{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T05:25:13Z","timestamp":1726464313254},"reference-count":103,"publisher":"Elsevier BV","issue":"10","license":[{"start":{"date-parts":[[2018,5,1]],"date-time":"2018-05-01T00:00:00Z","timestamp":1525132800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2022,5,15]],"date-time":"2022-05-15T00:00:00Z","timestamp":1652572800000},"content-version":"vor","delay-in-days":1475,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"funder":[{"DOI":"10.13039\/501100007047","name":"Norway Grants","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100007047","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005632","name":"Narodowe Centrum Bada\u0144 i Rozwoju","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100005632","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computers & Mathematics with Applications"],"published-print":{"date-parts":[[2018,5]]},"DOI":"10.1016\/j.camwa.2018.02.010","type":"journal-article","created":{"date-parts":[[2018,2,24]],"date-time":"2018-02-24T13:32:51Z","timestamp":1519479171000},"page":"3453-3470","update-policy":"http:\/\/dx.doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":4,"title":["Depth-averaged Lattice Boltzmann and Finite Element methods for single-phase flows in fractures with obstacles"],"prefix":"10.1016","volume":"75","author":[{"given":"Michal","family":"Dzikowski","sequence":"first","affiliation":[]},{"given":"Lukasz","family":"Jasinski","sequence":"additional","affiliation":[]},{"given":"Marcin","family":"Dabrowski","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.camwa.2018.02.010_b1","series-title":"SPE Annual Technical Conference and Exhibition","article-title":"Thirty years of gas shale fracturing: what have we learned?","author":"King","year":"2010"},{"issue":"7","key":"10.1016\/j.camwa.2018.02.010_b2","doi-asserted-by":"crossref","first-page":"1028","DOI":"10.1016\/j.ijrmms.2005.05.014","article-title":"Hydraulic fracturing in a sedimentary geothermal reservoir: Results and implications","volume":"42","author":"Legarth","year":"2005","journal-title":"Int. J. Rock Mech. Min. Sci."},{"issue":"7\u20138","key":"10.1016\/j.camwa.2018.02.010_b3","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1016\/j.crte.2010.01.006","article-title":"Contribution of the exploration of deep crystalline fractured reservoir of Soultz to the knowledge of enhanced geothermal systems (EGS)","volume":"342","author":"Genter","year":"2010","journal-title":"C. R. Geosci."},{"key":"10.1016\/j.camwa.2018.02.010_b4","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.petrol.2012.11.016","article-title":"Conductivity of narrow fractures filled with a proppant monolayer","volume":"100","author":"Khanna","year":"2012","journal-title":"J. Pet. Sci. Eng."},{"key":"10.1016\/j.camwa.2018.02.010_b5","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.petrol.2015.04.004","article-title":"Experimental and numerical studies of reduced fracture conductivity due to proppant embedment in the shale reservoir","volume":"130","author":"Zhang","year":"2015","journal-title":"J. Pet. Sci. Eng."},{"key":"10.1016\/j.camwa.2018.02.010_b6","series-title":"SPE Annual Technical Conference and Exhibition","article-title":"Maximizing fracture conductivity with proppant partial monolayers: theoretical curiosity or highly productive reality?","author":"Brannon","year":"2004"},{"key":"10.1016\/j.camwa.2018.02.010_b7","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1016\/j.ijheatmasstransfer.2014.04.016","article-title":"Capillary flow through rectangular micropillar arrays","volume":"75","author":"Hale","year":"2014","journal-title":"Int. J. Heat Mass Transfer"},{"issue":"10","key":"10.1016\/j.camwa.2018.02.010_b8","doi-asserted-by":"crossref","first-page":"2050","DOI":"10.1016\/j.apm.2007.06.033","article-title":"A novel lattice Boltzmann model for the Poisson equation","volume":"32","author":"Chai","year":"2008","journal-title":"Appl. Math. Model."