Session: 08-03-02 Free Surface Flows

Paper Number: 108097

108097 - A Systematic Approach of Developing a Numerical Wavetank to Simulate Driven Shallow- and Deep-Water Waves 

The maritime industry frequently uses wavetanks to study water waves and their interactions with maritime structures in an experimental environment. The water waves are generated in the wavetanks using different types of wavemakers whose specific form depends on the desired sea state, i.e., the relation between the water depth with the amplitude and wavelength of the water waves to be modelled. For example, to model shallow- or deep-water dynamics, wavetanks are equipped with piston- or waveflap-wavemakers respectively. Model basin tests can be used to validate numerical models. Once numerical models are validated they can complement model tests whose scope is often limited due to budget and time constraints. Also, numerical simulations are very useful in the early design stage when model tests are not yet an option. 

Thus motivated, a numerical model of a waveflap-wavemaker wavetank is developed by implementing the variational principle (VP) of nonlinear potential-flow equations in the finite-element-based environment Firedrake. Establishing the mathematical and numerical model of such a wavetank, based on the VP and domain-specific compiler architecture, is a novel challenge aimed at reducing development time and enabling new model experimentation. 

In the computational domain, the two-dimensional waveflap-wavemaker boundary motion increases the complexity far beyond that of the piston-wavemaker problem, in which the boundary motion is one-dimensional. This paper aims to explain a systematic approach to developing a numerical waveflap-wavemaker wavetank, using domain-specific finite-element-compiler architecture, that can simulate the dynamics of both shallow- and deep-water waves.

First, the VPs of linear and nonlinear shallow-water equations are implemented in Firedrake to develop a numerical piston-wavemaker wavetank. Second, the complexity of the first model is increased by deriving the VP based on potential-flow theory to develop a numerical piston-wavemaker wavetank. Third, the second model is extended to include a waveflap wavemaker. The proposed systematic approach facilitates not only cumulative validation of results but also understanding and implementation for both developer and user.

In addition, a novel implementation of the equations of motion is developed by using a time-discrete VP instead of weak formulations. The finite-element compiler architecture Firedrake allows this method to automatically generate the time-discrete weak formulation, thereby reducing both the likelihood of human error and the time taken to both develop and implement the code.

Presenting Author: Wajiha Rehman University of Leeds

Presenting Author Biography: Wajiha Rehman is a postgraduate researcher(PGR) in the School of Mathematics at the University of Leeds. She is a Marie Sklodowska-Curie Early-Stage Researcher (ESR) for the European Union European Industrial Doctorate (EID) program; Eagre/Aegir: High-seas wave-impact modelling. As an ESR, she is working on two projects; the first one is developing a numerical model of a wave tank driven by the waveflap wavemaker to generate water waves using the variational principle of potential flow theory. The second project is to perform the experimental study of an FSI problem, i.e., water-wave interactions with a flexible beam and to develop and validate the numerical FSI solver. The FSI solver performs the wave-structure interaction analysis of water waves and the flexible offshore wind-turbine mast using (dis)continuous Galerkin’s Finite Element Method. This paper deals with the first part of the project.

Authors:

Wajiha Rehman University of Leeds
Onno Bokhove University of Leeds
Mark Kelmanson University of Leeds