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The model can thus be approximated by means of the minimising movement (or JKO after Jordan, Kinderlehrer and Otto [<jats:italic>SIAM J. Math. Anal.<\/jats:italic><jats:bold>29<\/jats:bold>(1), 1\u201317]) scheme that we solve thanks to the ALG2-JKO scheme proposed in Benamou et\u00a0al. [<jats:italic>ESAIM Proc. Surv.<\/jats:italic><jats:bold>57<\/jats:bold>, 1\u201317]. The numerical results are compared to a classical upstream mobility finite volume scheme, for which strong stability properties can be established.<\/jats:p>","DOI":"10.1017\/s0956792518000633","type":"journal-article","created":{"date-parts":[[2018,10,31]],"date-time":"2018-10-31T10:46:57Z","timestamp":1540982817000},"page":"1123-1152","source":"Crossref","is-referenced-by-count":5,"title":["Simulation of multiphase porous media flows with minimising movement and finite volume schemes"],"prefix":"10.1017","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7682-1695","authenticated-orcid":false,"given":"CL\u00c9MENT","family":"CANC\u00c8S","sequence":"first","affiliation":[]},{"given":"THOMAS","family":"GALLOU\u00cbT","sequence":"additional","affiliation":[]},{"given":"MAXIME","family":"LABORDE","sequence":"additional","affiliation":[]},{"given":"L\u00c9ONARD","family":"MONSAINGEON","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,10,31]]},"reference":[{"key":"S0956792518000633_ref22","unstructured":"[22] Fortin, M. & Glowinski, R. 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