},{"issue":"1","key":"10.1016\/j.camwa.2018.02.010_b9","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/j.jcis.2006.08.050","article-title":"Electrokinetic pumping effects of charged porous media in microchannels using the lattice Poisson\u2013Boltzmann method","volume":"304","author":"Wang","year":"2006","journal-title":"J. Colloid Interface Sci."},{"issue":"1","key":"10.1016\/j.camwa.2018.02.010_b10","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1007\/s10915-014-9820-6","article-title":"A coupled lattice Boltzmann method to solve Nernst\u2013Planck model for simulating electro-osmotic flows","volume":"61","author":"Yang","year":"2014","journal-title":"J. Sci. Comput."},{"issue":"6","key":"10.1016\/j.camwa.2018.02.010_b11","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevE.91.063309","article-title":"Conservative phase-field lattice Boltzmann model for interface tracking equation","volume":"91","author":"Geier","year":"2015","journal-title":"Phys. Rev. E"},{"issue":"2","key":"10.1016\/j.camwa.2018.02.010_b12","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/S0021-9991(03)00279-1","article-title":"Incompressible limits of lattice Boltzmann equations using multiple relaxation times","volume":"190","author":"Dellar","year":"2003","journal-title":"J. Comput. Phys."},{"issue":"3\/4","key":"10.1016\/j.camwa.2018.02.010_b13","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1023\/B:JOSS.0000015179.12689.e4","article-title":"Lattice Boltzmann model for the incompressible Navier\u2013Stokes equation","volume":"88","author":"He","year":"1997","journal-title":"J. Stat. Phys."},{"issue":"2","key":"10.1016\/j.camwa.2018.02.010_b14","doi-asserted-by":"crossref","first-page":"023302","DOI":"10.1103\/PhysRevE.94.023302","article-title":"Consistent lattice Boltzmann methods for incompressible axisymmetric flows","volume":"94","author":"Zhang","year":"2016","journal-title":"Phys. Rev. E"},{"issue":"6","key":"10.1016\/j.camwa.2018.02.010_b15","doi-asserted-by":"crossref","first-page":"4823","DOI":"10.1103\/PhysRevE.48.4823","article-title":"Initial and boundary conditions for the lattice Boltzmann method","volume":"48","author":"Skordos","year":"1993","journal-title":"Phys. Rev. E"},{"key":"10.1016\/j.camwa.2018.02.010_b16","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1016\/j.jcp.2015.05.019","article-title":"Detailed analysis of the lattice Boltzmann method on unstructured grids","volume":"297","author":"Misztal","year":"2015","journal-title":"J. Comput. Phys."},{"issue":"20","key":"10.1016\/j.camwa.2018.02.010_b17","doi-asserted-by":"crossref","first-page":"2332","DOI":"10.1103\/PhysRevLett.61.2332","article-title":"Use of the Boltzmann equation to simulate lattice-gas automata","volume":"61","author":"McNamara","year":"1988","journal-title":"Phys. Rev. Lett."},{"issue":"8","key":"10.1016\/j.camwa.2018.02.010_b18","doi-asserted-by":"crossref","first-page":"R5339","DOI":"10.1103\/PhysRevA.45.R5339","article-title":"Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method","volume":"45","author":"Chen","year":"1992","journal-title":"Phys. Rev. A"},{"issue":"27","key":"10.1016\/j.camwa.2018.02.010_b19","doi-asserted-by":"crossref","first-page":"3776","DOI":"10.1103\/PhysRevLett.67.3776","article-title":"Lattice Boltzmann model for simulation of magnetohydrodynamics","volume":"67","author":"Chen","year":"1991","journal-title":"Phys. Rev. Lett."},{"issue":"5","key":"10.1016\/j.camwa.2018.02.010_b20","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1103\/PhysRevLett.31.276","article-title":"Time evolution of a two-dimensional classical lattice system","volume":"31","author":"Hardy","year":"1973","journal-title":"Phys. Rev. Lett."},{"issue":"4","key":"10.1016\/j.camwa.2018.02.010_b21","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1190\/1.1442482","article-title":"Cellular-automaton fluids: A model for flow in porous media","volume":"53","author":"Rothman","year":"1988","journal-title":"GEOPHYSICS"},{"issue":"4","key":"10.1016\/j.camwa.2018.02.010_b22","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1209\/0295-5075\/2\/4\/006","article-title":"Lattice gas models for 3d hydrodynamics","volume":"2","author":"d\u2019Humi\u00e8res","year":"1986","journal-title":"Europhys. Lett."