{"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/example-setups-of-navier-stokes-equations","title":"Example Setups of Navier-Stokes Equations with Control and Observation: Spatial Discretization and Representation via Linear-quadratic Matrix Coefficients","arxiv_id":"1707.08711","date":"2017-07-27","proceeding":null,"authors":["Maximilian Behr","Peter Benner","Jan Heiland"],"abstract":"We provide spatial discretizations of nonlinear incompressible Navier-Stokes equations with inputs and outputs in the form of matrices ready to use in any numerical linear algebra package. We discuss the assembling of the system operators and the realization of boundary conditions and inputs and outputs. We describe the two benchmark problems - the driven cavity and the cylinder wake - and provide the corresponding data. The use of the data is illustrated by numerous example setups. The test cases are provided as plain PYTHON or OCTAVE/MATLAB script files for immediate replication.","url_abs":"http://arxiv.org/abs/1707.08711v1","url_pdf":"http://arxiv.org/pdf/1707.08711v1.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":"example-setups-of-navier-stokes-equations","repo_url":"https://github.com/highlando/distr_control_fenics","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}