  The nonhydrostatic High Order Method Modeling Environment (HOMME-NH)
atmospheric dynamical core supports acoustic waves that propagate significantly
faster than the advective wind speed, thus greatly limiting the timestep size
that can be used with standard explicit time-integration methods. Resolving
acoustic waves is unnecessary for accurate climate and weather prediction. This
numerical stiffness is addressed herein by considering implicit-explicit
additive Runge-Kutta (ARK IMEX) methods that can treat the acoustic waves in a
stable manner without requiring implicit treatment of non-stiff modes. Various
ARK IMEX methods are evaluated for their efficiency in producing accurate
solutions, ability to take large timestep sizes, and sensitivity to grid cell
length ratio. Both the Gravity Wave test and Baroclinic Instability test from
the 2012 Dynamical Core Model Intercomparison Project (DCMIP) are used to
recommend 5 of the 27 ARK IMEX methods for use in HOMME-NH.
