HOMME-NH is the nonhydrostatic replacement for the current dynamical core in the Energy Exascale Earth System Model (E3SM). To this end, HOMME-NH solves a system of equations consisting of the Euler equations coupled with a modified ideal gas law as the equation of state. This system of equations includes acoustic waves that travel at speeds that are, in some areas, more than an order of magnitude greater than the convective wind speed. Furthermore, the computational grid has some cells with a vertical height that is two orders of magnitude smaller than the horizontal width. Thus, the corresponding CFL restriction is too restrictive for explicit time integration methods. Fully implicit methods do circumvent this timestep restriction, but the cost of solving the resulting nonlinear system at every timestep becomes too computationally expensive with high-resolution spatial grids. Thus, a class of Implicit-Explicit (IMEX), Additive Runge-Kutta (ARK) methods is considered. These methods treat vertical terms in the system implicitly while treating horizontal terms explicitly. Both existing and recently-developed ARK methods are implemented in HOMME-NH using the Suite of Nonlinear and Differential/Algebraic Equation Solvers (SUNDIALS) ARKode package. The methods are evaluated as to how well they preserve solution accuracy while minimizing computation wall-time for HOMME-NH. Additionally, the effects of hyperviscosity and vertical grid remapping on integrator performance are explored.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC