{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,13]],"date-time":"2024-09-13T16:41:30Z","timestamp":1726245690727},"reference-count":44,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2013,4,1]],"date-time":"2013-04-01T00:00:00Z","timestamp":1364774400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2017,4,1]],"date-time":"2017-04-01T00:00:00Z","timestamp":1491004800000},"content-version":"vor","delay-in-days":1461,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"funder":[{"DOI":"10.13039\/501100003593","name":"CNPq","doi-asserted-by":"crossref","award":["475480\/2010-4"],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2013,4]]},"DOI":"10.1016\/j.cam.2012.09.045","type":"journal-article","created":{"date-parts":[[2012,10,17]],"date-time":"2012-10-17T06:17:04Z","timestamp":1350454624000},"page":"12-27","source":"Crossref","is-referenced-by-count":19,"special_numbering":"C","title":["Numerical simulation of two-phase immiscible incompressible flows in heterogeneous porous media with capillary barriers"],"prefix":"10.1016","volume":"242","author":[{"given":"I.","family":"Mozolevski","sequence":"first","affiliation":[]},{"given":"L.","family":"Schuh","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.cam.2012.09.045_br000005","series-title":"Dynamic of Fluids in Porous Media","author":"Bear","year":"1978"},{"key":"10.1016\/j.cam.2012.09.045_br000010","series-title":"Mathematical Models and Finite Elements for Reservoir Simulation","author":"Chavent","year":"1978"},{"key":"10.1016\/j.cam.2012.09.045_br000015","series-title":"Computational Methods for Multiphase Flows in Porous Media","author":"Chen","year":"2006"},{"key":"10.1016\/j.cam.2012.09.045_br000020","series-title":"Multiphase Flow and Transport Processes in the Subsurface","author":"Helmig","year":"1997"},{"key":"10.1016\/j.cam.2012.09.045_br000025","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/BF00615335","article-title":"The effect of capillary forces on immiscible two-phase flow in heterogeneous porous media","volume":"21","author":"van Duijn","year":"1995","journal-title":"Transp. Porous Media"},{"issue":"3","key":"10.1016\/j.cam.2012.09.045_br000030","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1023\/A:1011554320427","article-title":"Numerical methods for flow in a porous medium with internal boundaries","volume":"2","author":"Ersland","year":"1998","journal-title":"Comput. Geosci."},{"key":"10.1016\/j.cam.2012.09.045_br000035","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1137\/S0036141002407375","article-title":"Analysis of oil trapping in porous media flow","volume":"35","author":"Bertsch","year":"2003","journal-title":"SIAM J. Math. Anal."},{"issue":"6","key":"10.1016\/j.cam.2012.09.045_br000040","doi-asserted-by":"crossref","first-page":"2402","DOI":"10.1137\/040602936","article-title":"Numerical approximation of a two-phase flow problem in a porous medium with discontinuous capillary forces","volume":"43","author":"Ench\u00e9ry","year":"2006","journal-title":"SIAM J. Numer. Anal."},{"issue":"1\u20132","key":"10.1016\/j.cam.2012.09.045_br000045","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/00036819508840360","article-title":"Effective model of two-phase flow in a porous medium made of different rock types","volume":"58","author":"Bourgeat","year":"1995","journal-title":"Appl. Anal."},{"issue":"1\u20132","key":"10.1016\/j.cam.2012.09.045_br000050","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1080\/00036819608840421","article-title":"Existence of solutions to various rock types model of two-phase flow in porous media","volume":"60","author":"Amaziane","year":"1996","journal-title":"Appl. Anal."},{"issue":"3","key":"10.1016\/j.cam.2012.09.045_br000055","first-page":"299","article-title":"Interface conditions for degenerate two-phase flow equations in one space dimension","volume":"29","author":"Buzzi","year":"2009","journal-title":"Analysis (Munich)"},{"key":"10.1016\/j.cam.2012.09.045_br000060","doi-asserted-by":"crossref","first-page":"239","DOI":"10.4171\/IFB\/210","article-title":"Two-phase flows involving capillary barriers in heterogeneous porous media","volume":"11","author":"Canc\u00e8s","year":"2009","journal-title":"Interfaces Free Bound."},{"key":"10.1016\/j.cam.2012.09.045_br000065","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1051\/m2an\/2009032","article-title":"Finite volume scheme for two-phase flow in heterogeneous porous media involving capillary pressure discontinuities","volume":"43","author":"Canc\u00e8s","year":"2009","journal-title":"M2AN Math. Model. Numer. Anal."