# Numerical simulation of Nonlinear water waves using a panel method: domain decomposition and applications

P.C.A. de Haas

Research output: ThesisPhD Thesis - Research UT, graduation externalAcademic

### Abstract

In studying the influence of water waves on constructions such as dikes, wave breakers and offshore constructions, on ships but also on natural processes such as sediment transport and changes in bottom topography, more and more use is made of numerical models. An important class of such models consists of models in which the flow is described by potential theory. On the one hand the assumptions made in potential theory are valid in many studies, on the other hand the description - its field equation is Laplace's equation for the velocity potential - offers many possibilities for finding solutions with numerical models. The panel method is a numerical method which makes use of a boundary integral formulation for Laplace's equation, so that only the boundaries of the fluid domain have to be covered with grid points. Moreover this enables a natural description of the movement of the free surface in the time domain, which is determined by nonlinear dynamical and kinematical boundary conditions. Nonlinearity of the free-surface boundary conditions is often of importance in studying the influence of waves in coastal and ocean engineering. In this thesis a two-dimensional and three-dimensional numerical model are studied, based on a panel method, for the description of nonlinear water waves. The focus is on two important aspects: firstly the dependence of the computational effort on the number of grid points and secondly some specific numerical difficulties which arise when the method is used in application-like computations. With respect to the former aspect, a domain decomposition technique is studied. The latter aspect is studied for some examples and the suitability and limitations of some parts of the method for these examples are investigated. In more detail the contents of this thesis is as follows. For the domain decomposition technique, an iterative method is chosen in which the domain is divided in the horizontal direction. The length-to-height ratios of the subdomains, among other things, determine the convergence of the iterative method. Because the domains in problems involving water waves generally have large length-to-height ratios, relatively many subdomains can be chosen with a limited loss of convergence. As a consequence the panel method can be applied much more efficiently with domain decomposition. In the case of subdomains with fixed length-to-height ratios, the computational costs per time step depend at most linearly on the length of the domain.
Language English Supervisor 10 Oct 1997 Enschede, The Netherlands FEBO druk b.v. 9036510384 Published - 10 Oct 1997

### Fingerprint

water wave
nonlinear wave
decomposition
simulation
boundary condition
bottom topography
method
nonlinearity
numerical method
sediment transport
dike
engineering
fluid
ocean
cost

• METIS-140284
• EWI-16291
• IR-29650

### Cite this

de Haas, P.C.A.. / Numerical simulation of Nonlinear water waves using a panel method: domain decomposition and applications. Enschede, The Netherlands : FEBO druk b.v., 1997. 191 p.
title = "Numerical simulation of Nonlinear water waves using a panel method: domain decomposition and applications",
abstract = "In studying the influence of water waves on constructions such as dikes, wave breakers and offshore constructions, on ships but also on natural processes such as sediment transport and changes in bottom topography, more and more use is made of numerical models. An important class of such models consists of models in which the flow is described by potential theory. On the one hand the assumptions made in potential theory are valid in many studies, on the other hand the description - its field equation is Laplace's equation for the velocity potential - offers many possibilities for finding solutions with numerical models. The panel method is a numerical method which makes use of a boundary integral formulation for Laplace's equation, so that only the boundaries of the fluid domain have to be covered with grid points. Moreover this enables a natural description of the movement of the free surface in the time domain, which is determined by nonlinear dynamical and kinematical boundary conditions. Nonlinearity of the free-surface boundary conditions is often of importance in studying the influence of waves in coastal and ocean engineering. In this thesis a two-dimensional and three-dimensional numerical model are studied, based on a panel method, for the description of nonlinear water waves. The focus is on two important aspects: firstly the dependence of the computational effort on the number of grid points and secondly some specific numerical difficulties which arise when the method is used in application-like computations. With respect to the former aspect, a domain decomposition technique is studied. The latter aspect is studied for some examples and the suitability and limitations of some parts of the method for these examples are investigated. In more detail the contents of this thesis is as follows. For the domain decomposition technique, an iterative method is chosen in which the domain is divided in the horizontal direction. The length-to-height ratios of the subdomains, among other things, determine the convergence of the iterative method. Because the domains in problems involving water waves generally have large length-to-height ratios, relatively many subdomains can be chosen with a limited loss of convergence. As a consequence the panel method can be applied much more efficiently with domain decomposition. In the case of subdomains with fixed length-to-height ratios, the computational costs per time step depend at most linearly on the length of the domain.",
keywords = "METIS-140284, EWI-16291, IR-29650",
author = "{de Haas}, P.C.A.",
year = "1997",
month = "10",
day = "10",
language = "English",
isbn = "9036510384",
publisher = "FEBO druk b.v.",

}

Enschede, The Netherlands : FEBO druk b.v., 1997. 191 p.