},{"issue":"6","key":"10.1016\/j.camwa.2018.02.010_b23","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1209\/0295-5075\/17\/6\/001","article-title":"Lattice BGK models for Navier-Stokes equation","volume":"17","author":"Qian","year":"1992","journal-title":"Europhys. Lett."},{"key":"10.1016\/j.camwa.2018.02.010_b24","series-title":"Numerical Methods for the Simulation of Multi-Phase and Complex Flow","first-page":"39","article-title":"Hydrodynamic behaviour of the Lattice Boltzmann Equation","author":"Succi","year":"1990"},{"issue":"1\u20132","key":"10.1016\/j.camwa.2018.02.010_b25","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/BF00616923","article-title":"Lattice-Boltzmann simulations of flow through Fontainebleau sandstone","volume":"20","author":"Ferr\u00e9ol","year":"1995","journal-title":"Transp. Porous Media"},{"key":"10.1016\/j.camwa.2018.02.010_b26","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.cageo.2012.09.008","article-title":"Digital rock physics benchmarks\u2014part II: Computing effective properties","volume":"50","author":"Andr\u00e4","year":"2013","journal-title":"Comput. Geosci."},{"year":"2001","series-title":"The Lattice Boltzmann Equation for Fluid Dynamics and Beyond","author":"Succi","key":"10.1016\/j.camwa.2018.02.010_b27"},{"key":"10.1016\/j.camwa.2018.02.010_b28","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1016\/j.ces.2015.06.043","article-title":"Pressure drop in flow across ceramic foams\u2014A numerical and experimental study","volume":"137","author":"Regulski","year":"2015","journal-title":"Chem. Eng. Sci."},{"key":"10.1016\/j.camwa.2018.02.010_b29","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/j.ijheatfluidflow.2013.07.013","article-title":"Permeability of microscale fibrous porous media using the lattice Boltzmann method","volume":"44","author":"Cho","year":"2013","journal-title":"Int. J. Heat Fluid Flow"},{"year":"2015","series-title":"Simulation of Shale Gas Transport in 3d Complex Nanoscale-Pore Structures Using the Lattice Boltzmann Method","author":"Ning","key":"10.1016\/j.camwa.2018.02.010_b30"},{"key":"10.1016\/j.camwa.2018.02.010_b31","doi-asserted-by":"crossref","first-page":"8089","DOI":"10.1038\/srep08089","article-title":"Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity","volume":"5","author":"Chen","year":"2015","journal-title":"Sci. Rep."},{"issue":"7","key":"10.1016\/j.camwa.2018.02.010_b32","doi-asserted-by":"crossref","first-page":"2305","DOI":"10.1016\/j.camwa.2009.08.063","article-title":"Lattice-Boltzmann studies of fluid flow in porous media with realistic rock geometries","volume":"59","author":"Boek","year":"2010","journal-title":"Comput. Math. Appl."},{"issue":"4","key":"10.1016\/j.camwa.2018.02.010_b33","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/s11440-006-0018-4","article-title":"Calculating the effective permeability of sandstone with multiscale lattice Boltzmann\/finite element simulations","volume":"1","author":"White","year":"2006","journal-title":"Acta Geotech."},{"year":"1991","series-title":"Mixed and Hybrid Finite Element Methods","author":"Brezzi","key":"10.1016\/j.camwa.2018.02.010_b34"},{"article-title":"Finite Elements and Fast Iterative Solvers : with Applications in Incompressible Fluid Dynamics: with Applications in Incompressible Fluid Dynamics","year":"2005","author":"Elman","key":"10.1016\/j.camwa.2018.02.010_b35"},{"key":"10.1016\/j.camwa.2018.02.010_b36","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.jsg.2016.01.001","article-title":"Folder: A numerical tool to simulate the development of structures in layered media","volume":"84","author":"Adamuszek","year":"2016","journal-title":"J. Struct. Geol."