Nodal discontinuous Galerkin methods for non-ideal equations of state: pressure equilibrium preservation and entropy correction

[2608.14506] Nodal discontinuous Galerkin methods for non-ideal equations of state: pressure equilibrium preservation and entropy correction Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2608.14506 (math) [Submitted on 14 Aug 2026] Title: Nodal discontinuous Galerkin methods for non-ideal equations of state: pressure equilibrium preservation and entropy correction Authors: Jesse CHan , Hendrik Ranocha , Raymond Park , Joshua Lampert , Eric Ching , Ayaboe Edoh View a PDF of the paper titled Nodal discontinuous Galerkin methods for non-ideal equations of state: pressure equilibrium preservation and entropy correction, by Jesse CHan and 5 other authors View PDF HTML (experimental) Abstract: Structure-preserving discontinuous Galerkin (DG) methods typically improve the robustness of high order simulations of real fluids. In addition to conservation, key structures include the preservation of pressure equilibrium and satisfaction of at least one entropy inequality. In this work, we investigate conservative discretizations using exactly pressure equilibrium conserving (EPEC) and approximately pressure equilibrium conserving (APEC) flux differencing DG formulations, as well as entropy stable formulations through the use of minimally dissipative corrections for non-ideal equations of state (EOS). We introduce an analysis of EPEC schemes and a new procedure for designing such fluxes based on a generalization of Tadmor's shuffle condition. We also analyze APEC DG schemes and show that the incorporation of dissipative interface penalization terms does not significantly increase pressure equilibrium errors, especially at higher orders of approximation. Finally, we observe that when combined with APEC flux differencing formulations, entropy correction improves robustness for under-resolved solutions and long-time simulations. Subjects: Numerical Analysis (math.NA) ; Computational Engineering, Finance, and Science (cs.CE) Cite as: arXiv:2608.14506 [math.NA] (or arXiv:2608.14506v1 [math.NA] for this version) https://doi.org/10.48550/arXiv.2608.14506 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jesse Chan [ view email ] [v1] Fri, 14 Aug 2026 17:22:04 UTC (12,070 KB) Full-text links: Access Paper: View a PDF of the paper titled Nodal discontinuous Galerkin methods for non-ideal equations of state: pressure equilibrium preservation and entropy correction, by Jesse CHan and 5 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2026-08 Change to browse by: cs cs.CE cs.NA math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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

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