},{"key":"10.1016\/j.cam.2012.09.045_br000070","unstructured":"C. Canc\u00e8s, M. Pierre, An existence result for multidimensional immiscible two-phase flows with discontinuous capillary pressure field, Technical Report, HAL: hal-00518219, 2011."},{"issue":"3","key":"10.1016\/j.cam.2012.09.045_br000075","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1029\/WR026i003p00399","article-title":"Exact integral solutions for twophase flow","volume":"26","author":"McWhorter","year":"1990","journal-title":"Water Resour. Res."},{"key":"10.1016\/j.cam.2012.09.045_br000080","doi-asserted-by":"crossref","first-page":"1477","DOI":"10.1029\/92WR00473","article-title":"Comment on \u201cExact integral solutions for two-phase flow\u201d by David B. McWhorter and Daniel K. Sunada","volume":"28","author":"Chen","year":"1992","journal-title":"Water Resour. Res."},{"key":"10.1016\/j.cam.2012.09.045_br000085","doi-asserted-by":"crossref","first-page":"1479","DOI":"10.1029\/92WR00474","article-title":"Replay","volume":"28","author":"McWhorter","year":"1992","journal-title":"Water Resour. Res."},{"key":"10.1016\/j.cam.2012.09.045_br000090","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/S0309-1708(97)00012-2","article-title":"Similarity solution for capillary redistribution of two phases in a porous medium with a single discontinuity","volume":"21","author":"van Duijn","year":"1998","journal-title":"Adv. Water Resour."},{"issue":"3","key":"10.1016\/j.cam.2012.09.045_br000095","doi-asserted-by":"crossref","first-page":"93","DOI":"10.2136\/vzj2006.0024","article-title":"An improved semianalytical solution for verification of numerical models of two-phase flow in porous media","volume":"6","author":"Fu\u010d\u00edk","year":"2007","journal-title":"Vadose Zone J."},{"issue":"3","key":"10.1016\/j.cam.2012.09.045_br000100","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.2136\/vzj2007.0155","article-title":"Semianalytical solution for two-phase flow in porous media with a discontinuity","volume":"7","author":"Fu\u010d\u00edk","year":"2008","journal-title":"Vadose Zone J."},{"key":"10.1016\/j.cam.2012.09.045_br000105","doi-asserted-by":"crossref","unstructured":"K. Brenner, C. Canc\u00e8s, D. Hilhorst, Finite volume approximation for an immiscible two-phase flow in porous media with discontinuous capillary pressure, HAL-00675681, Sept. 2011.","DOI":"10.1007\/978-3-642-20671-9_20"},{"key":"10.1016\/j.cam.2012.09.045_br000110","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1023\/B:COMG.0000024446.98662.36","article-title":"Modelling two-phase incompressible flow in porous media using mixed hybrid and discontinuous finite elements","volume":"8","author":"Nayagum","year":"2004","journal-title":"Comput. Geosci."},{"key":"10.1016\/j.cam.2012.09.045_br000115","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.advwatres.2007.06.006","article-title":"Numerical modeling of two-phase flow in heterogeneous permeable media with different capillary pressures","volume":"31","author":"Hoteit","year":"2008","journal-title":"Adv. Water Recour."},{"key":"10.1016\/j.cam.2012.09.045_br000120","article-title":"Mathematical Aspects of Discontinuous Galerkin Methods","volume":"vol. 69","author":"Di Pietro","year":"2011"},{"key":"10.1016\/j.cam.2012.09.045_br000125","series-title":"Frontiers in Mathematics","article-title":"Discontinuous Galerkin methods for solving elliptic and parabolic equations: Theory and implementation","author":"Rivi\u00e8re","year":"2008"},{"key":"10.1016\/j.cam.2012.09.045_br000130","article-title":"Nodal discontinuous Galerkin methods","volume":"vol. 54","author":"Hesthaven","year":"2008"},{"key":"10.1016\/j.cam.2012.09.045_br000135","unstructured":"P. Bastian, B. Rivi\u00e8re, Discontinuous Galerkin methods for two-phase flow in porous media, Technical Report 2004-28, 2004."},{"issue":"10","key":"10.1016\/j.cam.2012.09.045_br000140","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1002\/fld.562","article-title":"Superconvergence and H(div) projection for discontinuous Galerkin methods","volume":"42","author":"Bastian","year":"2003","journal-title":"Internat. J. Numer. Methods Fluids"},{"issue":"1\u20133","key":"10.1016\/j.cam.2012.09.045_br000145","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1016\/j.cma.2006.05.007","article-title":"Adaptive simulations of two-phase flow by discontinuous Galerkin methods","volume":"196","author":"Klieber","year":"2006","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/j.cam.2012.09.045_br000150","unstructured":"O.J. Eslinger, Discontinuous Galerkin Finite Element Methods applied to two-phase, air\u2013water flow problems, PhD Thesis, University of Texas, Austin, 2005."