A Framework to Evaluate IMEX Schemes for Atmospheric Models

Abstract:

We use the theory of normal modes to develop a new framework to evaluate implicit-explicit (IMEX) Runge-Kutta schemes in atmospheric applications. We adopt a linearized nonhydrostatic system of normal modes from works of Thuburn et al.. The system supports gravity, Rossby, and acoustic waves and is based on a nontrivial linearized state. This framework is more selective than frameworks based on the linearized 2D acoustic equations. There are IMEX methods that are stable for the 2D acoustic equations but are not stable for the system of normal modes.

Using a Lorenz staggered mass coodinate vertical discretization, we construct a discretized evolution operator. The operator provides information about the stability of an IMEX method as well as dispersion and dissipation properties of the method for each group of waves. We use stability, dispersion, and dissipation to investigate a family of low-storage, high CFL IMEX schemes.