Data driven non-equilibrium moist phase exchanges for atmospheric convection within a discontinuous Galerkin model of the compressible Euler equations

[2607.13360] Data driven non-equilibrium moist phase exchanges for atmospheric convection within a discontinuous Galerkin model of the compressible Euler equations Skip to main content Search Submit Donate Log in Mathematics > Numerical Analysis arXiv:2607.13360 (math) [Submitted on 15 Jul 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Data driven non-equilibrium moist phase exchanges for atmospheric convection within a discontinuous Galerkin model of the compressible Euler equations Authors: David Lee , Kieran Ricardo , Junwei Lyu View PDF HTML (experimental) Abstract: A discrete formulation of the multiphase moist compressible Euler equations is presented for which the energy and tracer variance conserving dynamics is coupled to the non-equilibrium moist phase exchanges in a thermodynamically consistent manner. A neural network is then trained to learn the mass exchanges between vapour, liquid and ice phases in atmospheric convection. The network is trained on convection resolving output from a regional configuration of the LFRic model with a multi-moment microphysics parameterisation (CASIM). The loss function for learning these phase exchanges is formulated under the assumptions of thermal and mechanical equilibrium (same temperature and pressure for all phases), and chemical dis-equilibrium (different Gibbs free energies for all phases). The network outputs determine the exchanges of vapour, liquid and ice so as to conserve mass, and the resulting change in entropy is determined from the network outputs so as to conserve energy. The neural network is implemented in a thermodynamically consistent manner within the discontinuous Galerkin moist compressible Euler model in order to simulate the formation of three-phase clouds for convection at sub-km resolution. The results are compared to those from a physics based representation of three-phase moist processes at thermodynamic equilibrium, as well as to an idealised configuration of LFRic model. Subjects: Numerical Analysis (math.NA) ; Fluid Dynamics (physics.flu-dyn) Cite as: arXiv:2607.13360 [math.NA] (or arXiv:2607.13360v2 [math.NA] for this version) https://doi.org/10.48550/arXiv.2607.13360 Focus to learn more arXiv-issued DOI via DataCite Submission history From: David Lee [ view email ] [v1] Wed, 15 Jul 2026 00:52:43 UTC (732 KB) [v2] Fri, 28 Aug 2026 04:59:03 UTC (694 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2026-07 Change to browse by: cs cs.NA math physics physics.flu-dyn References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Data driven non-equilibrium moist phase exchanges for atmospheric convection within a discontinuous Galerkin model of the compressible Euler equations#682759
• Implicit large eddy simulation of nearly incompressible flows with a discontinuous Galerkin–Boltzmann formulation#309432
• Bound-preserving second-order implicit pressure explicit concentration discontinuous Galerkin methods for compressible miscible displacements#628733
• Global High Resolution Climate Reconstruction#1082517
• Data for lossy compression by dimension reduction for 2-d meteorological fields#393180