},{"issue":"14","key":"10.1016\/j.camwa.2018.02.010_b37","doi-asserted-by":"crossref","first-page":"L14309","DOI":"10.1029\/2006GL026341","article-title":"3D finite amplitude folding: Implications for stress evolution during crustal and lithospheric deformation","volume":"33","author":"Kaus","year":"2006","journal-title":"Geophys. Res. Lett."},{"key":"10.1016\/j.camwa.2018.02.010_b38","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1016\/j.pepi.2008.08.007","article-title":"Evolution of large amplitude 3D fold patterns: A FEM study","volume":"171","author":"Schmid","year":"2008","journal-title":"Phys. Earth Planet. Inter."},{"issue":"5995","key":"10.1016\/j.camwa.2018.02.010_b39","doi-asserted-by":"crossref","first-page":"1033","DOI":"10.1126\/science.1191223","article-title":"The dynamics of plate tectonics and mantle flow: From local to global scales","volume":"329","author":"Stadler","year":"2010","journal-title":"Science"},{"issue":"5","key":"10.1016\/j.camwa.2018.02.010_b40","doi-asserted-by":"crossref","first-page":"3824","DOI":"10.1002\/2014JB011688","article-title":"Survival of llsvps for billions of years in a vigorously convecting mantle: Replenishment and destruction of chemical anomaly","volume":"120","author":"Mulyukova","year":"2015","journal-title":"J. Geophys. Res. Solid Earth"},{"issue":"B8","key":"10.1016\/j.camwa.2018.02.010_b41","first-page":"b08406","article-title":"A two-phase composite in simple shear: Effective mechanical anisotropy development and localization potential","volume":"117","author":"Dabrowski","year":"2012","journal-title":"J. Geophys. Res."},{"issue":"6\u20137","key":"10.1016\/j.camwa.2018.02.010_b42","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.1016\/S0191-8141(01)00090-6","article-title":"Finite-element modelling of shear zone development in viscoelastic materials and its implications for localisation of partial melting","volume":"24","author":"Mancktelow","year":"2002","journal-title":"J. Struct. Geol."},{"issue":"1\u20132","key":"10.1016\/j.camwa.2018.02.010_b43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.epsl.2009.11.041","article-title":"Direct numerical simulation of two-phase flow: Effective rheology and flow patterns of particle suspensions","volume":"290","author":"Deubelbeiss","year":"2010","journal-title":"Earth Planet. Sci. Lett."},{"key":"10.1016\/j.camwa.2018.02.010_b44","doi-asserted-by":"crossref","first-page":"022611","DOI":"10.1103\/PhysRevE.93.022611","article-title":"Transient cluster formation in sheared non-Brownian suspensions","volume":"93","author":"Th\u00f8gersen","year":"2016","journal-title":"Phys. Rev. E"},{"issue":"11","key":"10.1016\/j.camwa.2018.02.010_b45","doi-asserted-by":"crossref","first-page":"3001","DOI":"10.1029\/94WR01786","article-title":"Application of the mixed hybrid finite element approximation in a groundwater flow model: Luxury or necessity?","volume":"30","author":"Mos\u00e9","year":"1994","journal-title":"Water Resour. Res."},{"key":"10.1016\/j.camwa.2018.02.010_b46","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/j.advwatres.2012.05.008","article-title":"Numerical simulation of water resources problems: Models, methods, and trends","volume":"51","author":"Miller","year":"2013","journal-title":"Adv. Water Resour."},{"issue":"4","key":"10.1016\/j.camwa.2018.02.010_b47","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1007\/s10040-007-0254-1","article-title":"Numerical modeling of stress-permeability coupling in rough fractures","volume":"16","author":"Walsh","year":"2008","journal-title":"Hydrogeol. J."},{"issue":"4","key":"10.1016\/j.camwa.2018.02.010_b48","doi-asserted-by":"crossref","first-page":"592","DOI":"10.1111\/gfl.12129","article-title":"Multiphase flow simulation through porous media with explicitly resolved fractures","volume":"15","author":"Su","year":"2015","journal-title":"Geofluids"},{"issue":"6","key":"10.1016\/j.camwa.2018.02.010_b49","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1016\/j.advwatres.2008.02.004","article-title":"An efficient numerical model for incompressible two-phase flow in fractured media","volume":"31","author":"Hoteit","year":"2008","journal-title":"Adv. Water Resour."