{"paper":{"title":"Investigation of Shock-Capturing with Bound-Preserving Limiters for the Nonlinearly Stable Flux Reconstruction Method","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","physics.flu-dyn"],"primary_cat":"math.NA","authors_text":"Sai Shruthi Srinivasan, Siva Nadarajah","submitted_at":"2025-07-12T04:05:36Z","abstract_excerpt":"Nonlinearly stable flux reconstruction (NSFR) combines the key properties of provable nonlinear stability with the increased time step from energy-stable flux reconstruction. The NSFR scheme has been successfully applied to unsteady compressible flows. Through the use of a bound-preserving limiter, positivity of thermodynamic quantities is preserved, and this enables the extension of NSFR to hyperbolic conservation laws. We extend the limiter of Zhang and Shu [1] to ensure robustness for the proposed scheme. The limiter is modified to consider the minimum density and pressure at the solution n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.09131","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/2507.09131/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"}