Recent developments towards a hybrid method for fully nonlinear water waves

Numerical analysis is necessary for the design and optimization of dynamic systems that interact with ocean waves, such as e.g. floating offshore wind turbines or remotely operated vehicles. As one would expect, the important scales and physics may vary significantly depending on the system of interest. Regardless, the computational method used to solve the governing equations must be capable of dealing with moving boundaries and varying spatial/temporal resolution. If one considers the non-linear potential flow problem, the governing equations can be discretized in a time-varying domain using radial basis function-generated finite differences. However, the time-varying domain is computationally costly as the domain length must be several wave lengths in the horizontal directions and still resolve the smallest waves in the vicinity of the wave-body interface. Thus, recent developments towards a hybrid finite difference method for the solution of the fully nonlinear potential flow problem are investigated. The hybrid method combines the idea of traditional- and radial basis function-generated finite differences, which aims to increase the computational efficiency while maintaining the geometric flexibility and high-order accuracy near moving bodies. Numerical properties of the hybrid scheme are illustrated by examples.