Modelling Wave Interaction with Porous Structures Using Boussinesq Equations
01 Jan 2019-pp 573-583
TL;DR: In this article, a numerical model of the two-dimensional enhanced Boussinesq equations is presented to simulate wave transformations in the near-shore region, where the finite element-based discretisation over unstructured mesh with triangular elements uses mixed linear and quadratic shape functions.
Abstract: The paper presents a numerical model of the two-dimensional enhanced Boussinesq equations to simulate wave transformations in the near-shore region. The finite element-based discretisation over unstructured mesh with triangular elements uses mixed linear and quadratic shape functions. The domain integrals are calculated analytically. The model is extended to study flow through porous structures using Darcy velocity, with the energy dissipation within the porous medium modelled through additional laminar and turbulent resistance terms. A single set of empirical constants gives accurate prediction for various stone sizes and porosity. This paper reports the model development and its validation using existing experimental studies. Application of the model is demonstrated by studying the interaction between ship-generated waves in a narrow channel and the porous walls of the channel.
Citations
More filters
TL;DR: In this paper , a finite element model for depth integrated form of Boussinesq equations is presented, where the equations are solved on an unstructured triangular mesh using standard Galerkin method with mixed interpolation scheme.
2 citations
TL;DR: Agarwal et al. as mentioned in this paper presented coupling between a mesh-based finite element model for Boussinesq equations and a meshless local Petrov-Galerkin model for the Navier-Stokes equations in 3D.
1 citations
References
More filters
Book•
08 Jun 2005
TL;DR: This book provides first the fundamentals of numerical analysis that are particularly important to meshfree methods, and provides most of the basic meshfree techniques, and can be easily extended to other variations of more complex procedures of mesh free methods.
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.
1,119 citations
TL;DR: In this paper, a high-order numerical model based on the Boussinesq model was developed and applied to the study of two canonical problems: solitary wave shoaling on slopes and undular bore propagation over a horizontal bed.
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.
902 citations
TL;DR: In this paper, a new form of the Boussinesq equations applicable to irregular wave propagation on a slowly varying bathymetry from deep to shallow water is introduced, which incorporate excellent linear dispersion characteristics, and are formulated and solved in two horizontal dimensions.
783 citations
TL;DR: In this paper, a new form of the Boussinesq equations is introduced in order to improve their dispersion characteristics, and a numerical method for solving the new set of equations in two horizontal dimensions is presented.
694 citations
TL;DR: In this article, a method valid for highly dispersive and highly nonlinear water waves is presented, which combines a time-stepping of the exact surface boundary conditions with an approximate series expansion solution to the Laplace equation in the interior domain.
Abstract: A new method valid for highly dispersive and highly nonlinear water waves is presented. It combines a time-stepping of the exact surface boundary conditions with an approximate series expansion solution to the Laplace equation in the interior domain. The starting point is an exact solution to the Laplace equation given in terms of infinite series expansions from an arbitrary z-level. We replace the infinite series operators by finite series (Boussinesq-type) approximations involving up to fifth-derivative operators. The finite series are manipulated to incorporate Pade approximants providing the highest possible accuracy for a given number of terms. As a result, linear and nonlinear wave characteristics become very accurate up to wavenumbers as high as kh = 40, while the vertical variation of the velocity field becomes applicable for kh up to 12. These results represent a major improvement over existing Boussinesq-type formulations in the literature. A numerical model is developed in a single horizontal dimension and it is used to study phenomena such as solitary waves and their impact on vertical walls, modulational instability in deep water involving recurrence or frequency downshift, and shoaling of regular waves up to breaking in shallow water.
335 citations