{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/second-order-invariant-domain-preserving","title":"Second-order invariant domain preserving approximation of the compressible Navier--Stokes equations","arxiv_id":"2009.06022","date":"2020-09-13","proceeding":null,"authors":["Jean-Luc Guermond","Matthias Maier","Bojan Popov","Ignacio Tomas"],"abstract":"We present a fully discrete approximation technique for the compressible Navier-Stokes equations that is second-order accurate in time and space, semi-implicit, and guaranteed to be invariant domain preserving. The restriction on the time step is the standard hyperbolic CFL condition, ie $\\tau \\lesssim \\mathcal{O}(h)/V$ where $V$ is some reference velocity scale and $h$ the typical meshsize.","url_abs":"http://arxiv.org/abs/2009.06022v1","url_pdf":"http://arxiv.org/pdf/2009.06022v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"second-order-invariant-domain-preserving","repo_url":"https://github.com/conservation-laws/ryujin","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}