{"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/an-arbitrary-order-scheme-on-generic-meshes","title":"An arbitrary order scheme on generic meshes for miscible displacements in porous media","arxiv_id":"1707.04038","date":"2017-07-13","proceeding":null,"authors":["Daniel Anderson","Jerome Droniou"],"abstract":"We design, analyse and implement an arbitrary order scheme applicable to generic meshes for a coupled elliptic-parabolic PDE system describing miscible displacement in porous media. The discretisation is based on several adaptations of the Hybrid-High-Order (HHO) method due to Di Pietro et al. [Computational Methods in Applied Mathematics, 14(4), (2014)]. The equation governing the pressure is discretised using an adaptation of the HHO method for variable diffusion, while the discrete concentration equation is based on the HHO method for advection-diffusion-reaction problems combined with numerically stable flux reconstructions for the advective velocity that we have derived using the results of Cockburn et al. [ESAIM: Mathematical Modelling and Numerical Analysis, 50(3), (2016)]. We perform some rigorous analysis of the method to demonstrate its $L^2$ stability under the irregular data often presented by reservoir engineering problems and present several numerical tests to demonstrate the quality of the results that are produced by the proposed scheme.","url_abs":"http://arxiv.org/abs/1707.04038v4","url_pdf":"http://arxiv.org/pdf/1707.04038v4.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":"an-arbitrary-order-scheme-on-generic-meshes","repo_url":"https://github.com/DanielLiamAnderson/hho-peaceman","is_official":1,"mentioned_in_paper":1,"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}