Boundary element and integral methods in potential flow theory: a review with a focus on wave energy applications

Abstract

This paper presents a comprehensive review of boundary element methods for hydrodynamic modelling of wave energy systems. To design and optimise a wave energy converter (WEC), it is estimated that several million hours of WEC operation must be simulated. Linear boundary element methods are sufficiently fast to provide this volume of simulation and high speed of execution is one of the reasons why linear boundary element methods continue to underpin many, if not most, applied wave energy development efforts; however, the fidelity of the physics included is inadequate for some of the required design calculations. Judicious use of non-linear boundary element methods provides a route to increase the fidelity of the modeling while maintaining speed and other advantages over more computationally demanding alternatives such as Reynolds averaged Navier-Stokes (RANS) or smooth particle hydrodynamics (SPH). The paper presents some background to each aspect of the boundary methods reviewed, building up a relatively complete theoretical framework. Both linear and nonlinear methods are covered, and consideration is given to the computational complexity of the methods reviewed. The paper aims to provide a review that is useful in selection of the most appropriate techniques for the next generation of WEC design tools. KeywordsWave energy converter design tools • Potential flow theory • Boundary element method • Zero forward speed problem • Wave energy converter B John V. Ringwood

A review of wave energy technology from a research and commercial perspective

“…The mixed treatment combines the viscosity representation with the body‐exact or the weak‐scatter treatments, leading to body‐exact‐viscosity or the weak‐scatter‐viscosity models. The former is more generally used for modelling WEC hydrodynamics, as controlled WECs are expected to oscillate with a large motion, even in moderate sea states [27, 47]. So, the body‐exact‐viscosity treatment is useful for modelling WEC dynamics in normal operation mode, where the modelling fidelity of a heaving PA, considering non‐linear FK and viscous forces, can approach CFD results, with significantly lower computational cost [103].…”

“…For arbitrary WEC geometries, mesh‐based boundary element methods (BEMs) are generally used to obtain numerical approximations of and . Common BEM solvers include WAMIT, NEMOH, AQWA, AQUA+ and WADAM in the frequency domain, and ACHIL3D in the time domain [47]. Substituting , and in Equations () and () and omitting the quadratic term in Equation (), the pressure is obtained, to allow the hydrodynamic force in Equation () to be computed.…”

“…However, dominant non‐linear factors depend significantly on specific WEC concepts, structure sizes, control strategies and application scenarios, and should be carefully considered on a case‐by‐case basis [42, 45, 111]. Depending on the additional non‐linear term to , hybrid modelling methods are divided into four types [47], including the body‐exact, weak‐scatterer, viscosity and mixed treatments.…”

A Review of SPH Techniques for Hydrodynamic Simulations of Ocean Energy Devices

“…Historically, several popular commercial solvers based on the BE approach such as ANSYS AQWA and DNV SESAM have already provided corresponding modules (including both MCSs and mooring solvers) to tackle such problems. Nevertheless, as discussed in Section 1, these packages are incapable of capturing the nonlinearity behaviors of free-surface evolutions and are hard to be integrated into the SPH solver due to their closed-source property (for more details regarding the BE applications in simulating OEDs, the readers can refer to [174]). On the other hand, extensive efforts have been devoted to coupling FSI solvers with mooring dynamics solvers through different strategies.…”

Ocean Energy Systems Wave Energy Modeling Task 10.4: Numerical Modeling of a Fixed Oscillating Water Column

“…The state of the art for the numerical modeling of WECs in general can be classified into three levels of refinement: linear and weakly-nonlinear potential flow theory (e.g., Reference [8]); fully-nonlinear potential flow theory (e.g., Reference [9]); and Computational Fluid Dynamics (CFD), solving the Navier-Stokes equations for either a single-phase or a two-phase fluid (see, e.g., Reference [10]). Predicting the response and energy absorption of an OWC-type device presents special challenges, both in terms of numerical modeling and model-scale experimental testing.…”