{"paper":{"title":"High-order, long-time stable and parallel decoupled GBDF$k$ SAV ensemble schemes for the Navier--Stokes--Darcy flow with random hydraulic conductivity tensors","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Changxin Qiu, Fukeng Huang, Wei-Wei Han","submitted_at":"2026-05-22T07:03:19Z","abstract_excerpt":"We develop and analyze high-order ensemble schemes for the unsteady Navier--Stokes--Darcy system with uncertain initial conditions, forcing terms, hydraulic conductivity tensors, and Lions-Beavers-Joseph-Saffman interface conditions. The proposed schemes which are called GSAV-GBDF$k$-Ensemble schemes integrate a partitioned decoupling strategy, the generalized scalar auxiliary variable (GSAV) approach, and generalized BDF$k$ discretizations. This framework achieves high-order temporal accuracy and long-time stability, permits explicit treatment of the nonlinear term, and facilitates an efficie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23290","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/2605.23290/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"}