Surprisingly tight Courant–Friedrichs–Lewy condition in explicit high-order Arakawa schemes
Mario Raeth, Klaus Hallatschek
Abstract
The Arakawa scheme, which exactly conserves energy and enstrophy in two-dimensional hydrodynamics, severely reduces the maximum allowable stable time step compared to the Courant–Friedrichs–Lewy condition when combined with a spectral or spectral-like high-order discretization. We calculate the time step restriction by finding the responsible high frequency eigenfunctions and suggest a remedy. The phenomenon has relevance for analogous methods conserving multiple quadratic invariants in gyrokinetic or magnetohydrodynamic simulations.
BibTeX
@article{Raeth_2024,
title={Surprisingly tight Courant–Friedrichs–Lewy condition in explicit high-order Arakawa schemes},
volume={36},
ISSN={1089-7666},
url={http://dx.doi.org/10.1063/5.0223009},
DOI={10.1063/5.0223009},
number={10},
journal={Physics of Fluids},
publisher={AIP Publishing},
author={Raeth, Mario and Hallatschek, Klaus},
year={2024},
month=oct }