A discontinuous Galerkin weather dycore for triangular and quadrangular grids

Spectral methods have a well-established history in numerical weather prediction. However, stable formulations for high-order discontinuous Galerkin (DG) methods in both horizontal and vertical directions have only recently been developed using split-form DG (cf. Waruszewski et al. and Souza et al.).

This presentation provides an overview of the implementation of split-form DG methods for the compressible Euler equations, utilizing various formulations on both triangular and quadrangular spherical grids. Key focus areas include split-form versions on triangular grids and the linear algebra associated with HEVI-like (Horizontally Explicit, Vertically Implicit) temporal integration schemes. To manage vertically propagating sound waves implicitly, temporal integration is performed using W-Rosenbrock methods with an approximate Jacobian in the radial direction.

The framework is implemented in the Julia package CGDycore.jl, leveraging KernelAbstractions.jl and MPI for parallel execution across diverse architectures. We present numerical comparisons using the Held-Suarez test case, alongside comprehensive weak and strong scaling results for different computing environments.