A comparative study of two fast nonlinear free‐surface water wave models

Ducrozet, Guillaume; Bingham, Harry B.; Engsig-Karup, Allan Peter; Bonnefoy, Félicien; Ferrant, P.

doi:10.1002/fld.2672

Cited by 34 publications

(36 citation statements)

References 19 publications

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“…For the water wave modelling in a finite constant-depth domain, an even more efficient method than FDM and the HPC method might be the high-order spectral (HOS) method, as discussed in e.g. Ducrozet et al [4]. Fig.9.…”

Section: Comparison With a Finite Difference Methodsmentioning

confidence: 99%

A harmonic polynomial cell (HPC) method for 3D Laplace equation with application in marine hydrodynamics

Shao¹,

Faltinsen²

2014

Journal of Computational Physics

103

104

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We propose a new efficient and accurate numerical method based on harmonic polynomials to solve boundary value problems governed by 3D Laplace equation. The computational domain is discretized by overlapping cells. Within each cell, the velocity potential is represented by the linear superposition of a complete set of harmonic polynomials, which are the elementary solutions of Laplace equation. By its definition, the method is named as Harmonic Polynomial Cell (HPC) method. The characteristics of the accuracy and efficiency of the HPC method are demonstrated by studying analytical cases. Comparisons will be made with some other existing boundary element based methods, e.g. Quadratic Boundary Element Method (QBEM) and the Fast Multipole Accelerated QBEM (FMA-QBEM) and a fourth order Finite Difference Method (FDM). To demonstrate the applications of the method, it is applied to some studies relevant for marine hydrodynamics. Sloshing in 3D rectangular tanks, a fully-nonlinear numerical wave tank, fully-nonlinear wave focusing on a semi-circular shoal, and the nonlinear wave diffraction of a bottom-mounted cylinder in regular waves are studied. The comparisons with the experimental results and other numerical results are all in satisfactory agreement, indicating that the present HPC method is a promising method in solving potential-flow problems. The underlying procedure of the HPC method could also be useful in other fields than marine hydrodynamics involved with solving Laplace equation.

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Section: Comparison With a Finite Difference Methodsmentioning

confidence: 99%

A harmonic polynomial cell (HPC) method for 3D Laplace equation with application in marine hydrodynamics

Shao¹,

Faltinsen²

2014

Journal of Computational Physics

103

104

View full text Add to dashboard Cite

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“…For completeness, we mention alternative discretization methods that could also be employed for spatial discretization, for example, boundary element methods (BEMs) [27], also spectral methods [28] or finite element methods (FEMs) [29][30][31][32] including the high-order extension spectralnhp-FEM [33]. Spectral methods are particularly attractive because of the spectral accuracy and have the potential to be a competitive discretization strategy for logically structured domains [28,35] with a similar algorithmic strategy based on PDC as considered in this work. The class of FEMs are competitive candidates to finite difference discretizations presented here, because the FEM framework also provide basis for, for example, flexible-order discretizations, sparse operators and low-storage matrix-free implementations.…”

Section: Discretization Strategymentioning

confidence: 99%

Analysis of efficient preconditioned defect correction methods for nonlinear water waves

Engsig-Karup

2014

Numerical Methods in Fluids

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SUMMARYRobust computational procedures for the solution of non‐hydrostatic, free surface, irrotational and inviscid free‐surface water waves in three space dimensions can be based on iterative preconditioned defect correction (PDC) methods. Such methods can be made efficient and scalable to enable prediction of free‐surface wave transformation and accurate wave kinematics in both deep and shallow waters in large marine areas or for predicting the outcome of experiments in large numerical wave tanks. We revisit the classical governing equations are fully nonlinear and dispersive potential flow equations. We present new detailed fundamental analysis using finite‐amplitude wave solutions for iterative solvers. We demonstrate that the PDC method in combination with a high‐order discretization method enables efficient and scalable solution of the linear system of equations arising in potential flow models. Our study is particularly relevant for fast and efficient simulation of non‐breaking fully nonlinear water waves over varying bottom topography that may be limited by computational resources or requirements. To gain insight into algorithmic properties and proper choices of discretization parameters for different PDC strategies, we study systematically limits of accuracy, convergence rate, algorithmic and numerical efficiency and scalability of the most efficient known PDC methods. These strategies are of interest, because they enable generalization of geometric multigrid methods to high‐order accurate discretizations and enable significant improvement in numerical efficiency while incuring minimal storage requirements. We demonstrate robustness using such PDC methods for practical ranges of interest for coastal and maritime engineering, that is, from shallow to deep water, and report details of numerical experiments that can be used for benchmarking purposes. Copyright © 2014 John Wiley & Sons, Ltd.

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“…al. [3] que faz um estudo comparativo de dois métodos rápidos para o problema de ondas de superfície não lineares: o método espectral de ordem superior e método de diferenças finitas de alta ordem.…”

Section: Introductionunclassified

Ondas em Água: Um Estudo da Altura e Ângulo de Quebra

Franco¹,

Farina²

2014

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Resumo: Um método de aproximação de Fourieré utilizado para a modelagem e simulação de ondas completamente não lineares permanentes. O conjunto de equações não lineares resultanté e resolvido pelo método de Newton. O empinamento de ondasé simulado, usando como base, comparações com dados experimentais. As alturas eângulos de quebra são analisados até o limite de inadequação do método numérico. Os resultados se mostram bastante próximos dos critérios preditos pela teoria de ondas de superfície completamente não lineares e contribuem para proporcionar informações adicionais sobre o estudo da relação entre modelagem computacional e a teoria de ondas permanentes.Palavras-chave: Ondas aquáticas não lineares, ondas permanentes, empinamento de ondas, método espectral. IntroduçãoOndas emágua constitui um tópico que tem sido extensivamente estudados em diferentes domí-nios da ciência. Os fenômenos de empinamento e quebra de ondas possui um lugar de destaque neste contexto, visto que a energia de ondas está intrinsecamente associadaà altura de onda. Métodos experimentais, analíticos e computacionais têm sido utilizados para a investigação destes fenômenos. Entre estes, os dados de campo apresentados por Hansen [9] e de medições em laboratório, originalmente obtidos por Eagleson [7] são dados clássicos para a validação de métodos numéricos. Do ponto de vista analítico e computacional o artigo de Rienecker e Fenton [11] foi um dos primeiros a propor um método para a simulação de ondas aquáticas completamente não lineares permanentes. Denominado como método de Fourier, esta técnica não assume aproximações analíticas e a solução das equações não lineares governantes para a dinâmica de ondasé expressa por uma série de Fourier.Abordagens com aproximações analíticas para o cálculo de ondas não lineares também têm sido empregadas. Freilich e Guza [5] usam variantes das equações de Boussinesq para estudar o empinamento de ondas. Fenton [4] deduziu expressões de quinta ordem baseadas na teoria de Stokes e apresentou resultados numéricos, comparando-os com dados experimentais. Neste mesmo contexto, Pihl et. al. [6] examinou o empinamento de ondas descritas por uma aproximação de sexta ordem da teoria de Stokes na presença de uma corrente.

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A comparative study of two fast nonlinear free‐surface water wave models

Cited by 34 publications

References 19 publications

A harmonic polynomial cell (HPC) method for 3D Laplace equation with application in marine hydrodynamics

A harmonic polynomial cell (HPC) method for 3D Laplace equation with application in marine hydrodynamics

Analysis of efficient preconditioned defect correction methods for nonlinear water waves

Ondas em Água: Um Estudo da Altura e Ângulo de Quebra

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