IMplicit-EXplicit Formulations for Discontinuous Galerkin Non-Hydrostatic Atmospheric Models

TL;DR

This paper introduces IMEX formulations for discontinuous Galerkin methods applied to non-hydrostatic atmospheric models, effectively handling stiffness and discretization challenges for improved mesoscale and global simulations.

Contribution

The paper develops two novel IMEX formulations for DG discretizations of atmospheric equations, including efficient Schur complement derivations and analysis of their convergence and efficiency.

Findings

IMEX formulations achieve theoretical convergence rates

Formulations demonstrate efficiency in 2D and 3D tests

Effective handling of stiffness in atmospheric modeling

Abstract

This work presents IMplicit-EXplicit (IMEX) formulations for discontinuous Galerkin (DG) discretizations of the compressible Euler equations governing non-hydrostatic atmospheric flows. In particular, we show two different IMEX formulations that not only treat the stiffness due to the governing dynamics but also the domain discretization. We present these formulations for two different equation sets typically employed in atmospheric modeling. For both equation sets, efficient Schur complements are derived and the challenges and remedies for deriving them are discussed. The performance of these IMEX formulations of different orders are investigated on both 2D (box) and 3D (sphere) test problems and shown to achieve their theoretical rates of convergence and their efficiency with respect to both mesoscale and global applications are presented.