JuliaCon 2026

We have recently released TrixiAtmo.jl, a specialized extension of Trixi.jl that brings state-of-the-art numerical methods, drastically increased resolution, and high physical fidelity to Earth system models.

Current global climate models typically operate at horizontal resolutions of tens of kilometers. Increasing this resolution towards the kilometer scale would enable a substantially improved representation of key physical and chemical processes, which are currently treated by parametrizations and constitute a major source of uncertainty.

We address this challenge with two tightly coupled methodological advances: Discontinuous Galerkin (DG) methods and dynamic Adaptive Mesh Refinement (AMR). DG, as a high order method, offers high accuracy while maintaining a low memory footprint, thereby reaching unmatched efficiency. Historically, high-order methods have been susceptible to numerical instabilities and have struggled with unresolved physical processes like turbulence. However, recent advancements, particularly the development of entropy-conserving schemes, have significantly improved this situation. By incorporating a physics-based concept of stability, spurious disturbances in the numerical solution are effectively suppressed. Simultaneously, AMR allows us to concentrate computational effort in regions of interest, such as sharp gradients in prognostic quantities or chemically active zones. Consequently, overall computational and storage costs are drastically reduced, and simulations governed by local and regional processes achieve substantial gains in efficiency. Despite their undisputed potential, both DG and AMR, have seen limited adoption in global atmospheric and chemistry–climate simulations to date.

With TrixiAtmo.jl, we tailor Trixi.jl's numerical schemes to the requirements of atmospheric dynamical cores. So far, we have implemented the compressible Euler equations, including moist air and rain, on hex-based cubed sphere grids, and the shallow water equations on prism-based icosahedral grids, where the latter closely resembles the ICON model setup. We have added well-balanced, and entropy-conserving and dissipating split-form schemes. For idealized atmospheric flows, such as the barotropic and baroclinic instability, we observe stable simulations even on coarse meshes.

We now aim to extend TrixiAtmo.jl towards more realistic applications to put our methods to a compelling test. Among other tasks, this requires flexible import and remapping methods of reanalysis-based input data and easy to use analysis and visualization work flows for the resulting data. Julia already boasts an exceptionally rich geoscience community and software stack, which we plan to leverage. Several projects such as CliMA, SpeedyWeather.jl, and Breeze.jl, to name but a few, have already demonstrated Julia's viability for high-performance computing in the Earth and climate sciences.