A FULLY NONLINEAR BOUSSINESQ MODEL FOR WATER WAVE PROPAGATION

2011 ◽  
Vol 1 (32) ◽  
pp. 12
Author(s):  
Hong-sheng Zhang ◽  
Hua-wei Zhou ◽  
Guang-wen Hong ◽  
Jian-min Yang
Keyword(s):  
Wave Propagation ◽  
Numerical Model ◽  
Nonlinear Boundary Conditions ◽  
Boussinesq Model ◽  
Linear Dispersion ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
Sea Bed ◽  
Nonlinear Version ◽  
Nicolson Scheme

A set of high-order fully nonlinear Boussinesq-type equations is derived from the Laplace equation and the nonlinear boundary conditions. The derived equations include the dissipation terms and fully satisfy the sea bed boundary condition. The equations with the linear dispersion accurate up to [2,2] padé approximation is qualitatively and quantitatively studied in details. A numerical model for wave propagation is developed with the use of iterative Crank-Nicolson scheme, and the two-dimensional fourth-order filter formula is also derived. With two test cases numerically simulated, the modeled results of the fully nonlinear version of the numerical model are compared to those of the weakly nonlinear version.

A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves

1995 ◽  
Vol 294 ◽  
pp. 71-92 ◽  
Author(s):  
Ge Wei ◽  
James T. Kirby ◽  
Stephan T. Grilli ◽  
Ravishankar Subramanya
Keyword(s):  
Boussinesq Equations ◽  
Intermediate Water ◽  
Strong Nonlinearity ◽  
Boussinesq Model ◽  
Linear Dispersion ◽  
Fully Nonlinear ◽  
Surface Wave Propagation ◽  
Highly Nonlinear ◽  
Nonlinear Potential ◽  
Nonlinear Extensions

Fully nonlinear extensions of Boussinesq equations are derived to simulate surface wave propagation in coastal regions. By using the velocity at a certain depth as a dependent variable (Nwogu 1993), the resulting equations have significantly improved linear dispersion properties in intermediate water depths when compared to standard Boussinesq approximations. Since no assumption of small nonlinearity is made, the equations can be applied to simulate strong wave interactions prior to wave breaking. A high-order numerical model based on the equations is developed and applied to the study of two canonical problems: solitary wave shoaling on slopes and undular bore propagation over a horizontal bed. Results of the Boussinesq model with and without strong nonlinearity are compared in detail to those of a boundary element solution of the fully nonlinear potential flow problem developed by Grilli et al. (1989). The fully nonlinear variant of the Boussinesq model is found to predict wave heights, phase speeds and particle kinematics more accurately than the standard approximation.

scholarly journals NUMERICAL COMPUTATION OF INFRAGRAVITY WAVE DYNAMICS AND VELOCITY PROFILES USING A FULLY NONLINEAR BOUSSINESQ MODEL

2011 ◽  
Vol 1 (32) ◽  
pp. 48 ◽  
Author(s):  
Rodrigo Cienfuegos ◽  
L. Duarte ◽  
L. Suarez ◽  
P. A. Catalán
Keyword(s):  
Wave Propagation ◽  
Complex Dynamics ◽  
Velocity Profiles ◽  
Wave Generation ◽  
Type Model ◽  
Random Wave ◽  
Boussinesq Model ◽  
Frequency Wave ◽  
Fully Nonlinear ◽  
Infragravity Wave

We present experimental and numerical analysis of nonlinear processes responsible for generating infragravity waves in the nearshore. We provide new experimental data on random wave propagation and associated velocity profiles in the shoaling and surf zones of a very mild slope beach. We analyze low frequency wave generation mechanisms and dynamics along the beach and examine in detail the ability of the fully nonlinear Boussinesq- type model SERR1D (Cienfuegos et al., 2010) to reproduce the complex dynamics of high frequency wave propagation and energy transfer mechanisms that enhance infragravity wave generation in the laboratory.

scholarly journals POST-BOUSSINESQ MODEL FOR NONLINEAR IRREGULAR WAVE PROPAGATION IN PORTS AND WAVE-STRUCTURE INTERACTION

2020 ◽  
pp. 27
Author(s):  
Theofanis Karambas ◽  
Christos Makris ◽  
Vasilis Baltikas
Keyword(s):  
Wave Propagation ◽  
Water Waves ◽  
Wave Breaking ◽  
Wave Structure ◽  
Wave Transformation ◽  
Boussinesq Model ◽  
Weakly Nonlinear ◽  
Structure Interaction ◽  
Irregular Wave ◽  
Wave Structure Interaction

