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publications
Using nonlinear interactions to quantify and improve timestepping accuracy in the Rotating Shallow Water Equations
Posted in 2024
PhD Thesis from the University of Exeter
The effect of linear dispersive errors on nonlinear timestepping accuracy in the f-plane rotating shallow water equations
Posted in 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.
A conservative, discontinuous Galerkin, tracer transport scheme using compatible finite elements
Posted in 2026
This paper describes and tests a conservative transport scheme for scalar tracers using compatible finite elements.
A mountain-generated mesoscale test case from DCMIP-2025: Gap flow and vortex shedding variants
Posted in 2026
This paper describes a new test case developed for the evaluation of dynamical cores. The test either initiates a gap flow in a mountain chain, or vortex shedding behind an isolated mountain. The test is applied to four dynamical cores.
A perfectly matched layer for damping vertically propagating waves in the compressible Boussinesq equations
Posted in 2026
This paper investigates the use of a perfectly matched layer to damp waves near the model top for geophysical flow applications. Comparisons are made to standard sponge layers.
Stability analyses of divergence and vorticity damping on gnomonic cubed-sphere grids
Published in Monthly Weather Review, 2026
This paper derives linear stability limits to divergence and vorticity damping on gnomonic cubed-sphere grids. The linear theory is then applied to baroclinic wave simulations using the finite-volume cubed (FV3) dynamical core.
A numerical study of mean corrected phase-averaging in geophysical flow equations
Published in Theoretical and Computational Fluid Dynamics, 2026
A study of a mean corrected version of the phase-averaged timestepping method to improve its accuracy. 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 numerical tests, including with the one-dimensional rotating shallow water equations.
talks
Quantifying the accuracy of large timesteps
Published:
Visiting seminar at NIWA Wellington (NZ) office
Quantifying the accuracy of large time-steps in highly oscillatory systems
Published:
Poster presentation at the 2023 EGU conference.
The effect of linear dispersive errors on nonlinear time- stepping accuracy in weather and climate PDEs
Published:
A talk at the 2023 ‘PDEs on the Sphere’ conference.
Triadic initial conditions for testing a phase-averaged coarse propagator for Parareal
Published:
Presentation at the 2023 Parallel-in-time (PinT) conference
Stability analyses of divergence and vorticity damping on cubed-sphere grids
Published:
A talk at the 2025 ‘PDEs on the Sphere’ conference.
New mountain-generated meso-scale flow test cases for dynamical cores
Published:
Poster presentation at the 2025 AGU conference.
teaching
Teaching experience 1
Undergraduate course, University 1, Department, 2014
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Teaching experience 2
Workshop, University 1, Department, 2015
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