{"as_of":"2026-08-22T02:05:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a1ec9f23ea55a8058667fb52e87afbacc15a782505efbee3c5480d44167cc1e6","coverage":[{"denominator":72,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":72,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T13:37:21.523790Z","state":"measured"},{"denominator":72,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":72,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2509.26284/citation-record","integrity":"/paper/2509.26284/integrity","json":"/paper/2509.26284/citation-record.json","paper":"/paper/2509.26284"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:14.758676Z","title":"A high-order nonconservative ap- proach for hyperbolic equations in fluid dynamics","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:14.758676Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:9c0b7e8506e5bf36ecae09659f2679834e343066700ae23ed38acb2c88148870","observation_id":"97f6ceb6-9845-4451-bd92-0df7ccb7db12","resolution":{"observed_at":"2026-08-04T13:37:14.758676Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:14.821198Z","title":"A comment on the computation of non-conservative products","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:14.821198Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:8ea4868ea3a9e15f18c6cd286203a7e78381ed70e8db49d905a91b24c08a3502","observation_id":"862b6deb-1f9c-4b03-93dc-0f7cf3748bc6","resolution":{"observed_at":"2026-08-04T13:37:14.821198Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:14.857204Z","title":"High order methods for CFD","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:14.857204Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:818ae9fc1ef1e323fd6eb63109f538114ea67a77be1a6cd6785f2997f813dc5d","observation_id":"a1fd3940-44ab-4e65-8bc2-b8f697a265a1","resolution":{"observed_at":"2026-08-04T13:37:14.857204Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:14.954564Z","title":"A five-equation model for the simulation of interfaces between compressible fluids","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:14.954564Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:45bc7624c2ec346b7942206262be11d0512f0e6694c98eac8db0340d7f7dd6c0","observation_id":"d24b2811-9147-470c-80ec-cb90eade6ea1","resolution":{"observed_at":"2026-08-04T13:37:14.954564Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:15.090861Z","title":"An efficient covariant frame for the spherical shallow water equations: well balanced DG approximation and application to tsunami and storm surge","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:15.090861Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:82df524f8a5df8dae2976171505d33d8c59b859de583aff1d13ab201f74848fc","observation_id":"e3ba172f-9f62-47cf-b76d-fa2b22f3f50b","resolution":{"observed_at":"2026-08-04T13:37:15.090861Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.18743","last_updated":"2026-05-20T00:28:07Z","snapshot_observed_at":"2026-08-03T23:10:30.363603Z","submitted_at":"2025-05-24T15:21:44Z","title":"High-order adaptive discontinuous finite elements for the shallow water equations with sub-grid irregular bathymetry","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.18743","snapshot_observed_at":"2026-08-04T13:37:15.202783Z","title":"Arpaia et al","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:15.202783Z"},"links":{"cited_paper":"/paper/2505.18743","citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:25f2b8f8a72a696af367dc80b061f9b76e2f73781cc08906f9014ba7760b9152","observation_id":"f6fcadc9-b01f-45a6-84be-f88c1e66fe42","resolution":{"observed_at":"2026-08-04T13:37:15.202783Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:15.325147Z","title":"A two-phase mixture theory for the deflagration- to-detonation transition (DDT) in reactive granular materials","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:15.325147Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:0b5a85aee73a56e4df87fe97828980ba84277552320606cc5e9ff414c06717fc","observation_id":"aec90056-ee45-4f29-8316-20484ef01de6","resolution":{"observed_at":"2026-08-04T13:37:15.325147Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:15.372712Z","title":"A High-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:15.372712Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:6fad3afa6a5013fc6bd6a4028d4a9b96d463326c9562154944d2a28c843d3cb7","observation_id":"ebe3fab0-76e3-4015-bda6-85f8c5d5a943","resolution":{"observed_at":"2026-08-04T13:37:15.372712Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:15.458141Z","title":"Multidimensional fully adaptive lattice Boltzmann methods with error control based on multiresolution