Clive G. Mingham

Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations

A one-dimensional high-resolution finite volume model capable of simulating storm waves propagating in the coastal surf zone and overtopping a sea wall is presented. The model (AMAZON) is based on solving the non-linear shallow water (NLSW) equations. A modern upwind scheme of the Godunov-type using an HLL approximate Riemann solver is described which captures bore waves in both transcritical and supercritical flows. By employing a finite volume formulation, the method can be implemented on an irregular, structured, boundary-fitted computational mesh. The use of the NLSW equations to model wave overtopping is computationally efficient and practically flexible, though the detailed structure of wave breaking is of course ignored. It is shown that wave overtopping at a vertical wall may also be approximately modelled by representing the wall as a steep bed slope. The AMAZON model solutions have been compared with analytical solutions and laboratory data for wave overtopping at sloping and vertical seawalls and good agreement has been found. The model requires more verification tests for irregular waves before its application as a generic design tool.

Developments in Cartesian cut cell methods

This paper describes the Cartesian cut cell method, which provides a flexible and efficient alternative to traditional boundary fitted grid methods. The Cartesian cut cell approach uses a background Cartesian grid for the majority of the flow domain with special treatments being applied to cells which are cut by solid bodies, thus retaining a boundary conforming grid. The development of the method is described with applications to problems involving both moving bodies and moving material interfaces.

Calculation of shallow water flows using a Cartesian cut cell approach

A new grid generation method for the computation of shallow water flows is presented. The procedure, based on the use of cut cells on a Cartesian background mesh, can cope with shallow water problems having arbitrarily complex geometries. Although the method provides a fully boundary-fitted capability, no mesh generation in the conventional sense is required. Solid regions are simply cut out of a background Cartesian mesh with their boundaries represented by different types of cut cell. For the flow calculations a multi-dimensional high resolution upwind finite volume scheme is used in conjunction with an efficient approximate Riemann solver to deal with complex shallow water problems involving steady or unsteady hydraulic discontinuities. The method is validated for several test problems involving unsteady shallow water flows.

A global-local artificial neural network with application to wave overtopping prediction

We present a hybrid Radial Basis Function (RBF) - sigmoid neural network with a three-step training algorithm that utilises both global search and gradient descent training. We test the effectiveness of our method using four synthetic datasets and demonstrate its use in wave overtopping prediction. It is shown that the hybrid architecture is often superior to architectures containing neurons of a single type in several ways: lower errors are often achievable using fewer hidden neurons and with less need for regularisation. Our Global-Local Artificial Neural Network (GL-ANN) is also seen to compare favourably with both Perceptron Radial Basis Net (PRBFN) and Regression Tree RBFs.

A bore-capturing finite volume method for open-channel flows

A high-resolution finite volume hydrodynamic solver is presented for open-channel flows based on the 2D shallow water equations. This Godunov-type upwind scheme uses an efficient Harten-Lax-van Leer (HLL) approximate Riemann solver capable of capturing bore waves and simulating supercritical flows. Second-order accuracy is achieved by means of MUSCL reconstruction in conjunction with a Hancock two-stage scheme for the time integration. By using a finite volume approach, the computational grid can be irregular which allows for easy boundary fitting. The method can be applied directly to model 1D flows in an open channel with a rectangular cross-section without the need to modify the scheme. Such a modification is normally required for solving the 1D St Venant equations to take account of the variation of channel width. The numerical scheme and results of three test problems are presented in this paper.

A free-surface capturing method for two fluid flows with moving bodies

A two-fluid solver has been developed for flow problems with both moving solid bodies and free surfaces. The underlying scheme is based on the solution of the incompressible Navier–Stokes equations for a variable density fluid system with a free surface. The cut cell method is used for tracking moving solid boundaries across a stationary background Cartesian grid. The computational domain encompasses fully both fluid regions and the fluid interface is treated as a contact discontinuity in the density field, which is captured automatically without special provision as part of the numerical solution using a time-accurate artificial compressibility method and high resolution Godunov-type scheme. A pressure-splitting algorithm is proposed for the accurate treatment of the normal pressure gradient at the interface in the presence of a gravity term. The Cartesian cut cell technique provides a highly efficient and fully automated process for generating body fitted meshes, which is particularly useful for moving boundary problems. Several test cases have been calculated using the present approach including a moving paddle as a wave generator and the initial stages of entry into still water of rigid wedges. The results compare well with other theoretical results and experimental data. Finally, test cases involving the entry into water and subsequent total immersion of a two-dimensional rigid wedge-shaped body as well as the inverse problem of wedge egress have been calculated to demonstrate the ability of the current method to tackle more general two fluid flows with interface break-up, reconnection, entrapment of one fluid into the other, as well as handling moving bodies of complex geometry.

