{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T07:57:09Z","timestamp":1789718229006,"version":"4.0.1"},"reference-count":39,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS1418754"],"award-info":[{"award-number":["DMS1418754"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-SC0009301"],"award-info":[{"award-number":["DE-SC0009301"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-AC52-06NA25396"],"award-info":[{"award-number":["DE-AC52-06NA25396"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>Multiphase flow is a critical process in a wide range of applications, including carbon sequestration, contaminant remediation, and groundwater management. Typically, this process is modeled by a nonlinear system of partial differential equations derived by considering the mass conservation of each phase (e.g., oil, water), along with constitutive laws for the relationship of phase velocity to phase pressure. In this study, we develop and study efficient solution algorithms for solving the algebraic systems of equations derived from a fully coupled and time-implicit treatment of models of multiphase flow. We explore the performance of several preconditioners based on algebraic multigrid (AMG) for solving the linearized problem, including \u201cblack-box\u201d AMG applied directly to the system, a new version of constrained pressure residual multigrid (CPR-AMG) preconditioning, and a new preconditioner derived using an approximate Schur complement arising from the block factorization of the Jacobian. We show that the new methods are the most robust with respect to problem character, as determined by varying effects of capillary pressures, and we show that the block factorization preconditioner both is efficient and scales optimally with problem size.<\/jats:p>","DOI":"10.1137\/16m1082652","type":"journal-article","created":{"date-parts":[[2017,10,26]],"date-time":"2017-10-26T16:24:40Z","timestamp":1509035080000},"page":"S662-S680","source":"Crossref","is-referenced-by-count":25,"title":["Algebraic Multigrid Preconditioners for Multiphase Flow in Porous Media"],"prefix":"10.1137","volume":"39","author":[{"given":"Quan M.","family":"Bui","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Howard C.","family":"Elman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J. David","family":"Moulton","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,10,26]]},"reference":[{"key":"atypb1","unstructured":"U.S. Department of Energy,\n                      ASCEM\n                      , software project,http:\/\/esd.lbl.gov\/research\/projects\/ascem\/thrusts\/hpc\/, 2009."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511624100"},{"key":"atypb3","volume-title":"Petroleum Reservoir Simulation","author":"Aziz K.","year":"1979"},{"key":"atypb4","volume-title":"Habilitationsschrift, Department of Mathematics","author":"Bastian P.","year":"1999"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/S0309-1708(99)00014-7"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.2118\/9303-PA"},{"key":"atypb7","volume-title":"Hydrology Papers","author":"Brooks R.","year":"1964"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.2118\/66599-MS"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0018531"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.2118\/105789-PA"},{"key":"atypb11","unstructured":"E. Coon, J. D. Moulton, and S. Painter,\n                      Managing complexity in simulations of land surface and near-surface processes\n                      , Technical Report LA-UR 14-25386, Applied Mathematics and Plasma Physics Group, Los Alamos National Laboratory, Los Alamos, NV, 2014."},{"key":"atypb12","volume-title":"Mechanics of Immiscible Fluids in Porous Media","author":"Corey A. T.","year":"1995"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011521413158"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1002\/aic.690010421"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1956-0084194-4"},{"key":"atypb16","first-page":"267","volume-title":"A library of parallel high performance preconditioners, in Numerical Solution of Partial Differential Equations on Parallel Computers","author":"Falgout R. D.","year":"2006"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-47789-6_66"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2013.04.021"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(01)00115-5"},{"key":"atypb20","volume-title":"Two-stage preconditioners for inexact Newton methods in multiphase reservoir simulation, technical report","author":"Klie H.","year":"1996"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1137\/S106482750240443X"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1016\/j.advwatres.2011.04.021"},{"key":"atypb23","doi-asserted-by":"crossref","unstructured":"B. Lu,\n                      Iteratively Coupled Reservoir Simulation for Multiphase Flow in Porous Media\n                      , Ph.D. thesis, Center for Subsurface Modeling, ICES, The University of Texas - Austin, 2008.","DOI":"10.2523\/110114-MS"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1016\/0017-9310(72)90054-3"},{"key":"atypb25","volume-title":"Fundamentals of Numerical Reservoir Simulation","author":"Peaceman D.","year":"1977"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1137\/0103003"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971057.ch4"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971071.ch2"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718003"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1137\/0907058"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00516-1"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.2118\/105832-MS"},{"key":"atypb33","volume-title":"Multigrid","author":"Trottenberg U.","year":"2001"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.2118\/13536-MS"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.2118\/182723-MS"},{"key":"atypb36","volume-title":"Proceedings of the SPE Reservoir Simulation Symposium, Society of Petroleum Engineers (SPE)","author":"Watts J.","year":"1985"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1007\/s10596-011-9233-7"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1016\/S0169-7722(00)00180-7"},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-31619-1_6"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1082652","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:10:49Z","timestamp":1787328649000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1082652"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":39,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/16M1082652"],"URL":"https:\/\/doi.org\/10.1137\/16m1082652","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}