{"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/lagrangian-transport-through-surfaces-in-1","title":"Lagrangian Transport Through Surfaces in Compressible Flows","arxiv_id":"1707.00518","date":"2017-07-03","proceeding":null,"authors":["Florian Hofherr","Daniel Karrasch"],"abstract":"A material-based, i.e., Lagrangian, methodology for exact integration of flux by volume-preserving flows through a surface has been developed recently in [Karrasch, SIAM J. Appl. Math., 76 (2016), pp. 1178-1190]. In the present paper, we first generalize this framework to general compressible flows, thereby solving the donating region problem in full generality. Second, we demonstrate the efficacy of this approach on a slightly idealized version of a classic two-dimensional mixing problem: transport in a cross-channel micromixer, as considered recently in [Balasuriya, SIAM J. Appl. Dyn. Syst., 16 (2017), pp. 1015-1044].","url_abs":"http://arxiv.org/abs/1707.00518v2","url_pdf":"http://arxiv.org/pdf/1707.00518v2.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":"lagrangian-transport-through-surfaces-in-1","repo_url":"https://github.com/dkarrasch/FluxDoRe2D","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}