{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T01:07:36Z","timestamp":1780448856297,"version":"3.54.1"},"reference-count":28,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100002674","name":"Russian Academy of Sciences","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002674","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational Physics"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.jcp.2026.115008","type":"journal-article","created":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T15:35:55Z","timestamp":1777995355000},"page":"115008","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["HLL-based approximate Riemann solver for the seven-equation model"],"prefix":"10.1016","volume":"562","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1564-205X","authenticated-orcid":false,"given":"P.A.","family":"Chuprov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.jcp.2026.115008_bib0001","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1007\/BF01387046","article-title":"Equations of hydromechanics and compression shock in two-velocity and two-temperature continuum with phase transformations","volume":"2","author":"Nigmatulin","year":"1967","journal-title":"Fluid Dyn."},{"key":"10.1016\/j.jcp.2026.115008_bib0002","doi-asserted-by":"crossref","first-page":"1773","DOI":"10.1016\/S0017-9310(02)00473-8","article-title":"One-dimensional drift\u2013flux model for two-phase flow in a large diameter pipe","volume":"46","author":"Hibiki","year":"2003","journal-title":"Int. J. Heat Mass Transf."},{"issue":"2","key":"10.1016\/j.jcp.2026.115008_bib0003","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1006\/jcph.1999.6236","article-title":"A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)","volume":"152","author":"Fedkiw","year":"1999","journal-title":"J. Comput. Phys."},{"issue":"6","key":"10.1016\/j.jcp.2026.115008_bib0004","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1016\/0301-9322(86)90033-9","article-title":"A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials","volume":"12","author":"Baer","year":"1986","journal-title":"Int. J. Multiph. Flow"},{"issue":"2","key":"10.1016\/j.jcp.2026.115008_bib0005","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1006\/jcph.1999.6187","article-title":"A multiphase godunov method for compressible multifluid and multiphase flows","volume":"150","author":"Saurel","year":"1999","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115008_bib0006","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1017\/S0022112000003098","article-title":"A multiphase model for compressible flows with interfaces, shocks, detonation waves and cavitation","volume":"431","author":"Saurel","year":"2001","journal-title":"J. Fluid Mech."},{"issue":"10","key":"10.1016\/j.jcp.2026.115008_bib0007","doi-asserted-by":"crossref","first-page":"3573","DOI":"10.1016\/j.jcp.2010.01.016","article-title":"HLLC-type Riemann solver for the Baer\u2013Nunziato equations of compressible two-phase flow","volume":"229","author":"Tokareva","year":"2010","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115008_bib0008","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1016\/j.jcp.2016.09.015","article-title":"HLLC-type Riemann solver with approximated two-phase contact for the computation of the Baer\u2013Nunziato two-fluid model","volume":"326","author":"Lochon","year":"2016","journal-title":"J. Comput. Phys."},{"issue":"2","key":"10.1016\/j.jcp.2026.115008_bib0009","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2005.07.012","article-title":"The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow","volume":"212","author":"Schwendeman","year":"2006","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115008_bib0010","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.compfluid.2015.01.016","article-title":"A simple HLLC-type Riemann solver for compressible non-equilibrium two-phase flows","volume":"111","author":"Furfaro","year":"2015","journal-title":"Comput. Fluids"},{"key":"10.1016\/j.jcp.2026.115008_bib0011","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.compfluid.2014.04.021","article-title":"Solving seven-equation model for compressible two-phase flow using multiple GPUs","volume":"99","author":"Liang","year":"2014","journal-title":"Comput. Fluids"},{"key":"10.1016\/j.jcp.2026.115008_bib0012","series-title":"Advances in Theory and Practice of Computational Mechanics","first-page":"167","article-title":"Numerical simulation of combustion wave propagation in a black powder charge using a two-fluid model","author":"Chuprov","year":"2022"},{"key":"10.1016\/j.jcp.2026.115008_bib0013","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.jcp.2015.09.056","article-title":"On the computation of the Baer\u2013Nunziato model using ALE formulation with HLL- and HLLC-type solvers towards fluid\u2013structure interactions","volume":"304","author":"Daude","year":"2016","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115008_bib0014","doi-asserted-by":"crossref","DOI":"10.1016\/j.ijmultiphaseflow.2021.103718","article-title":"Numerical simulation of a normally incident shock wave\u2013dense particles layer interaction using the Godunov solver for the Baer\u2013Nunziato equations","volume":"142","author":"Poroshyna","year":"2021","journal-title":"Int. J. Multiph. Flow"},{"issue":"1","key":"10.1016\/j.jcp.2026.115008_bib0015","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1006\/jcph.1996.0085","article-title":"How to prevent pressure oscillations in multicomponent flow calculations: a quasi conservative approach","volume":"125","author":"Abgrall","year":"1996","journal-title":"J. Comput. Phys."