analysis","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:15.458141Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:65433f66282999f8a9f49724501bc01cf8f355e7c21077dee3bd8f99b6893890","observation_id":"432c3316-d7d0-4838-9116-579a57f80937","resolution":{"observed_at":"2026-08-04T13:37:15.458141Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:15.542616Z","title":"Vanishing viscosity solutions of nonlinear hyper- bolic systems","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:15.542616Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:fd2ca3c91a735ed90b1a55466766a5bffb0b7924c7efd45d070d98525d03d216","observation_id":"f0a11d74-2789-41d3-bbb1-98352f733df7","resolution":{"observed_at":"2026-08-04T13:37:15.542616Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:15.640283Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:15.640283Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:b882c45ccf595074786511abb3432d87a50a93fca5de5b0e9af5f279a1abbaac","observation_id":"a34cb46a-828b-4a4d-a089-5c732efdb6be","resolution":{"observed_at":"2026-08-04T13:37:15.640283Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:15.725705Z","title":"An entropy satisfying scheme for two-layer shal- low water equations with uncoupled treatment","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:15.725705Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:6b0d590fd3a165143a4372429f5db47cd8c97548a09aed8546d89487232b351e","observation_id":"81aea716-9524-4f7a-b568-6165935c6bbb","resolution":{"observed_at":"2026-08-04T13:37:15.725705Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:15.790072Z","title":"On thermodynamically compatible finite volume methods and path-conservative ADER discontinuous Galerkin schemes for turbulent shallow water flows","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:15.790072Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:85e77de60d0924d8039d461a0b4858abb53588880c2804782eb472adc43d24a5","observation_id":"c2a924fc-2a86-4534-9770-00154d697755","resolution":{"observed_at":"2026-08-04T13:37:15.790072Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:15.871446Z","title":"High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:15.871446Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:f0d7a2e600f7639376e2c304c3c467609cecc833ab5a8d02c914cf8a475c24bc","observation_id":"1ed281b9-ddea-477a-9b8a-2df98f32373e","resolution":{"observed_at":"2026-08-04T13:37:15.871446Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:15.961081Z","title":"Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:15.961081Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:4ea3d110953c9a3fa836628d994b04ed24cfcb7600ef5959d983fac3c187c522","observation_id":"5a283822-f4ad-4c3b-8fe6-3f5cb30e0652","resolution":{"observed_at":"2026-08-04T13:37:15.961081Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:16.046650Z","title":"High order extensions of Roe schemes for two-dimensional nonconservative hyperbolic systems","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:16.046650Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:3dd9a43351d608f89436ea8aea381bc3cf79023d8dbf9e39633994ce61b3db48","observation_id":"8959f6ba-5d19-4d07-a49f-efa3a4327e86","resolution":{"observed_at":"2026-08-04T13:37:16.046650Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:16.107152Z","title":"A new comment on the computation of non-conservative products using Roe-type path conservative schemes","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:16.107152Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:b9e9db3de53f6c1b23487b9f52a44d0b1233827748334bba4435914a0dae9cf4","observation_id":"6fcbd032-c904-47ca-aaf3-7be06b02ad19","resolution":{"observed_at":"2026-08-04T13:37:16.107152Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:16.204860Z","title":"A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:16.204860Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:52bcb4809f682d7d431cc226873baa332e213c4629460bfa031993c5c01e03a4","observation_id":"518b434e-fc5c-4370-afe8-355fd9158bd4","resolution":{"observed_at":"2026-08-04T13:37:16.204860Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:16.284965Z","title":"Approximate solutions of the Baer-Nunziato model","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:16.284965Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:94a6c0f4337125b032d77536ce23b9846d7488a4916667f40c421ccfe4ff38ff","observation_id":"c2646c93-d7a9-4f68-aa05-6271458f9a2c","resolution":{"observed_at":"2026-08-04T13:37:16.284965Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:16.356401Z","title":"Definition and weak stability of nonconservative products","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:16.356401Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:485bc12209a85e72704b15c13e71a12e62e0fa1e5fc1878e0f11b75a68f7fec3","observation_id":"ec725da8-15ee-4bc0-a40b-b684f4af827c","resolution":{"observed_at":"2026-08-04T13:37:16.356401Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:16.442598Z","title":"Simplified