},{"issue":"1","key":"10.1016\/j.camwa.2018.02.010_b50","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1111\/gfl.12042","article-title":"Modeling thermal convection in supradetachment basins: example from western norway","volume":"14","author":"Souche","year":"2014","journal-title":"Geofluids"},{"issue":"3","key":"10.1016\/j.camwa.2018.02.010_b51","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1007\/s11242-005-0108-z","article-title":"Multiphase thermohaline convection in the earth\u2019s crust: I. a new finite element \u2013finite volume solution technique combined with a new equation of state for NaCl\u2013H2O","volume":"63","author":"Geiger","year":"2006","journal-title":"Transp. Porous Media"},{"issue":"7497","key":"10.1016\/j.camwa.2018.02.010_b52","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1038\/nature13174","article-title":"Hybrid shallow on-axis and deep off-axis hydrothermal circulation at fast-spreading ridges","volume":"508","author":"Hasenclever","year":"2014","journal-title":"Nature"},{"issue":"5","key":"10.1016\/j.camwa.2018.02.010_b53","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1016\/S0309-1708(97)00003-1","article-title":"Coupled groundwater flow and transport: 2. thermohaline and 3d convection systems","volume":"21","author":"Diersch","year":"1998","journal-title":"Adv. Water Resour."},{"issue":"4","key":"10.1016\/j.camwa.2018.02.010_b54","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1111\/j.1468-8123.2004.00093.x","article-title":"Combining finite element and finite volume methods for efficient multiphase flow simulations in highly heterogeneous and structurally complex geologic media","volume":"4","author":"Geiger","year":"2004","journal-title":"Geofluids"},{"issue":"7","key":"10.1016\/j.camwa.2018.02.010_b55","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1016\/S0264-8172(99)00061-6","article-title":"Finite element analysis and ray tracing modeling of petroleum migration","volume":"17","author":"Hantschel","year":"2000","journal-title":"Mar. Pet. Geol."},{"issue":"2","key":"10.1016\/j.camwa.2018.02.010_b56","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1111\/gfl.12070","article-title":"Effects of episodic fluid flow on hydrocarbon migration in the newport-inglewood fault zone, southern california","volume":"14","author":"Jung","year":"2014","journal-title":"Geofluids"},{"issue":"4","key":"10.1016\/j.camwa.2018.02.010_b57","doi-asserted-by":"crossref","first-page":"2064","DOI":"10.1002\/2014WR015815","article-title":"Modification of the local cubic law of fracture flow for weak inertia, tortuosity, and roughness","volume":"51","author":"Wang","year":"2015","journal-title":"Water Resour. Res."},{"issue":"2","key":"10.1016\/j.camwa.2018.02.010_b58","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1007\/s11242-011-9915-6","article-title":"Pore-scale modeling of viscous flow and induced forces in dense sphere packings","volume":"92","author":"Chareyre","year":"2012","journal-title":"Transp. Porous Media"},{"issue":"12","key":"10.1016\/j.camwa.2018.02.010_b59","doi-asserted-by":"crossref","first-page":"1508","DOI":"10.1016\/j.advwatres.2010.08.008","article-title":"Efficient flow and transport simulations in reconstructed 3d pore geometries","volume":"33","author":"Zaretskiy","year":"2010","journal-title":"Adv. Water Resour."},{"key":"10.1016\/j.camwa.2018.02.010_b60","doi-asserted-by":"crossref","first-page":"1726","DOI":"10.1002\/2016JB013536","article-title":"Self-similar distributions of fluid velocity and stress heterogeneity in a dissolving porous limestone","volume":"122","author":"Linga","year":"2017","journal-title":"J. Geophys. Res. Solid Earth"},{"issue":"3","key":"10.1016\/j.camwa.2018.02.010_b61","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s10596-007-9043-0","article-title":"A computational method for approximating a darcy\u2013stokes system governing a vuggy porous medium","volume":"11","author":"Arbogast","year":"2007","journal-title":"Comput. Geosci."