},{"issue":"5","key":"10.1016\/j.jcp.2026.115008_bib0016","doi-asserted-by":"crossref","first-page":"1678","DOI":"10.1016\/j.jcp.2008.11.002","article-title":"Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures","volume":"228","author":"Richard Saurel","year":"2009","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115008_bib0017","article-title":"A simple and accurate coupled HLL-type approximate Riemann solver for the two-fluid two-pressure model of compressible flows","author":"Chalons","year":"2016","journal-title":"Int. J. Finite Vol."},{"issue":"2","key":"10.1016\/j.jcp.2026.115008_bib0018","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1006\/jcph.1997.5730","article-title":"A numerical method using upwind schemes for the resolution of two-phase flows","volume":"136","author":"Coquel","year":"1997","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115008_bib0019","series-title":"R\u00e9solution Num\u00e9rique Des Probl\u00e8mes Multidimensionnels De La Dynamique Des Gaz","author":"Godounov","year":"1979"},{"issue":"1","key":"10.1016\/j.jcp.2026.115008_bib0020","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s001930050096","article-title":"Experimental and numerical investigation of the shock-induced fluidization of a particles bed","volume":"8","author":"Rogue","year":"1998","journal-title":"Shock Waves"},{"issue":"11","key":"10.1016\/j.jcp.2026.115008_bib0021","doi-asserted-by":"crossref","DOI":"10.1063\/5.0172796","article-title":"Numerical simulation of shock wave propagation over a dense particle layer using the Baer\u2013Nunziato model","volume":"35","author":"Utkin","year":"2023","journal-title":"Phys. Fluids"},{"key":"10.1016\/j.jcp.2026.115008_bib0022","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1017\/jfm.2015.728","article-title":"A multiphase model for compressible granular\u2013gaseous flows: formulation and initial tests","volume":"789","author":"Houim","year":"2016","journal-title":"J. Fluid Mech."},{"issue":"6","key":"10.1016\/j.jcp.2026.115008_bib0023","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1134\/S1990793117050141","article-title":"Mathematical modeling of the interaction of a shock wave with a dense cloud of particles within the framework of the two-fluid approach","volume":"11","author":"Utkin","year":"2017","journal-title":"Russ. J. Phys. Chem. B"},{"key":"10.1016\/j.jcp.2026.115008_bib0024","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.20537\/2076-7633-2024-16-6-1361-1384","article-title":"Numerical simulation of the propagation of probing pulses in a dense bed of a granular medium","volume":"16","author":"Utkin","year":"2024","journal-title":"Comput. Res. Model."},{"issue":"3","key":"10.1016\/j.jcp.2026.115008_bib0025","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1134\/S1063785022040022","article-title":"Sounding of water-gas-saturated bulk media by rereflected waves immediately after the impact of a shock wave","volume":"48","author":"Akhmetov","year":"2022","journal-title":"Tech. Phys. Lett."},{"issue":"3","key":"10.1016\/j.jcp.2026.115008_bib0026","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1007\/BF00745122","article-title":"Instability of the interface between colliding metals","volume":"9","author":"Yakovlev","year":"1973","journal-title":"Combust. Explos. Shock Waves"},{"issue":"8","key":"10.1016\/j.jcp.2026.115008_bib0027","doi-asserted-by":"crossref","DOI":"10.3390\/met11081233","article-title":"Numerical simulation of a high-speed impact of metal plates using a three-fluid model","volume":"11","author":"Chuprov","year":"2021","journal-title":"Metals"},{"key":"10.1016\/j.jcp.2026.115008_bib0028","series-title":"A Textbook of Sound","author":"Wood","year":"1941"}],"container-title":["Journal of Computational Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S002199912600361X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S002199912600361X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T00:42:37Z","timestamp":1780447357000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S002199912600361X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":28,"alternative-id":["S002199912600361X"],"URL":"https:\/\/doi.org\/10.1016\/j.jcp.2026.115008","relation":{},"ISSN":["0021-9991"],"issn-type":[{"value":"0021-9991","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"HLL-based approximate Riemann solver for the seven-equation model","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational Physics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jcp.2026.115008","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"115008"}}