Second-Order Godunov-Type Methods","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:16.442598Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:d6c221f0fe2d312b6f8daceefc93fc819f6fe8723de6f9dadbdb98c4404326fd","observation_id":"aef65289-2ed8-4091-b726-79bead3d2fa2","resolution":{"observed_at":"2026-08-04T13:37:16.442598Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:16.525597Z","title":"HLLC-type and path-conservative schemes for a single-velocity six-equation two-phase flow model: A comparative study","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:16.525597Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:ee852f712fee34cb4042ec60a0b31c558de00943b106f3bd79ec8749b4fd4480","observation_id":"07e8d917-a4ef-49ee-8ea0-e47ee8e41032","resolution":{"observed_at":"2026-08-04T13:37:16.525597Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:16.572410Z","title":"A new efficient formulation of the HLLEM Rie- mann solver for general conservative and non-conservative hyperbolic systems","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:16.572410Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:80622b4d0a79f6c7c98d74a9403977703eda96927219dc67ed402bfdc26a2f8f","observation_id":"accc27f7-02cb-41ce-84d1-5c34800fd5f6","resolution":{"observed_at":"2026-08-04T13:37:16.572410Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:16.670704Z","title":"High-order unstructured Lagrangian one-step WENO finite volume schemes for non-conservative hyperbolic systems: applica- tions to compressible multi-phase flows","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:16.670704Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:278f3f08d7b1281a3704620336f5a81e5deb0fbe891f8ab862ec4a7cca29864e","observation_id":"9d1537b0-3f54-4018-a02c-511b1fa70480","resolution":{"observed_at":"2026-08-04T13:37:16.670704Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:16.760485Z","title":"A simple extension of the Osher Riemann solver to non-conservative hyperbolic systems","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:16.760485Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:be4df2c61faf76a7640aef27276aef97891918974c5f066a0e05e32b60578bfe","observation_id":"0b881653-4f5f-472b-a11d-27df3d45b940","resolution":{"observed_at":"2026-08-04T13:37:16.760485Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:16.855784Z","title":"ADER schemes on unstructured meshes for nonconservative hyperbolic systems: Applications to geophysical flows","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:16.855784Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:deaba4a6fe5242ef55e15fc618388de59ed5790803882556c250fa695746435f","observation_id":"e2362668-e428-4cb9-a078-13f71e7eed26","resolution":{"observed_at":"2026-08-04T13:37:16.855784Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:16.935284Z","title":"FORCE schemes on unstructured meshes II: Non-conservative hyperbolic systems","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:16.935284Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:55ac4bc209c7ac094f165c48187b79d0acc12a0655c47c8a57a87734deadb4b9","observation_id":"c8a8af59-1a0a-4811-8584-97a01dcbc4ff","resolution":{"observed_at":"2026-08-04T13:37:16.935284Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:17.047279Z","title":"Upwind methods for the Baer-Nunziato equations and higher- order reconstruction using artificial viscosity","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:17.047279Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:d0add7613391408472ea0a2fedf65b9bcd8ca34fe34a54088b1a66edc961467c","observation_id":"9878b4e7-fddb-4885-a59a-4532e8c0d1b7","resolution":{"observed_at":"2026-08-04T13:37:17.047279Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:17.106463Z","title":"Discontinuous Galerkin schemes for hyperbolic systems in non-conservative variables: quasi-conservative formulation with subcell finite vol- ume corrections","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:17.106463Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:1d9a75d30097d5166b1e2a34f195a104994371527b57f8380f7c78b65475fe3b","observation_id":"53b58555-5475-4a87-a8a5-c5d338aaae25","resolution":{"observed_at":"2026-08-04T13:37:17.106463Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:17.230933Z","title":"Numerical modeling of two-phase flows using the two-fluid two-pressure approach","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:17.230933Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:8ff76f0be27e7532a4e82bd24d447d24f22f48aabe31c50e7107435b5ca3e6fe","observation_id":"eba2a22d-3943-4b9e-a86c-624206154e5c","resolution":{"observed_at":"2026-08-04T13:37:17.230933Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:17.332297Z","title":"A scalable well-balanced numerical scheme for the modeling of two-phase shallow granular landslide