{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T21:44:39Z","timestamp":1780609479625,"version":"3.54.1"},"reference-count":33,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,10,30]],"date-time":"2023-10-30T00:00:00Z","timestamp":1698624000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Brazilian Agency CNPq","award":["304962\/2022-8"],"award-info":[{"award-number":["304962\/2022-8"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This work uses a mixture theory approach to describe kinematically constrained flows through porous media using an adequate constitutive relation for pressure that preserves the problem hyperbolicity even when the flow becomes saturated. This feature allows using the same mathematical tool for handling unsaturated and saturated flows. The mechanical model can represent the saturated\u2013unsaturated transition and vice-versa. The constitutive relation for pressure is a continuous and differentiable function of saturation: an increasing function with a strictly convex, increasing, and positive first derivative. This significant characteristic permits the fluid to establish a tiny controlled supersaturation of the porous matrix. The associated Riemann problem\u2019s complete solution is addressed in detail, with explicit expressions for the Riemann invariants. Glimm\u2019s semi-analytical scheme advances from a given instant to a subsequent one, employing the associated Riemann problem solution for each two consecutive time steps. The simulations employ a variation in Glimm\u2019s scheme, which uses the mean of four independent sequences for each considered time, ensuring computational solutions with reliable positions of rarefaction and shock waves. The results permit verifying this significant characteristic.<\/jats:p>","DOI":"10.3390\/axioms12111023","type":"journal-article","created":{"date-parts":[[2023,10,30]],"date-time":"2023-10-30T12:07:45Z","timestamp":1698667665000},"page":"1023","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Numerical Simulation of Constrained Flows through Porous Media Employing Glimm\u2019s Scheme"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2947-8142","authenticated-orcid":false,"given":"Rog\u00e9rio M. Saldanha","family":"da Gama","sequence":"first","affiliation":[{"name":"Mechanical Engineering Graduate Program (FEN), Rio de Janeiro State University, Rio de Janeiro 20550-013, RJ, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jos\u00e9 Julio","family":"Pedrosa Filho","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Graduate Program (FEN), Rio de Janeiro State University, Rio de Janeiro 20550-013, RJ, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rog\u00e9rio Pazetto S.","family":"da Gama","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Graduate Program (FEN), Rio de Janeiro State University, Rio de Janeiro 20550-013, RJ, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-9779-4176","authenticated-orcid":false,"given":"Daniel Cunha","family":"da Silva","sequence":"additional","affiliation":[{"name":"Mathematics and Design Department (CEH-CAp), Rio de Janeiro State University, Rio de Janeiro 20550-013, RJ, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9408-4644","authenticated-orcid":false,"given":"Carlos Henrique","family":"Alexandrino","sequence":"additional","affiliation":[{"name":"Laboratory of Theoretical and Applied Mechanics (LMTA), Mechanical Engineering Graduate Program (TEM-PGMEC), Federal Fluminense University, Niter\u00f3i 24210-240, RJ, Brazil"},{"name":"Institute of Science Engineering and Technology, Federal University of Vales do Jequitinhonha e Mucuri, Te\u00f3filo Otoni 39800-371, MG, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6586-3670","authenticated-orcid":false,"given":"Maria Laura","family":"Martins-Costa","sequence":"additional","affiliation":[{"name":"Laboratory of Theoretical and Applied Mechanics (LMTA), Mechanical Engineering Graduate Program (TEM-PGMEC), Federal Fluminense University, Niter\u00f3i 24210-240, RJ, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"vzj2011.0197","DOI":"10.2136\/vzj2011.0197","article-title":"Dynamic nonequilibrium of water flow in porous media: A review","volume":"11","author":"Diamantopoulos","year":"2012","journal-title":"Vadose Zone J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"109672","DOI":"10.1016\/j.petrol.2021.109672","article-title":"A review on measurement of the dynamic effect in capillary pressure","volume":"208","author":"Li","year":"2022","journal-title":"J. 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