},{"key":"10.1016\/j.cam.2012.09.045_br000155","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/j.apnum.2006.04.004","article-title":"Fully implicit discontinuous finite element methods for two-phase flow","volume":"57","author":"Epshteyn","year":"2007","journal-title":"Appl. Numer. Math."},{"issue":"23\u201324","key":"10.1016\/j.cam.2012.09.045_br000160","doi-asserted-by":"crossref","first-page":"1491","DOI":"10.1016\/j.cma.2009.12.014","article-title":"Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures","volume":"199","author":"Ern","year":"2010","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/j.cam.2012.09.045_br000165","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1016\/j.crma.2007.10.036","article-title":"An accurate H(div) flux reconstruction for discontinuous Galerkin approximation of elliptic problems","volume":"375","author":"Ern","year":"2007","journal-title":"C. R. Acad. Sci. Paris, Ser.I"},{"issue":"9\u201310","key":"10.1016\/j.cam.2012.09.045_br000170","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1016\/j.crma.2009.02.011","article-title":"Accurate velocity reconstruction for discontinuous Galerkin approximations of two-phase porous media flows","volume":"347","author":"Ern","year":"2009","journal-title":"C. R. Math. Acad. Sci. Paris"},{"issue":"2","key":"10.1016\/j.cam.2012.09.045_br000175","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1093\/imanum\/drm050","article-title":"A discontinuous Galerkin method with weighted averages for advection\u2013diffusion equations with locally small and anisotropic diffusivity","volume":"29","author":"Ern","year":"2009","journal-title":"IMA J. Numer. Anal."},{"key":"10.1016\/j.cam.2012.09.045_br000180","doi-asserted-by":"crossref","first-page":"152","DOI":"10.2118\/941152-G","article-title":"Capillary behavior in porous solids","volume":"142","author":"Leverett","year":"1941","journal-title":"Trans. AIME"},{"key":"10.1016\/j.cam.2012.09.045_br000185","series-title":"Sobolev Spaces","author":"Adams","year":"1975"},{"issue":"2","key":"10.1016\/j.cam.2012.09.045_br000190","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1137\/060676106","article-title":"Discontinuous Galerkin methods for anisotropic semidefinite diffusion with advection","volume":"46","author":"Di Pietro","year":"2008","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.cam.2012.09.045_br000195","article-title":"Theory and practice of finite elements","volume":"vol. 159","author":"Ern","year":"2004"},{"key":"10.1016\/j.cam.2012.09.045_br000200","unstructured":"L. Chen, iFEM: an innovative finite element methods package in MATLAB. Technical Report, University of California at Irvine, 2008."},{"key":"10.1016\/j.cam.2012.09.045_br000205","article-title":"Direct methods for sparse linear systems","volume":"vol. 2","author":"Davis","year":"2006"},{"issue":"3","key":"10.1016\/j.cam.2012.09.045_br000210","first-page":"183","article-title":"Convergence of a mixed finite elements\u2014finite volume method for the two phase flow in porous media","volume":"5","author":"Ohlberger","year":"1997","journal-title":"East-West J. Numer. Math."},{"key":"10.1016\/j.cam.2012.09.045_br000215","series-title":"Understanding and Implementing the Finite Element Method","author":"Gockenbach","year":"2006"},{"issue":"35","key":"10.1016\/j.cam.2012.09.045_br000220","doi-asserted-by":"crossref","first-page":"3833","DOI":"10.1016\/S0045-7825(02)00318-3","article-title":"Nonlinear diffusion and discrete maximum principle for stabilized Galerkin approximations of the convection\u2014diffusion\u2013reaction equation","volume":"191","author":"Burman","year":"2002","journal-title":"Comput. Methods Appl. Mech. Engrg."}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042712004189?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042712004189?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2022,1,30]],"date-time":"2022-01-30T09:01:20Z","timestamp":1643533280000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042712004189"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,4]]},"references-count":44,"alternative-id":["S0377042712004189"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2012.09.045","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2013,4]]}}}