consolidation","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:17.332297Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:d438a139ff6ae431a556c2cc3755d652c3089c2de6668045b1aaead8ba8ea470","observation_id":"9ef4a0b3-0df4-4f1d-9875-551d9c125869","resolution":{"observed_at":"2026-08-04T13:37:17.332297Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:17.424792Z","title":"An arbitrary high order well-balanced ADER-DG numerical scheme for the multilayer shallow-water model with variable density","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:17.424792Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:2302dfc9855915b371afa2df2a3c265c4215156bc96c565d6896237e264f2d5d","observation_id":"fcb0bf9d-eae3-4ede-990b-c324c467b00a","resolution":{"observed_at":"2026-08-04T13:37:17.424792Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:17.495252Z","title":"Numerical methods and relaxation techniques for diffuse interface models in high-velocity two-phase flow simulations","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:17.495252Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:021116657a8d86eb8e0de047ac46b33feb531a9d3b57c5ebfb7088a997aa1fa1","observation_id":"c389b9eb-7cfd-4a60-ab18-fc5503897229","resolution":{"observed_at":"2026-08-04T13:37:17.495252Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:17.586867Z","title":"Haegeman et al","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:17.586867Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:2e5da6d8de974d470181a7d0dc1ecee1c83fd8c0c146df34535d6c6b46dea52b","observation_id":"8b253d1c-9838-45b5-91d2-c45e190e18f9","resolution":{"observed_at":"2026-08-04T13:37:17.586867Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:17.655701Z","title":"Multiresolution Algorithms for the Numerical Solution of Hyperbolic Conservation Laws","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:17.655701Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:dfe877d00c7594253d2e88979e5c0d275894ad171f40a09f1de8f90cbfb110ce","observation_id":"a266c09a-bb91-469b-8699-b43003326a15","resolution":{"observed_at":"2026-08-04T13:37:17.655701Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:17.750322Z","title":"Two approaches to compute unsteady compress- ible two-phase flow models with stiff relaxation terms","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:17.750322Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:fc0031635d85a104b2111f5126cd92906a3381b26e4407fd7c6a8bca5d8d45c0","observation_id":"6d672519-d870-42c5-b806-cea510b53508","resolution":{"observed_at":"2026-08-04T13:37:17.750322Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:17.844679Z","title":"Why nonconservative schemes converge to wrong solutions: error analysis","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:17.844679Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:ced8b7006185466f2ce50ba82a1905f85fb368c893fdc136aa001db898f8c3d0","observation_id":"815dd7a9-7629-4361-8495-4205caef1e6d","resolution":{"observed_at":"2026-08-04T13:37:17.844679Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:17.941136Z","title":"Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:17.941136Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:5d9331ff2307146fd7fbedde0b8f6548343cce85eaff7eeac4617949e780dd6a","observation_id":"2901b765-f9af-46b0-865d-855027833e9c","resolution":{"observed_at":"2026-08-04T13:37:17.941136Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:18.043047Z","title":"Ketcheson, R.J","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:18.043047Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:629fd5d944d99d5e7979413d75bbfb876e2614e8e59580f85ba745759decf11b","observation_id":"d7882cc1-d411-481f-8b6f-a9e74ca5644a","resolution":{"observed_at":"2026-08-04T13:37:18.043047Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:18.138178Z","title":"High-order wave propagation algorithms for hyperbolic systems","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:18.138178Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:c0930d736e22782173d06371ae8e6c6c535931614aaeffdbe83750675ca65c92","observation_id":"540de362-8211-47b4-b2a4-7d840a7c5e0c","resolution":{"observed_at":"2026-08-04T13:37:18.138178Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:18.220899Z","title":"The Noble-Abel Stiffened-Gas equation of state","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:18.220899Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:4e998795d378ac0fa4f616ee1190641789db7a0f1f30533c468e16ac0f72234d","observation_id":"9d8f2e0a-9ea0-4fb8-bc07-4fa46001b20e","resolution":{"observed_at":"2026-08-04T13:37:18.220899Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:18.355283Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:18.355283Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:1c7df57fabe2678629c6332613766db3984a7d1a0c50f90d7974781edf96186a","observation_id":"4e4e2e5e-2b62-48d4-afdc-803036e4b48f","resolution":{"observed_at":"2026-08-04T13:37:18.355283Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:18.458209Z","title":"HLLC-type