Modelling Wave Interaction with Porous Structures Using Boussinesq Equations

An Introduction to Meshfree Methods and Their Programming

Abstract: This book aims to present meshfree methods in a friendly and straightforward manner, so that beginners can very easily understand, comprehend, program, implement, apply and extend these methods. It provides first the fundamentals of numerical analysis that are particularly important to meshfree methods. Typical meshfree methods, such as EFG, RPIM, MLPG, LRPIM, MWS and collocation methods are then introduced systematically detailing the formulation, numerical implementation and programming. Many well-tested computer source codes developed by the authors are attached with useful descriptions. The application of the codes can be readily performed using the examples with input and output files given in table form. These codes consist of most of the basic meshfree techniques, and can be easily extended to other variations of more complex procedures of meshfree methods. Readers can easily practice with the codes provided to effective learn and comprehend the basics of meshfree methods.

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

Abstract: 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.

A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly-varying bathymetry

Abstract: A new form of the Boussinesq equations applicable to irregular wave propagation on a slowly varying bathymetry from deep to shallow water is introduced. The equations incorporate excellent linear dispersion characteristics, and are formulated and solved in two horizontal dimensions. In an earlier paper we concentrated on wave propagation and diffraction on a horizontal bottom in deep water. In this paper these principles are generalized and the Boussinesq equations are extended to include terms proportional to the bottom slope, which are essential for the shoaling properties of the equations. The paper contains a linear shoaling analysis of the new equations and a verification of the numerical model with respect to shoaling and refraction-diffraction in deep and shallow water.

A new form of the Boussinesq equations with improved linear dispersion characteristics

Abstract: A new form of the Boussinesq equations is introduced in order to improve their dispersion characteristics. It is demonstrated that the depth-limitation of the new equations is much less restrictive than for the classical forms of the Boussinesq equations, and it is now possible to simulate the propagation of irregular wave trains travelling from deep water to shallow water. In deep water, the new equations become effectively linear and phase celerities agree with Stokes first-order theory. In more shallow water, the new equations converge towards the standard Boussinesq equations, which are known to provide good results for waves up to at least 75% of their breaking height. A numerical method for solving the new set of equations in two horizontal dimensions is presented. This method is based on a time-centered implicit finite-difference scheme. Finally, model results for wave propagation and diffraction in relatively deep water are presented.

Verification of numerical wave propagation models for simple harmonic linear water waves

Abstract: When applying numerical methods to study short-wave propagation in the horizontal plane (refraction and/or diffraction problems) it is important to know which method can best be used with respect to accuracy, computer costs and practical flexibility. In this paper three models, indicated as the refraction model, the parabolic refraction-diffraction model and the full refraction-diffraction model, are briefly described, together with a comparison of the computational results of these models with measurements in a hydraulic scale model. Conclusions with respect to the practical use of the models are also given.