Tidal Turbine Array Modelling using Goal-Oriented Mesh Adaptation

Wallwork, Joseph G.; Angeloudis, Athanasios; Barral, Nicolas; Mackie, Lucas; Kramer, Stephan C.; Piggott, Matthew

doi:10.31223/x5h06b

Cited by 1 publication

(2 citation statements)

References 35 publications

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“…The shallow water equations are often solved in their time-dependent formulation rather than to steady-state. As such, a major piece of future work is to train a network to perform goaloriented error estimation for time-dependent problems, such as the tidally reversing array example considered in [23]. Conceptually, this would be very similar to the present work, mapping feature data to error indicators.…”

Section: Discussionmentioning

confidence: 92%

“…Previous work by the authors of this paper has applied goal-oriented error estimation techniques to tidal energy resource assessment with power or energy output as the QoI (see [3] for the steady-state case and [23] for the time-dependent case). We build upon this work and seek to accelerate the numerical experiments presented in [3] using neural networks.…”

Section: Novel Aspects Of the Present Workmentioning

confidence: 99%

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E2N: Error Estimation Networks for Goal-Oriented Mesh Adaptation

Wallwork¹,

Lu²,

Zhang³

et al. 2022

Preprint

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Given a partial differential equation (PDE), goal-oriented error estimation allows us to understand how errors in a diagnostic quantity of interest (QoI), or goal, occur and accumulate in a numerical approximation, for example using the finite element method. By decomposing the error estimates into contributions from individual elements, it is possible to formulate adaptation methods, which modify the mesh with the objective of minimising the resulting QoI error. However, the standard error estimate formulation involves the true adjoint solution, which is unknown in practice. As such, it is common practice to approximate it with an 'enriched' approximation (e.g. in a higher order space or on a refined mesh). Doing so generally results in a significant increase in computational cost, which can be a bottleneck compromising the competitiveness of (goal-oriented) adaptive simulations. The central idea of this paper is to develop a "data-driven" goal-oriented mesh adaptation approach through the selective replacement of the expensive error estimation step with an appropriately configured and trained neural network. In doing so, the error estimator may be obtained without even constructing the enriched spaces. An element-byelement construction is employed here, whereby local values of various parameters related to the mesh geometry and underlying problem physics are taken as inputs, and the corresponding contribution to the error estimator is taken as output. We demonstrate that this approach is able to obtain the same accuracy with a reduced computational cost, for adaptive mesh test cases related to flow around tidal turbines, which interact via their downstream wakes, and where the overall power output of the farm is taken as the QoI. Moreover, we demonstrate that the element-byelement approach implies reasonably low training costs.

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Section: Discussionmentioning

confidence: 92%