Using nonlinear interactions to quantify and improve timestepping accuracy in the Rotating Shallow Water Equations
Published on 2024
PhD Thesis from the University of Exeter
Publications
PhD Thesis
Preprints
A mean correction for improved phase-averaging accuracy in oscillatory, multiscale, differential equations
Published on 2024
This paper investigates improving the accuracy of the phase-averaged timestepping method. Phase-averaging reduces numerical stiffness to enable large, accurate, timesteps in oscillatory PDEs. However, this introduces an averaging error, which we aim to offset with an additional mean correction term. This new method is shown to enable accuracy improvements in three numerical tests, including the one-dimensional rotating shallow water equations.
The effect of linear dispersive errors on nonlinear timestepping accuracy in the f-plane rotating shallow water equations
Published on 2024
This paper investigates new ways to quantify timestepping error in the f-plane rotating shallow water equations. The first part constructs a new triadic error that measures error within the nonlinear interactions of linear waves. The second part develops two new test cases to highlight slowly developing nonlinear interactions. These are tested with three numerical models, including LFRic from the UK Met Office.