Riemann solver with approximated two-phase con- tact for the computation of the Baer-Nunziato two-fluid model","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:18.458209Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:2f7a8606e6d1c381746066ed37723df9d12af8c7eb5c61ebe478480240f90dd0","observation_id":"28c56817-a682-40ab-9df1-b3fd784b1a6e","resolution":{"observed_at":"2026-08-04T13:37:18.458209Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:18.582387Z","title":"A five equation reduced model for compressible two phase flow problems","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:18.582387Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:94741e6e9c35213ab9270dfcdfee4160d014a7b8a4f3a8ecbcb93cc56234ebf0","observation_id":"c57af282-1c9a-464f-864b-c986089573b2","resolution":{"observed_at":"2026-08-04T13:37:18.582387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:18.653150Z","title":"A path-conservative finite volume scheme for compressible multi-phase flows with surface tension","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:18.653150Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:1d410db89bfbe616b8bb887c6699d8e9e9f46e33c3c5ecaa9b3af24c0a66e883","observation_id":"980b8b54-f407-491e-a7bb-0641284fc6dc","resolution":{"observed_at":"2026-08-04T13:37:18.653150Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:18.742982Z","title":"Modelling and simulations of two-phase flows including geometric variables","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:18.742982Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:f6dd916254d37e92ac2c3674d6c8dfbb916f033a5c4478c667b33f678e077f01","observation_id":"3a558061-c9cb-47ec-ac92-fc01f7b397da","resolution":{"observed_at":"2026-08-04T13:37:18.742982Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:18.846227Z","title":"A comparative Fourier analysis of discontinuous Galerkin schemes for advection-diffusion with respect to BR1, BR2, and local discontinuous Galerkin diffusion discretization","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:18.846227Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:2366c1cfada3c773a017fd9846dfb3f71b2cc51f564e0aedfbfe0621d4d462d6","observation_id":"f458a3bb-d65a-42fa-be47-c5d61ecab1f5","resolution":{"observed_at":"2026-08-04T13:37:18.846227Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:18.970217Z","title":"Numerical methods for nonconservative hyperbolic systems: a theo- retical framework","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:18.970217Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:ed4b6687aa950789671953c2b48975915a696b72aa5e2a28c13b06f98c781fbc","observation_id":"86f27440-a2ca-473f-8c1f-dc534274c3bd","resolution":{"observed_at":"2026-08-04T13:37:18.970217Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:19.068756Z","title":"Wave structure similarity of the HLLC and Roe Riemann solvers: Application to low Mach number preconditioning","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:19.068756Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:ae10298629d53ed74e219faa030ba091d0a0ea1bf8cfc551e4f8b3c29750539c","observation_id":"76c6df73-cd01-44cc-8bb1-9c65a74be2da","resolution":{"observed_at":"2026-08-04T13:37:19.068756Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:19.158521Z","title":"Arbitrary-rate relaxation techniques for the numerical modeling of compressible two-phase flows with heat and mass transfer","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:19.158521Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:749e84e1801cd3ce1e8e5017c0e66d6f91c9f1150bd71744eecbf172130232b3","observation_id":"1ab98cb3-4ebb-4b39-ac83-affa2eb20730","resolution":{"observed_at":"2026-08-04T13:37:19.158521Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:19.242166Z","title":"A mixture-energy-consistent six-equation two- phase numerical model for fluids with interfaces, cavitation and evaporation waves","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:19.242166Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:dc9894708dd3511cd291fe3e5b60be26e25acd849d6570b0661853e555da4a7e","observation_id":"8076ccb1-1b6e-4082-9fb7-4c790230d28c","resolution":{"observed_at":"2026-08-04T13:37:19.242166Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:19.325554Z","title":"A relaxation-projection method for compressible flows. Part II: Artificial heat exchanges for multiphase shocks","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:19.325554Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:b7e5becffae6bd32a8dcbdfefbc76ced8ecb046e240a996c19fe18aa255ce412","observation_id":"1a23345a-9d26-4fcb-abdc-1bfdf5ac387d","resolution":{"observed_at":"2026-08-04T13:37:19.325554Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:19.383192Z","title":"A