{"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/accurate-iteration-free-mixed-stabilised","title":"Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier-Stokes: Applications to fluid-structure interaction","arxiv_id":"2001.04925","date":"2020-01-14","proceeding":null,"authors":["Chennakesava Kadapa","Wulf G Dettmer","Djordje Peric"],"abstract":"Stabilised mixed velocity-pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier-Stokes. In these formulations, the Newton-Raphson scheme is employed to solve the nonlinearity in the convection term. One fundamental issue with this approach is the computational cost incurred in the Newton-Raphson iterations at every load/time step. In this paper, we present an iteration-free mixed finite element formulation for incompressible Navier-Stokes that preserves second-order temporal accuracy of the generalised-alpha and related schemes for both velocity and pressure fields. First, we demonstrate the second-order temporal accuracy using numerical convergence studies for an example with a manufactured solution. Later, we assess the accuracy and the computational benefits of the proposed scheme by studying the benchmark example of flow past a fixed circular cylinder. Towards showcasing the applicability of the proposed technique in a wider context, the inf-sup stable P2-P1 pair for the formulation without stabilisation is also considered. Finally, the resulting benefits of using the proposed scheme for fluid-structure interaction problems is illustrated using two benchmark examples in fluid-flexible structure interaction.","url_abs":"https://arxiv.org/abs/2001.04925v2","url_pdf":"https://arxiv.org/pdf/2001.04925v2.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":"accurate-iteration-free-mixed-stabilised","repo_url":"https://github.com/chennachaos/cfdsfemmpi","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"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}