{"paper":{"title":"Entropy stable finite difference schemes for One-Fluid Two-Temperature Euler Non-equilibrium Hydrodynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Reformulating non-conservative terms enables entropy-stable finite difference schemes for the one-fluid two-temperature Euler equations.","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Chetan Singh, Harish Kumar","submitted_at":"2026-05-15T04:58:18Z","abstract_excerpt":"In this work, we consider the One-Fluid Two-Temperature Euler (OFTT-Euler) equations used for modeling non-equilibrium hydrodynamics. The model comprises a system of nonlinear hyperbolic partial differential equations with non-conservative products. The model decomposed the total pressure into two scalar components: one for electrons and one for ions. Our aim in this work is to design entropy-stable finite difference numerical schemes for the model. This is achieved by reformulating the equations such that the reformulated non-conservative part does not contribute to the entropy. Then, we desi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We design entropy-stable finite difference numerical schemes for the OFTT-Euler model by reformulating the equations such that the reformulated non-conservative part does not contribute to the entropy. Then we design higher-order entropy-conservative numerical schemes by using Tadmor's relation for the conservative part and higher-order central differences for the non-conservative parts.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The reformulation of the non-conservative products ensures they do not contribute to the entropy production in the system, allowing Tadmor's relation and central differences to produce entropy-conservative schemes before dissipation is added (abstract, paragraph on scheme design).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Entropy-stable finite difference schemes are constructed for the OFTT-Euler model by reformulating non-conservative products to not affect entropy and adding dissipation via entropy-scaled eigenvectors.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Reformulating non-conservative terms enables entropy-stable finite difference schemes for the one-fluid two-temperature Euler equations.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"04bf0bd64e2d544554d463447f520c16fe5642a8502e2e4ac8bffc7844d8b720"},"source":{"id":"2605.15616","kind":"arxiv","version":1},"verdict":{"id":"422ead98-5703-43e3-9076-e5974212e812","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:34:48.345711Z","strongest_claim":"We design entropy-stable finite difference numerical schemes for the OFTT-Euler model by reformulating the equations such that the reformulated non-conservative part does not contribute to the entropy. Then we design higher-order entropy-conservative numerical schemes by using Tadmor's relation for the conservative part and higher-order central differences for the non-conservative parts.","one_line_summary":"Entropy-stable finite difference schemes are constructed for the OFTT-Euler model by reformulating non-conservative products to not affect entropy and adding dissipation via entropy-scaled eigenvectors.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The reformulation of the non-conservative products ensures they do not contribute to the entropy production in the system, allowing Tadmor's relation and central differences to produce entropy-conservative schemes before dissipation is added (abstract, paragraph on scheme design).","pith_extraction_headline":"Reformulating non-conservative terms enables entropy-stable finite difference schemes for the one-fluid two-temperature Euler equations."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15616/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:01:19.703556Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T22:42:11.572483Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T19:34:34.616861Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:41:56.041378Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"50aff17daa576e8bef3d4ccbe71891cf1fce2f1b01be94d325887a28f5577002"},"references":{"count":57,"sample":[{"doi":"","year":2007,"title":"Astrophysical radiation dynamics: The prospects for scaling.Astrophysics and Space Science, 307(1):207–211, 2007","work_id":"1a0af7df-1abe-4329-9db0-36eed289d285","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2010,"title":"Smoothed particle hydrodynamics in astrophysics.Annual Review of Astronomy and Astrophysics, 48:391–430, 2010","work_id":"bdf20ff8-32ea-45b9-96d6-b53859eeb192","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2015,"title":"Grid-based hydrodynamics in astrophysical fluid flows.Annual Review of Astronomy and Astrophysics, 53(1):325–364, 2015","work_id":"1610d76b-2dbd-4330-9a38-ce4f77da34ed","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2012,"title":"Springer Science & Business Media, 2012","work_id":"48b6e0d5-b2c9-4a97-a0f8-dc0779bae25a","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2004,"title":"Stefano Atzeni and Jürgen Meyer-ter Vehn.The Physics of Inertial Fusion: BeamPlasma Interaction, Hydrodynamics, Hot Dense Matter. 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