{"paper":{"title":"Higher Accuracy Modular Data Assimilation for the Navier-Stokes Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Troy Yang","submitted_at":"2026-06-17T18:46:49Z","abstract_excerpt":"This paper develops an accurate and effective combination of second order backward differentiation time discretization (BDF2) with modular, 2-step nudging-based data assimilation \\begin{align} \\text{Forecast step: } \\quad &\\frac{3\\widetilde{v}^{n+2}-4v^{n+1}+v^n}{2\\Delta t}+\\widetilde{v}^{n+2} \\cdot \\nabla \\widetilde{v}^{n+2} - \\nu \\Delta \\widetilde{v}^{n+2} + \\nabla q^{n+2}=f(x) \\notag \\\\ &\\nabla \\cdot \\widetilde{v}^{n+2} = 0 \\notag \\\\ \\text{Analysis step: } \\quad &\\frac{3v^{n+2}-3\\widetilde{v}^{n+2}}{2\\Delta t}-\\chi I_H(u(t^{n+2})-v^{n+2})=0. \\notag \\end{align} If $I_H=I_H^2$, the analysis s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19508","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.19508/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}