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


Haas de, Paulus Cornelis Antonius (1997) Numerical simulation of Nonlinear water waves using a panel method; domain decomposition and applications. thesis.

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.
Furthermore the approriateness of the numerical model is studied for three
types of problems. Firstly the use of the model for the simulation of waves
generated by a translating or rotating wavemaker is studied. An important
improvement for such computations is the use of descriptions in the physical
domain rather than in the computational domain for extrapolations towards
lateral boundaries such as the wavemaker boundary. Secondly the propagation
of wave groups is simulated and the use of various formulations of the wave
group signal is studied. The domain decomposition technique proves to be a
succesful method for these computations. Thirdly the approriateness of the numerical model for the simulation of waves diffracting around a surface-piercing construction is studied. Because of the large differences in horizontal velocities on the free surface, the use of a mixed Eulerian-Lagrangian description is necessary.
Item Type:Thesis
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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