Research output: ThesisPhD Thesis - Research UT, graduation externalAcademic

TY - THES

T1 - Numerical simulation of Nonlinear water waves using a panel method: domain decomposition and applications

AU - de Haas, P.C.A.

PY - 1997/10/10

Y1 - 1997/10/10

N2 - In studying the influence of water waves on constructions such as dikes, wave breakers and offshore constructions, on ships but also on natural processes such as sediment transport and changes in bottom topography, more and more use is made of numerical models. An important class of such models consists of models in which the flow is described by potential theory. On the one hand the assumptions made in potential theory are valid in many studies, on the other hand the description - its field equation is Laplace's equation for the velocity potential - offers many possibilities for finding solutions with numerical models. The panel method is a numerical method which makes use of a boundary integral formulation for Laplace's equation, so that only the boundaries of the fluid domain have to be covered with grid points. Moreover this enables a natural description of the movement of the free surface in the time domain, which is determined by nonlinear dynamical and kinematical boundary conditions. Nonlinearity of the free-surface boundary conditions is often of importance in studying the influence of waves in coastal and ocean engineering. In this thesis a two-dimensional and three-dimensional numerical model are studied, based on a panel method, for the description of nonlinear water waves. The focus is on two important aspects: firstly the dependence of the computational effort on the number of grid points and secondly some specific numerical difficulties which arise when the method is used in application-like computations. With respect to the former aspect, a domain decomposition technique is studied. The latter aspect is studied for some examples and the suitability and limitations of some parts of the method for these examples are investigated. In more detail the contents of this thesis is as follows. For the domain decomposition technique, an iterative method is chosen in which the domain is divided in the horizontal direction. The length-to-height ratios of the subdomains, among other things, determine the convergence of the iterative method. Because the domains in problems involving water waves generally have large length-to-height ratios, relatively many subdomains can be chosen with a limited loss of convergence. As a consequence the panel method can be applied much more efficiently with domain decomposition. In the case of subdomains with fixed length-to-height ratios, the computational costs per time step depend at most linearly on the length of the domain.

AB - In studying the influence of water waves on constructions such as dikes, wave breakers and offshore constructions, on ships but also on natural processes such as sediment transport and changes in bottom topography, more and more use is made of numerical models. An important class of such models consists of models in which the flow is described by potential theory. On the one hand the assumptions made in potential theory are valid in many studies, on the other hand the description - its field equation is Laplace's equation for the velocity potential - offers many possibilities for finding solutions with numerical models. The panel method is a numerical method which makes use of a boundary integral formulation for Laplace's equation, so that only the boundaries of the fluid domain have to be covered with grid points. Moreover this enables a natural description of the movement of the free surface in the time domain, which is determined by nonlinear dynamical and kinematical boundary conditions. Nonlinearity of the free-surface boundary conditions is often of importance in studying the influence of waves in coastal and ocean engineering. In this thesis a two-dimensional and three-dimensional numerical model are studied, based on a panel method, for the description of nonlinear water waves. The focus is on two important aspects: firstly the dependence of the computational effort on the number of grid points and secondly some specific numerical difficulties which arise when the method is used in application-like computations. With respect to the former aspect, a domain decomposition technique is studied. The latter aspect is studied for some examples and the suitability and limitations of some parts of the method for these examples are investigated. In more detail the contents of this thesis is as follows. For the domain decomposition technique, an iterative method is chosen in which the domain is divided in the horizontal direction. The length-to-height ratios of the subdomains, among other things, determine the convergence of the iterative method. Because the domains in problems involving water waves generally have large length-to-height ratios, relatively many subdomains can be chosen with a limited loss of convergence. As a consequence the panel method can be applied much more efficiently with domain decomposition. In the case of subdomains with fixed length-to-height ratios, the computational costs per time step depend at most linearly on the length of the domain.

KW - METIS-140284

KW - EWI-16291

KW - IR-29650

M3 - PhD Thesis - Research UT, graduation external

SN - 9036510384

PB - FEBO druk b.v.

CY - Enschede, The Netherlands

ER -

de Haas PCA. Numerical simulation of Nonlinear water waves using a panel method: domain decomposition and applications. Enschede, The Netherlands: FEBO druk b.v., 1997. 191 p.