Marco Artiano presents our research at the ECCOMAS 8th Young Investigators Conference 2025 in Pescara, Italy

Marco Artiano will present some of our research at the ECCOMAS 8th Young Investigators Conference 2025 in Pescara, Italy.

Marco Artiano’s talk

Entropy-Stable High-Order Methods for the Compressible Euler Equations in Potential Temperature Formulation for Atmospheric Flows

Over the past decade, there has been increasing interest in the development and analysis of new dynamical cores for weather and climate simulations based on the Discontinuous Galerkin (DG) method [1, 2]. Various numerical methods and formulations of the Euler equations are employed to achieve accuracy, efficiency, and stability [3, 4, 5]. In this work, we develop novel structure-preserving numerical methods for the Euler equations, employing potential temperature as a prognostic variable. We construct three numerical fluxes designed to ensure the conservation of entropy and total energy, and we extend the formulation to incorporate a geopotential source term within the DG framework on general curvilinear meshes. Furthermore, we investigate the generalization of kinetic and potential energy-preserving (KPEP) property in the presence of a generic geopotential term, as first introduced by Souza et al. [4], and of total and potential energy conservation (TPEC). To this end, a flux-differencing approach is adopted for the discretization of the source term, and based on the recent work of Waruszewski et al. [3], we present well-balanced schemes for different constant background states for both formulations (total energy and potential temperature). Finally, we present a series of benchmark test cases to validate the theoretical properties of the proposed methods and compare the potential temperature formulation with the traditional Euler equations formulation across a range of classical atmospheric scenarios.