Goal-Oriented Error Estimation and Mesh Adaptation for Shallow Water Modelling

This is a Preprint and has not been peer reviewed.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.

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Authors

Joseph Wallwork , Nicolas Barral, Stephan C. Kramer, David Ham, Matthew Piggott 

Abstract

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.

DOI

https://doi.org/10.31223/osf.io/cs4we

Subjects

Applied Mathematics, Computer Sciences, Engineering, Non-linear Dynamics, Numerical Analysis and Computation, Numerical Analysis and Scientific Computing, Partial Differential Equations, Physical Sciences and Mathematics

Keywords

Discontinuous Galerkin, Adjoint methods, Firedrake, Mesh adaptation, Tidal turbine modelling

Dates

Published: 2019-12-31 12:45

Last Updated: 2020-07-28 16:24

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License

CC BY Attribution 4.0 International

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