In this work a non-conservative balance law formulation is considered that encompasses the
rotating, compressible Euler equations for dry atmospheric flows. We develop a semi …

We systematically validate the static local mesh refinement capabilities of a recently
proposed implicit–explicit discontinuous Galerkin scheme implemented in the framework of …

We conduct a thorough study of different forms of horizontally explicit and vertically implicit
(HEVI) time-integration strategies for the compressible Euler equations on spherical …

In the numerical solution of partial differential equations using a method-of-lines approach,
the availability of high order spatial discretization schemes motivates the development of …

Dynamical cores used to study the circulation of the atmosphere employ various numerical
methods ranging from finite‐volume, spectral element, global spectral, and hybrid methods …

Abstract We propose IMEX HDG-DG schemes for planar and spherical shallow water
systems. Of interest is subcritical flow, where the speed of the gravity wave is faster than that …

A solver for the Euler equations with optional diffusion based on the Discontinuous Galerkin
(DG) method is presented. To be usable for simulation problems in the atmosphere from the …

In numerical time-integration with implicit-explicit (IMEX) methods, a within-step adaptable
decomposition called residual balanced (RB) decomposition is introduced. This new …

Focusing on future global atmospheric simulations with grid spacing of O (10–100 m), we
developed a global nonhydrostatic atmospheric dynamical core with high-order accuracy by …

A 3D compressible nonhydrostatic dynamic core based on a three-point multi-moment
constrained finite-volume (MCV) method is developed by extending the previous 2D …