The TRR 181 seminar Series/Joint Seminar is held by Michael Cox (Durham University) on October 9th, 11:00 am in Bundesstr. 53, Hamburg, room 22/23.

Numerical Phase Averaging with Deferred Correction Methods

Abstract

In the atmosphere and ocean, fast oscillations such as gravity waves coexist with slow features such as geostrophic vortices. Resolving both the fast and slow dynamics numerically requires a small time step and long simulation time, which is computationally costly. Phase averaging is a mathematical technique which filters out the fast oscillations of a system whilst capturing their effect on the slow features, allowing for larger time steps. 

We propose a modification to the standard numerical implementation of phase averaging. We combine phase averaging with a deferred correction method. An initial phase-averaged prediction is corrected by solving an error equation. Unlike classical deferred correction methods, the error equation is also phase averaged. Our method increases the accuracy of the phase-averaged solution, reduces the solution’s sensitivity to averaging window size and allows for parallelisation in time by stacking predictions and corrections. We demonstrate the method’s efficacy by simulating the swinging spring, a system which exhibits complicated multi-timescale behaviour.