Solution-driven Mesh Adaptation Method for Unsteady Tidal Turbine Array Simulation and Optimisation

Abstract

Numerical simulations play a central role in understanding engineering problems, such as the scale-up and design optimisation challenges of energy generation from complex, non-linear renewable sources including wind and tidal. In such geophysical fluid dynamics problems, the  multi-scale spatial discretisation required to achieve a reasonable level of accuracy may come at a high computational cost. Mesh adaptation can improve the accuracy of numerical simulations by modifying the underlying discretized structure. Choosing the applied mesh adaption method based on the time evolution characteristics of the related solution fields could further improve the overall computational efficiency For example, mesh movement methods are well suited to following physics with a fixed number of degrees of freedom, while mesh optimisation methods allow changing the number of computational nodes and their connectivity to more flexibly adapt to rapidly varying solution fields.  

We study the application of a mesh adaptation workflow utilizing time and space optimisation to effectively alternate the use of mesh movement and mesh optimisation methods as applied to numerical simulations motivated by tidal energy applications. The unsteady tidal turbine array test case as presented by Divett et al.¹ and further explored by Wallwork et al 2024² serves as a benchmark for investigating the potential advantages and pitfalls of this workflow. We employ adjoint based error estimation techniques to derive the most effective distribution of mesh resolution to maximize accuracy in a specific output of the model. Here this output is chosen to be the power generated by the tidal turbine array, of direct relevance for resource assessment and micro-siting studies. The discussion is focused on trade-offs between accuracy preservation and efficiency gain achieved over the full simulation, and how this feeds into array design opimisation tasks. 

REFERENCES 

1. T Divett, R. Vennell, and C. Stevens, Optimization of multiple turbine arrays in a channel with tidally reversing flow by numerical modelling with adaptive mesh, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 371, no. 1985, (2013) 

1. J. G. Wallwork, N. Barral, L. Mackie, S. C. Kramer, and M. D. Piggott, Tidal turbine array modelling using goal-oriented mesh adaptation, J. Ocean Eng. Mar. Energy, vol. 10, no. 1, 193–216, (2024). 

1. B. Sauvage, F. Alauzet, and A. Dervieux, A space and time fixed point mesh adaptation method, Journal of Comp. Physics., vol. 519, 113389, (2024).