# Evaluation of Implicit-Explicit Additive Runge-Kutta Integrators for the HOMME-NH Dynamical Core

## TL;DR

This paper evaluates implicit-explicit additive Runge-Kutta methods to efficiently handle acoustic wave stiffness in the HOMME-NH atmospheric model, enabling larger timesteps without sacrificing accuracy.

## Contribution

It identifies and recommends five ARK IMEX methods suitable for HOMME-NH, improving computational efficiency in atmospheric simulations.

## Key findings

- Five ARK IMEX methods are recommended for HOMME-NH.
- The methods effectively handle acoustic wave stiffness.
- Large timestep sizes are achievable without loss of accuracy.

## Abstract

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.

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Source: https://tomesphere.com/paper/1904.10115