pressure-based method for weakly compressible two- phase flows under a Baer-Nunziato type model with generic equations of state and pressure and velocity disequilibrium","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:19.383192Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:c8b1ccbeb4462bf97d89ecd1be5709fc5babd478fa79b400dcbe6319ddbadb7d","observation_id":"1bc4a031-8158-4af3-8f54-aca3f849012c","resolution":{"observed_at":"2026-08-04T13:37:19.383192Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:19.461538Z","title":"Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equa- tions","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:19.461538Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:4d7b8ce91412556c52729a37e84d34fb3021c80e9bc30c91e9eedadb6c49d4ca","observation_id":"0ba93234-c4f9-4fc3-b189-d458226dbe53","resolution":{"observed_at":"2026-08-04T13:37:19.461538Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:19.546301Z","title":"An accurate and efficient semi-implicit method for section- averaged free-surface flow modelling","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:19.546301Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:1eab2e9eb4c1865503266cb58d4e6f277462e720e3004e73f1849d087c6b0f83","observation_id":"142729bd-0d3a-4cc9-920c-d4de4aaee5fc","resolution":{"observed_at":"2026-08-04T13:37:19.546301Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:19.604398Z","title":"The calculation of the interaction of non-stationary shock waves and obstacles","venue":null,"work_id":null,"year":1962},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:19.604398Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:9a9c49e72b15644f3f30f80439e03dce32239594c4424a2821a5a9d398a7cb34","observation_id":"d7ba7a0f-7ac1-4fec-9d29-7d4253144f87","resolution":{"observed_at":"2026-08-04T13:37:19.604398Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:19.743840Z","title":"A relaxation scheme for a hyperbolic multiphase flow model - Part I: Barotropic EOS","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:19.743840Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:efe3553f18ad2cc44c0e92f84e54428f3ef145b6d91a24290f55277697e2aaff","observation_id":"5f5ec6eb-7388-4db8-b222-42509cbdab06","resolution":{"observed_at":"2026-08-04T13:37:19.743840Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:19.890315Z","title":"A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:19.890315Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:95ff8e10a83bc53df7433b8c030e88fd4b0e45b0f30979f667d99a5eed2d5bcc","observation_id":"550fe637-82ca-4e2f-a974-16b9b0965f04","resolution":{"observed_at":"2026-08-04T13:37:19.890315Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:20.040738Z","title":"Modelling phase transition in metastable liquids: application to cavitating and flashing flows","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:20.040738Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:580fcea3cb9cc767ab2dcb7d617aba1d234f4d0b58d8f421c9eb0219ce6a46d1","observation_id":"08ee9afc-e1c1-43c2-8e8e-efaf556c6f18","resolution":{"observed_at":"2026-08-04T13:37:20.040738Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:20.144566Z","title":"Simple and efficient relaxation meth- ods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:20.144566Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:14be0b6e866e2cf820beaec35a6ab602129b3c6414cfffd56a672a6756d813e0","observation_id":"e0f5024a-68a9-4819-822f-e319c2f870b3","resolution":{"observed_at":"2026-08-04T13:37:20.144566Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:20.263805Z","title":"Shock Jump Relations for Multiphase Mixtures with Stiff Me- chanical Relaxation","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:20.263805Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:2b55977d85d5a9ed34aee93ccfda3f4d8054eeb441becbb4e49ad9737dc5861e","observation_id":"411e4046-cfcc-4f8f-8e3c-d6dc788bd1c2","resolution":{"observed_at":"2026-08-04T13:37:20.263805Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:20.370290Z","title":"Modelling interactions between waves and diffused in- terfaces","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:20.370290Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:7861f2073d47177f77f2425d366e19ad3ab030dd0e3550fd82c969052563549d","observation_id":"7ca06b76-e0b5-4962-aa92-4007672430b9","resolution":{"observed_at":"2026-08-04T13:37:20.370290Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:20.499044Z","title":"The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:20.499044Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:1bfa80193cdefd98b2df139317801689f74215560c1c9d4e181e5b9b5fda6a69","observation_id":"f5ab398e-e198-42c8-8c15-a19c18ed4760","resolution":{"observed_at":"2026-08-04T13:37:20.499044Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:20.640625Z","title":"Mixture-conservative