In this work, an updated version of the Karambas and Memos (2009) Boussinesq model for weakly nonlinear fully dispersive water waves, is introduced. It is implemented for wave propagation and transformation (due to shoaling, refraction, diffraction, bottom friction, wave breaking, runup, wave-structure interaction etc.) in nearshore zones and inside ports. One of the main goals is the model's thorough validation, thus it is tested against experimental data of wave transmission over and through breakwaters, uni- and multi-directional spectral wave transformation over complex bathymetries and diffraction through a breakwater gap. Case studies of model application over realistic variable bathymetries at characteristic Greek ports are also presented. Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/w8-AfAW6EYM

A Dispersive Numerical Model for the Formation of Undular Bores Generated by Tsunami Wave Fission

2017 ◽  
Vol 7 (4) ◽  
pp. 767-784
Author(s):  
I. Magdalena
Keyword(s):  
Wave Propagation ◽  
Dispersion Relation ◽  
Numerical Model ◽  
Tsunami Wave ◽  
Hydrodynamic Pressure ◽  
Free Surface Flows ◽  
Numerical Dispersion ◽  
Test Case ◽  
Linear Wave ◽  
Linear Dispersion

AbstractA two-layer non-hydrostatic numerical model is proposed to simulate the formation of undular bores by tsunami wave fission. These phenomena could not be produced by a hydrostatic model. Here, we derived a modified Shallow Water Equations with involving hydrodynamic pressure using two layer approach. Staggered finite volume method with predictor corrector step is applied to solve the equation numerically. Numerical dispersion relation is derived from our model to confirm the exact linear dispersion relation for dispersive waves. To illustrate the performance of our non-hydrostatic scheme in case of linear wave dispersion and non-linearity, four test cases of free surface flows are provided. The first test case is standing wave in a closed basin, which test the ability of the numerical scheme in simulating dispersive wave motion with the correct frequency. The second test case is the solitary wave propagation as the examination of owing balance between dispersion and nonlinearity. Regular wave propagation over a submerged bar test by Beji is simulated to show that our non-hydrostatic scheme described well the shoaling process as well as the linear dispersion compared with the experimental data. The last test case is the undular bore propagation.

scholarly journals Comparison of Fully Nonlinear and Weakly Nonlinear Potential Flow Solvers for the Study of Wave Energy Converters Undergoing Large Amplitude Motions

2014 ◽  
Author(s):  
Lucas Letournel ◽  
Pierre Ferrant ◽  
Aurélien Babarit ◽  
Guillaume Ducrozet ◽  
Jeffrey C. Harris ◽  
...  
Keyword(s):  
Wave Energy ◽  
Nonlinear Boundary Conditions ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
Wave Energy Converters ◽  
Submerged Sphere ◽  
Large Amplitude Motions ◽  
Nonlinear Potential ◽  
Realistic Problem ◽  
Energy Converters

We present a comparison between two distinct numerical codes dedicated to the study of wave energy converters. Both are developed by the authors, using a boundary element method with linear triangular elements. One model applies fully nonlinear boundary conditions in a numerical wavetank environnment (and thus referred later as NWT), whereas the second relies on a weak-scatterer approach in open-domain and can be considered a weakly nonlinear potential code (referred later as WSC). For the purposes of comparison, we limit our study to the forces on a heaving submerged sphere. Additional results for more realistic problem geometries will be presented at the conference.

Fully Nonlinear Dispersive HAWASSI-VBM for Coastal Zone Simulations

2016 ◽  
Author(s):  
Didit Adytia ◽  
Lawrence
Keyword(s):  
Gravity Waves ◽  
Laboratory Experiments ◽  
Hamiltonian Structure ◽  
Wave Model ◽  
Nonlinear Property ◽  
Irregular Waves ◽  
Boussinesq Model ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
Finite Element Implementation

The accuracy of a wave model for simulating waves in deep and coastal areas is highly determined by the dispersive properties as well as by the nonlinearity of the model. The Variational Boussinesq Model (VBM) for waves [1–4], available publicly as HAWASSI-VBM software [5], is based on the Hamiltonian structure of surface gravity waves. The model has tailor-made dispersive properties, which can be set to be sufficiently accurate for simulating a desired wave field. In this paper, we extend the nonlinear property of the HAWASSI-VBM from weakly nonlinear to be fully nonlinear. To show the improvement in nonlinearity, simulations of the model with a Finite Element implementation is tested against laboratory experiments, of regular and irregular waves propagating above a submerged bar and the dam-break problem.

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