{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:M7BLLPJLJJXYKOJMT27YCDVO5B","short_pith_number":"pith:M7BLLPJL","schema_version":"1.0","canonical_sha256":"67c2b5bd2b4a6f85392c9ebf810eaee87b13cf284ba2042d4dd2fc841ad4e448","source":{"kind":"arxiv","id":"1811.03041","version":2},"attestation_state":"computed","paper":{"title":"A Numerical method for coupling the BGK model and Euler equation through the linearized Knudsen layer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hongxu Chen, Jianfeng Lu, Qin Li","submitted_at":"2018-11-07T17:59:41Z","abstract_excerpt":"The Bhatnagar-Gross-Krook (BGK) model, a simplification of the Boltzmann equation, in the absence of boundary effect, converges to the Euler equations when the Knudsen number is small. In practice, however, Knudsen layers emerge at the physical boundary, or at the interfaces between the two regimes. We model the Knudsen layer using a half-space kinetic equation, and apply a half-space numerical solver [ESAIM: M2AN 51 (2017) 1583-1615] [Math. Comp. 86 (2017), 1269-1301] to quantify the transition between the kinetic to the fluid regime. A full domain numerical solver is developed with a domain-"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1811.03041","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-07T17:59:41Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"2f58fc97ffaa5d513a04a17b3cc3d749508ea47dce7fbbdd0ee95bc4c28d6fb4","abstract_canon_sha256":"5c97ca0f86bf83d450f7ad512bfec65e77600e373a0c7dae44f76738f1e22c0d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T20:13:39.925407Z","signature_b64":"bXYaQC95w0jndo5q8TEF06OWMqi8Ii49gIvGpQDEWSmDn3xCxkYQ3LmzhMSE372ytNEJIuzn0f8RjwX2Ow0FAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67c2b5bd2b4a6f85392c9ebf810eaee87b13cf284ba2042d4dd2fc841ad4e448","last_reissued_at":"2026-06-04T20:13:39.924880Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T20:13:39.924880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Numerical method for coupling the BGK model and Euler equation through the linearized Knudsen layer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hongxu Chen, Jianfeng Lu, Qin Li","submitted_at":"2018-11-07T17:59:41Z","abstract_excerpt":"The Bhatnagar-Gross-Krook (BGK) model, a simplification of the Boltzmann equation, in the absence of boundary effect, converges to the Euler equations when the Knudsen number is small. In practice, however, Knudsen layers emerge at the physical boundary, or at the interfaces between the two regimes. We model the Knudsen layer using a half-space kinetic equation, and apply a half-space numerical solver [ESAIM: M2AN 51 (2017) 1583-1615] [Math. Comp. 86 (2017), 1269-1301] to quantify the transition between the kinetic to the fluid regime. A full domain numerical solver is developed with a domain-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03041","kind":"arxiv","version":2},"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/1811.03041/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1811.03041","created_at":"2026-06-04T20:13:39.924936+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.03041v2","created_at":"2026-06-04T20:13:39.924936+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03041","created_at":"2026-06-04T20:13:39.924936+00:00"},{"alias_kind":"pith_short_12","alias_value":"M7BLLPJLJJXY","created_at":"2026-06-04T20:13:39.924936+00:00"},{"alias_kind":"pith_short_16","alias_value":"M7BLLPJLJJXYKOJM","created_at":"2026-06-04T20:13:39.924936+00:00"},{"alias_kind":"pith_short_8","alias_value":"M7BLLPJL","created_at":"2026-06-04T20:13:39.924936+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/M7BLLPJLJJXYKOJMT27YCDVO5B","json":"https://pith.science/pith/M7BLLPJLJJXYKOJMT27YCDVO5B.json","graph_json":"https://pith.science/api/pith-number/M7BLLPJLJJXYKOJMT27YCDVO5B/graph.json","events_json":"https://pith.science/api/pith-number/M7BLLPJLJJXYKOJMT27YCDVO5B/events.json","paper":"https://pith.science/paper/M7BLLPJL"},"agent_actions":{"view_html":"https://pith.science/pith/M7BLLPJLJJXYKOJMT27YCDVO5B","download_json":"https://pith.science/pith/M7BLLPJLJJXYKOJMT27YCDVO5B.json","view_paper":"https://pith.science/paper/M7BLLPJL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.03041&json=true","fetch_graph":"https://pith.science/api/pith-number/M7BLLPJLJJXYKOJMT27YCDVO5B/graph.json","fetch_events":"https://pith.science/api/pith-number/M7BLLPJLJJXYKOJMT27YCDVO5B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M7BLLPJLJJXYKOJMT27YCDVO5B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M7BLLPJLJJXYKOJMT27YCDVO5B/action/storage_attestation","attest_author":"https://pith.science/pith/M7BLLPJLJJXYKOJMT27YCDVO5B/action/author_attestation","sign_citation":"https://pith.science/pith/M7BLLPJLJJXYKOJMT27YCDVO5B/action/citation_signature","submit_replication":"https://pith.science/pith/M7BLLPJLJJXYKOJMT27YCDVO5B/action/replication_record"}},"created_at":"2026-06-04T20:13:39.924936+00:00","updated_at":"2026-06-04T20:13:39.924936+00:00"}