temperature-based Baer-Nunziato solver for efficient full-disequilibrium simulations of real fluids","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:20.640625Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:3a7cdad1ffad4a2e3dd24c1de5dd64713ccd85369d40fc39dc78a981198c0749","observation_id":"6abe2b83-fca0-4c04-a44e-2b762d03cb5f","resolution":{"observed_at":"2026-08-04T13:37:20.640625Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:20.751345Z","title":"An explicit primitive conservative solver for the Euler equations with arbitrary equation of state","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:20.751345Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:1daf307060a0b9fd6bd674a886c2f9f5bf13bd3f1f62a6bcf0beea08b84571c1","observation_id":"65fbc167-a787-4533-a215-d8f38b0fae7e","resolution":{"observed_at":"2026-08-04T13:37:20.751345Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:20.869861Z","title":"HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:20.869861Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:989086c27589b786896cfb34b8eb419215b6d05828e1c522dc06454d7c8d2826","observation_id":"4334f648-37e2-4e40-9163-bc3cba1ce1a1","resolution":{"observed_at":"2026-08-04T13:37:20.869861Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:20.983383Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:20.983383Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:0f5c19f30190bf90e5edddd03150cd20837a26dd785f11bd1a8b97ea4deca31f","observation_id":"f1912824-3c55-4ea1-8b44-3e06ad7f8459","resolution":{"observed_at":"2026-08-04T13:37:20.983383Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:21.114518Z","title":"A semi-implicit, semi-Lagrangian discontinu- ous Galerkin framework for adaptive numerical weather prediction","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:21.114518Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:6a889d46e38a8281aae2ce2b7d2a014de87568e1ad92c5d81f00c214fc74a48f","observation_id":"6d9e8db7-79ee-4453-a9c4-f74e2aa69ce2","resolution":{"observed_at":"2026-08-04T13:37:21.114518Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:21.218570Z","title":"A limiter-based well-balanced discontin- uous Galerkin method for shallow-water flows with wetting and drying: Trian- gular grids","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:21.218570Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:dd1b81e9be0b69a24c72fd8588e58c591ba64476c5258797c48b1d197e6fd092","observation_id":"e0625d51-426b-451b-b199-1fa0f2dce337","resolution":{"observed_at":"2026-08-04T13:37:21.218570Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:21.334128Z","title":"Numerical Treatment of the Nonconservative Product in a Multiscale Fluid Model for Plasmas in Thermal Nonequilibrium: Application to Solar Physics","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:21.334128Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:3b1ce63389e5ed020d40373b5f4e445c75c0bc2043d9f7c5c34f6871cc3da163","observation_id":"f32487e1-7d0f-4fb2-b7e5-99387b466d92","resolution":{"observed_at":"2026-08-04T13:37:21.334128Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:21.440727Z","title":null,"venue":null,"work_id":null,"year":1930},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:21.440727Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:68d7d5e7113ce629580afd82329ed34c937113e6fcb6ed860df28dddbf2fcbe8","observation_id":"4f919978-d8f2-44f1-b52b-674e9f7c695e","resolution":{"observed_at":"2026-08-04T13:37:21.440727Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T13:37:21.523790Z","title":"Modeling phase transition for compress- ible two-phase flows applied to metastable liquids","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms","version":3},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-04T13:37:21.523790Z"},"links":{"citing_paper":"/paper/2509.26284"},"observation_digest":"sha256:b5f28d3117fd6c0db22a979705d9680167bfab4f405ee4153ea0490e2934e3bf","observation_id":"48a34c10-9bd0-4677-a297-6ff35e87cecc","resolution":{"observed_at":"2026-08-04T13:37:21.523790Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2509.26284","last_updated":"2026-06-19T18:45:47Z","latest_version":3,"primary_category":"math.NA","snapshot_observed_at":"2026-08-19T13:42:35.702135Z","submitted_at":"2025-09-30T14:05:21Z","title":"A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms"},"reference_resolution":{"displayed":72,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":72,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":72},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 72 of 72 outbound references and 0 inbound Pith citation observations for arXiv:2509.26284."}