This is a Preprint and has not been peer reviewed. The published version of this Preprint is available: https://doi.org/10.1007/s42452-020-2745-9. This is version 3 of this Preprint.
This is a Preprint and has not been peer reviewed. The published version of this Preprint is available: https://doi.org/10.1007/s42452-020-2745-9. This is version 3 of this Preprint.
Numerical modelling frequently involves a diagnostic quantity of interest (QoI) - often of greater importance than the PDE solution - which we seek to accurately approximate. In the case of coastal ocean modelling the power output of a tidal turbine farm is one such example. Goal-oriented error estimation and mesh adaptation can be used to provide meshes which are well-suited to achieving this goal, using fewer computational resources than required by other methods, such as uniform refinement.
A mixed discontinuous/continuous Galerkin approach is applied to solve the nonlinear shallow water equations within the Thetis coastal ocean finite element model. An implementation of goal-oriented mesh adaptation is outlined, including an error estimate which takes account of the discontinuities in the discrete solution and a method for approximating the adjoint error. Results are presented for simulations of two model tidal farm configurations. Convergence analysis indicates that the anisotropic goal-oriented adaptation strategy yields meshes which permit accurate QoI estimation using fewer computational resources than uniform refinement.
https://doi.org/10.31223/osf.io/cs4we
Applied Mathematics, Computer Sciences, Engineering, Non-linear Dynamics, Numerical Analysis and Computation, Numerical Analysis and Scientific Computing, Partial Differential Equations, Physical Sciences and Mathematics
Discontinuous Galerkin, Adjoint methods, Firedrake, Mesh adaptation, Tidal turbine modelling
Published: 2019-12-31 18:15
Last Updated: 2020-07-28 21:54
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