{"paper":{"title":"Defect Subspaces and Localized Instabilities in Cut-Cell Finite-Volume Operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Justo E. Karell","submitted_at":"2026-07-30T20:09:42Z","abstract_excerpt":"Cut-cell instability in explicit finite-volume methods arises when an embedded boundary clips a background cell to a small volume fraction~$\\alpha$, forcing the local CFL number to $\\lambda_\\alpha = \\lambda/\\alpha \\gg 1$. This paper characterizes the spectral structure of this instability and derives a minimum SRD blending parameter per cut cell computable from local mesh geometry. The update operator has exactly $m$ unstable eigenvalues, one per cut cell, with dominant eigenvalue $\\mu_u = 1 - \\lambda/\\alpha + O(1)$ and eigenvector $v_u = e_c + O(\\alpha)$. The growth rate is governed by the de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28808","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/2607.28808/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"}