Development of a high-order potential flow solver for nonlinear wave-structure interaction

Accurate modelling and evaluation of nonlinear wave loads on marine structures is of critical importance to ensure longevity in their designs. To that end, the focus of this research is the extension and subsequent application of a fully nonlinear, finite-difference based potential flow solver to nonlinear wave-structure interactions at high order. Both forced and free-body motions are considered.

The solver utilizes a sigma-transformation of the vertical coordinate, which maps the timevarying physical domain to a time-invariant computational domain. This is combined with an Immersed Boundary Method (IBM) based on Weighted Least Squares (WLS) stencils for satisfying the body boundary condition, which provides a sharp-interface method for including moving bodies in the domain. The time-stepping solution proceeds via an explicit, fourth-order Runge-
Kutta scheme. The combination of an IBM with both a sigma-transformation and a multi-stage time-stepping method presents several difficulties, which are addressed in this research by the introduction of body-free-surface intersection point tracking and an acceleration potential method for the evaluation of wave loads. These improvements eliminate the spurious oscillations in the calculated force signals, reported in previous work and thought to be related to the IBM, and are implemented at flexible order. Initial testing of free-body motions indicates a weak numerical instability related to the implicit body boundary condition. However, application of a high-order filter to the free-surface variables appears to mitigate this, and allows for favourable comparison with experimental data for the free decay of a circular cylinder.

An optimization procedure is developed for the generation of stable wave fields up to second order. While the procedure is applicable to wavemakers of arbitrary shape, in this work it is applied to a heaving wedge wavemaker. Results show a significant reduction in both mean error and variation across a given test section, for waves in intermediate and deep water and up to 50% of the theoretical breaking limit.