Joseph Gregory Wallwork , Athanasios Angeloudis, Nicolas Barral , Lucas Mackie , Stephan C Kramer, Matthew D Piggott

Purpose: To examine the accuracy and sensitivity of tidal array performance assessment by numerical techniques applying goal-oriented mesh adaptation.

Methods: The goal-oriented framework is designed to give rise to adaptive meshes upon which a given diagnostic quantity of interest (QoI) can be accurately captured, whilst maintaining a low overall computational cost. We seek to improve the accuracy of the discontinuous Galerkin method applied to a depth-averaged shallow water model of a tidal energy farm, where turbines are represented using a drag parametrisation and the energy output is specified as the QoI. Two goal-oriented adaptation strategies are considered, which give rise to meshes with isotropic and anisotropic elements.

Results: We present both fixed mesh and goal-oriented adaptive mesh simulations for an established test case involving an idealised tidal turbine array positioned in a channel. With both the fixed meshes and the goal-oriented methodologies, we reproduce results from the literature which demonstrate how a staggered array configuration extracts more
energy than an aligned array. We also make detailed qualitative and quantitative comparisons between the fixed mesh and adaptive outputs.

Conclusion: The proposed goal-oriented mesh adaptation strategies are validated for the purposes of tidal energy resource assessment. Using 10% as many degrees of freedom as a high resolution fixed mesh benchmark, they are shown to enable energy output differences smaller than 10%. Applied to a tidal array with aligned rows of turbines, the anisotropic adaptation scheme is shown to yield differences smaller than 1%.