoutsellis²,

Athanassoulis³

2019

J Eng Math

Self Cite

View full text Add to dashboard Cite

The Hamiltonian Coupled-Mode Theory (HCMT), recently derived by Athanassoulis and Papoutsellis [1], provides an efficient new approach for solving fully nonlinear water-wave problems over arbitrary bathymetry. This theory exactly transforms the free-boundary problem to a fixedboundary one, with space and time varying coefficients. In calculating these coefficients, heavy use is made of the roots of a local, water-wave dispersion relation with varying parameter, which have to be calculated at every horizontal position and every time instant. Thus, fast and accurate calculation of these roots, valid for all possible values of the varying parameter, are of fundamen-tal importance for the efficient implementation of HCMT. In this paper, new, semi-explicit and highly accurate root-finding formulae are derived, especially for the roots corresponding to evanescent modes. The derivation is based on the successive application of a Picard-type iteration and the Householders root finding method. Explicit approximate formulae of very good accuracy are obtained, and machineaccurate determination of the required roots is easily achieved by no more than three iterations, using the explicit forms as initial values. Exploiting this procedure in the HCMT, results in an efficient, dimensionallyreduced, numerical solver able to treat fully non-linear water waves over arbitrary bathymetry. Applications to four demanding nonlinear problems demonstrate the efficiency and the robustness of the present approach. Specifically, we consider the classical tests of strongly nonlinear steady wave propagation and the transformation of regular waves due to trapezoidal and sinusoidal bathymetry. Novel results are also given for the disintegration of a solitary wave due to an abrupt deepening. The derived root-finding formulae can be used with any other multimodal methods as well.

show abstract

“…The latter is calculated by solving the system (8), which gives accurate results even for strongly nonlinear and very steep (smooth) bathymetries. See Athanassoulis and Papoutsellis (2017) for a detailed discussion on this issue.…”

Section: The Hamiltonian Coupled-mode Theorymentioning

confidence: 99%

A numerical study of the run-up and the force exerted on a vertical wall by a solitary wave propagating over two tandem trenches

Athanassoulis

Mavroeidis

Koutsogiannakis

et al. 2019

J. Ocean Eng. Mar. Energy

Self Cite

View full text Add to dashboard Cite

1. Introduction 2. An overview of the fully non-linear Hamiltonian Coupled-Mode Theory 2.1. Classical differential and variational formulation 2.2. The Hamiltonian Coupled-Mode Theory 3. A concise description of the numerical implementation 3.1. Numerical solution of the kinematical substrate problem 3.2. Numerical solution of the Hamiltonian evolution equations 4. Propagation of a solitary wave over some typical bathymetries. Validation and limitations of the present method 4.1. Propagation over a shelf 4.2. Propagation over a step 4.3. Comparison and assessment of the findings of Sec. 4.1 and 4.2 4.4. Propagation over a trench 5. Propagation of a solitary wave over two trenches and reflection at a vertical wall 5.1. Propagation over the trenches 5.2. Run-up on the wall 5.3. Maximum force exerted on the vertical wall Conclusions A numerical study of the run-up and the force exerted on a vertical wall by a solitary wave propagating over two tandem trenches and impinging on the wall AbstractThe propagation and transformation of water waves over varying bathymetries is a subject of fundamental interest to ocean, coastal and harbor engineers. The specific bathymetry considered in this paper consists of one or two, naturally formed or man-made, trenches. The problem we focus on is the transformation of an incoming solitary wave by the trench(es), and the impact of the resulting wave system on a vertical wall located after the trench(es). The maximum run-up and the maximum force exerted on the wall are calculated for various lengths and heights of the trench(es), and are compared with the corresponding quantities in the absence of them. The calculations have been performed by using the fully nonlinear water-wave equations, in the form of the Hamiltonian coupled-mode theory, recently developed in Papoutsellis et al (Eur. J. Mech. B/Fluids, Vol. 72, 2018, pp. 199-224). Comparisons of the calculated free-surface elevation with existing experimental results indicate that the effect of the vortical flow, inevitably developed within and near the trench(es) but not captured by any potential theory, is not important concerning the frontal wave flow regime. This suggests that the predictions of the run-up and the force on the wall by nonlinear potential theory are expected to be nearly realistic.The main conclusion of our investigation is that the presence of two tandem trenches in front of the wall may reduce the run-up from (about) 20% to 45% and the force from 15% to 38%., depending on the trench dimensions and the wave amplitude. The percentage reduction is greater for higher waves. The presence of only one trench leads to reductions 1.4 -1.7 times smaller.Keywords: nonlinear water waves; wave-trench interaction; solitary wave over varying bathymetry; run-up on vertical wall; force on vertical wall; submerged breakwater

show abstract

Exact semi-separation of variables in waveguides with non-planar boundaries

Cited by 14 publications

References 46 publications

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

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

Semi-explicit solutions to the water-wave dispersion relation and their role in the non-linear Hamiltonian coupled-mode theory

A numerical study of the run-up and the force exerted on a vertical wall by a solitary wave propagating over two tandem trenches

Contact Info

Product

Resources

About