A Cartesian cut cell method for shallow water flows with moving boundaries

A new computational method for the calculation of shallow water flows with moving physical boundaries is presented. The procedure can cope with shallow water problems having arbitrarily complex geometries and moving boundary elements. Although the method provides a fully boundary-fitted capability, no mesh generation is required in the conventional sense. Solid regions are simply cut out of a background Cartesian mesh with their boundaries represented by different types of cut cell. Moving boundaries are accommodated by up-dating the local cut cell information on a stationary background mesh as the boundaries move. No large-scale re-meshing is required. For the flow calculations, a multi-dimensional high resolution upwind finite volume scheme is used in conjunction with an efficient approximate Riemann solver at flow interfaces, and an exact Riemann solution for a moving piston at moving boundary elements. The method is validated for test problems that include a ships hull moving at supercritical velocity and two hypothetical landslide events where material plunges laterally into a quiescent shallow lake and a fiord.

On global-local artificial neural networks for function approximation

We present a hybrid radial basis function (RBF) sigmoid neural network with a three-step training algorithm that utilizes both global search and gradient descent training. The algorithm used is intended to identify global features of an input-output relationship before adding local detail to the approximating function. It aims to achieve efficient function approximation through the separate identification of aspects of a relationship that are expressed universally from those that vary only within particular regions of the input space. We test the effectiveness of our method using five regression tasks; four use synthetic datasets while the last problem uses real-world data on the wave overtopping of seawalls. It is shown that the hybrid architecture is often superior to architectures containing neurons of a single type in several ways: lower mean square errors are often achievable using fewer hidden neurons and with less need for regularization. Our global-local artificial neural network (GL-ANN) is also seen to compare favorably with both perceptron radial basis net and regression tree derived RBFs. A number of issues concerning the training of GL-ANNs are discussed: the use of regularization, the inclusion of a gradient descent optimization step, the choice of RBF spreads, model selection, and the development of appropriate stopping criteria.

A JOINT NUMERICAL AND EXPERIMENTAL STUDY OF A SURGING POINT ABSORBING WAVE ENERGY CONVERTER (WRASPA)

This paper presents the findings from using several commercial computational fluid dynamics codes in a joint numerical and experimental project to simulate WRASPA, a new wave energy converter (WEC) device. A series of fully 3D non-linear simulations of WRASPA are presented. Three commercial codes STAR-CCM, CFX and FLOW-3D are considered for simulating the WRASPA device and final results are presented based on the use of Flow-3D. Results are validated by comparison to experimental data obtained from small scale tank tests undertaken at Lancaster University (LU). The primary aim of the project is to use numerical simulation to optimize the collector geometry for power production over a range of likely wave climates. A secondary aim is to evaluate the ability of commercial codes to simulate rigid body motion in linear and non-linear wave climates in order to choose the optimal code with respect to compute speed and ease of problem setup. Issues relating to the ability of a code in terms of numerical dissipation of waves, wave absorption, wave breaking, grid generation and moving bodies will all be discussed. The findings of this paper serve as a basis for an informed choice of commercial package for such simulations. However the capability of these commercial codes is increasing with every new release.Copyright

A compressible multiphase flow model for violent aerated wave impact problems

This paper focuses on the numerical modelling of wave impact events under air entrapment and aeration effects. The underlying flow model treats the dispersed water wave as a compressible mixture of air and water with homogeneous material properties. The corresponding mathematical equations are based on a multiphase flow model which builds on the conservation laws of mass, momentum and energy as well as the gas-phase volume fraction advection equation. A high-order finite volume scheme based on monotone upstream-centred schemes for conservation law reconstruction is used to discretize the integral form of the governing equations. The numerical flux across a mesh cell face is estimated by means of the HLLC approximate Riemann solver. A third-order total variation diminishing Runge–Kutta scheme is adopted to obtain a time-accurate solution. The present model provides an effective way to deal with the compressibility of air and water–air mixtures. Several test cases have been calculated using the present approach, including a gravity-induced liquid piston, free drop of a water column in a closed tank, water–air shock tubes, slamming of a flat plate into still pure and aerated water and a plunging wave impact at a vertical wall. The obtained results agree well with experiments, exact solutions and other numerical computations. This demonstrates the potential of the current method to tackle more general wave–air–structure interaction problems.