Abstract
Abstract. We present a new evaluation framework for implicit and explicit (IMEX) Runge–Kutta time-stepping schemes. The new framework uses a linearized nonhydrostatic system of normal modes. We utilize the framework to investigate the stability of IMEX methods and their dispersion and dissipation of gravity, Rossby, and acoustic waves. We test the new framework on a variety of IMEX schemes and use it to develop and analyze a set of second-order low-storage IMEX Runge–Kutta methods with a high Courant–Friedrichs–Lewy (CFL) number. We show that the new framework is more selective than the 2-D acoustic system previously used in the literature. Schemes that are stable for the 2-D acoustic system are not stable for the system of normal modes.
Highlights
Differences in phase speeds between slow and fast waves in atmospheric models motivate development of time-stepping schemes with an implicit component to avoid expensive time-step restrictions imposed by fast waves on explicit methods
We developed a new framework to evaluate IMEX RK methods for atmospheric modeling
The framework uses a system of normal modes and is proven to be simple but more selective than the 2-D acoustics system used in the literature
Summary
Differences in phase speeds between slow and fast waves in atmospheric models motivate development of time-stepping schemes with an implicit component to avoid expensive time-step restrictions imposed by fast waves on explicit methods. Compared with the previously used 2-D acoustic system and the compressible Boussinesq equations (Durran and Blossey, 2012; Weller et al, 2013; Lock et al, 2014; Rokhzadi et al, 2018), this system provides more complexity and more closely resembles the equations used in modern dynamical cores. It contains a full set of modes: east- and west-propagating acoustic and gravity waves and westwardpropagating Rossby waves.
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