A Comparison of IMEX- Spectral Deferred Correction, Multistep and Runge-Kutta Methods for the rotating Shallow Water Equations (Joscha Fregin, TU Hamburg)

03.10.2023 14:00

Atmospheric motion covers a broad range of time- and spatial scales. Low and high pressure systems can influence us for days or even weeks and they extend up to hundreds of kilometers. In contrast, sound waves pass by in seconds with wavelengths of centimeters to meters. Implicit-explicit (IMEX) time stepping methods can help to avoid drastic limitations on the time step induced by the variety of scales without requiring computationally expensive fully nonlinear implicit solves.
In our talk, we compare IMEX- Spectral Deferred Correction (SDC), multistep and Runge-Kutta time integrators for the Galewsky test case using the Python spectral method framework Dedalus. We demonstrate that SDC methods have superior stability properties and can provide shorter time to solution for comparable errors. In addition, we outline strategies that could further reduce simulation times by using the SDC residual to minimise the computational effort and by parallelising SDC "across the method". Finally, we discuss the interpretation of SDC as a Runge-Kutta method.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Séminaire d'analyse numérique

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