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.