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.

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

A literature survey which concerns a variety of wave generation and absorption methods was accomplished. The survey deals with the methods used for the experiment wave tank and numerical wave tank. Their implementations are also described very briefly. The numerical wave tank (NWT) was set up using the hybrid particle-mesh method with the emphasis on the wave generation of solitary wave and linear progressive wave, and passive absorption at the far side of the wave tank. The Discontinuous Galerkin method was applied to solve the Navier-Stokes equations on the background mesh while the particles are used for solving the non-linear advection term. The waves are generated by using a piston-type wavemaker with the use of first-order linear wavemaker theory. For the absorption of reflected waves at the termination end, the sponge layer approach was implemented making use of viscous damping or internal friction among water particles. The hyperbolic tangent function is found to be applicable for smoothly increasing viscosity in the damping zone, which is also be able to prevent the formation of rigid body at the transition point. The drawbacks of the passive absorption technique are not only the extra cost of computational power and domain size, but also the rising slope of average water surface elevation induced by the accumulation of water particles near the end of the wave tank. The solitary waves of small amplitude could be simulated with reliable accuracy and also did the linear progressive waves in the intermediate water. The short waves and the long waves need to paid more attention for the wave generation boundary condition. Regarding the passive absorption for both of solitary waves and progressive waves, the same hyperbolic tangent function was used for viscosity functions which increases spatially. The solitary wave can be damped out using this function while the latter one cannot be damped, leading to the instability of the computation induced by the loss of the particles in the mesh system.

/pdf/setting-up-a-numerical-flume-using-a-hybrid-particle-mesh-39egah0t0g.pdf

Setting up a numerical flume using a hybrid particle-mesh method

The correct generation of a second order wave field in a laboratory wave tank is of importance in several experimental investigations, particularly those of nonlinear evolutions and sediment transport. In the present work, which was carried out under the MLTP (medium long-term planning) of DELFT HYDRAULICS for improving experimental techniques, expressions are found for the motion of a waveboard to generate a correct second order wave field. These expressions are valid for both regular and irregular waves. Two important features of the procedure adopted here are that the computing time for the motion of the waveboard is signifcantly smaller compared to a method based on the frequency domain and that the accuracy of the physical representation increases with decreasing spectral width. The assumption of a narrow band spectrum is sufficient for realistic sea states described by spectral shapes of JONSWAP and Pierson-Moskowitz types. Results of some experimental investigations into the performance of the software based on the wave generation theory are also included in the report. Although the overall agreement between the theory and the experiment is good, some discrepancies are apparent from the limited analysis carried out so far, all of which cannot be attributed to the wave generation theory. Further analysis (and possibly a set of new experiments) is required in order to resolve aH the discrepancies.

/pdf/laboratory-wave-generation-a-second-order-theory-for-regular-57tbsv3iuj.pdf

A.K. Otta

Papers

Laboratory wave generation: A second-order theory for regular and irregular waves in wave channels