},{"key":"10.1016\/j.camwa.2018.02.010_b62","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.4208\/cicp.290610.020211a","article-title":"On the importance of the stokes-brinkman equations for computing effective permeability in karst reservoirs","volume":"10","author":"Krotkiewski","year":"2011","journal-title":"Commun. Comput. Phys."},{"issue":"3","key":"10.1016\/j.camwa.2018.02.010_b63","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/BF01341756","article-title":"Lattice-gas and lattice-boltzmann models of miscible fluids","volume":"68","author":"Holme","year":"1992","journal-title":"J. Stat. Phys."},{"issue":"5","key":"10.1016\/j.camwa.2018.02.010_b64","doi-asserted-by":"crossref","first-page":"4952","DOI":"10.1103\/PhysRevE.52.4952","article-title":"Hydrodynamic dispersion at stagnation points: Simulations and experiments","volume":"52","author":"Flekk\u00f8y","year":"1995","journal-title":"Phys. Rev. E"},{"issue":"1","key":"10.1016\/j.camwa.2018.02.010_b65","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1103\/PhysRevE.61.616","article-title":"Hydraulic permeability of (un)bounded fibrous media using the lattice Boltzmann method","volume":"61","author":"Clague","year":"2000","journal-title":"Phys. Rev. E"},{"key":"10.1016\/j.camwa.2018.02.010_b66","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1017\/S0022112091002318","article-title":"Viscous flow in a channel with periodic cross-bridging fibres: exact solutions and Brinkman approximation","volume":"226","author":"Tsay","year":"1991","journal-title":"J. Fluid Mech."},{"key":"10.1016\/j.camwa.2018.02.010_b67","doi-asserted-by":"crossref","first-page":"3120","DOI":"10.1063\/1.1410120","article-title":"Wavelength selection of fingering instability inside Hele-Shaw cells","volume":"13","author":"Fernandez","year":"2001","journal-title":"Phys. Fluids"},{"issue":"1821","key":"10.1016\/j.camwa.2018.02.010_b68","doi-asserted-by":"crossref","first-page":"1723","DOI":"10.1098\/rsta.2004.1398","article-title":"Structural and dynamical characterization of Hele\u2013Shaw viscous fingering","volume":"362","author":"Grosfils","year":"2004","journal-title":"Phil. Trans. R. Soc. A"},{"issue":"1","key":"10.1016\/j.camwa.2018.02.010_b69","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.physa.2005.09.006","article-title":"Two-dimensional lattice-Boltzmann simulations of single phase flow in a pseudo two-dimensional micromodel","volume":"362","author":"Venturoli","year":"2006","journal-title":"Physica A"},{"issue":"12","key":"10.1016\/j.camwa.2018.02.010_b70","doi-asserted-by":"crossref","first-page":"2677","DOI":"10.1007\/s12541-014-0642-0","article-title":"Analytic correlation for the capillary pressure of micro-square-pillar arrays","volume":"15","author":"Hong","year":"2014","journal-title":"Int. J. Precis. Eng. Manuf."},{"key":"10.1016\/j.camwa.2018.02.010_b71","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/j.ces.2013.08.031","article-title":"Experimental and numerical study of two-phase flows in arrays of cylinders","volume":"102","author":"Horgue","year":"2013","journal-title":"Chem. Eng. Sci."},{"key":"10.1016\/j.camwa.2018.02.010_b72","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1016\/j.compfluid.2014.10.016","article-title":"Boundary elements method for microfluidic two-phase flows in shallow channels","volume":"107","author":"Nagel","year":"2015","journal-title":"Comput. & Fluids"},{"issue":"4","key":"10.1016\/j.camwa.2018.02.010_b73","doi-asserted-by":"crossref","first-page":"600","DOI":"10.3390\/computation3040600","article-title":"An incompressible, depth-averaged lattice Boltzmann method for liquid flow in microfluidic devices with variable aperture","volume":"3","author":"Laleian","year":"2015","journal-title":"Computation"},{"issue":"4","key":"10.1016\/j.camwa.2018.02.010_b74","doi-asserted-by":"crossref","DOI":"10.1029\/2007GC001719","article-title":"Milamin: Matlab-based finite element method solver for large problems","volume":"9","author":"Dabrowski","year":"2008","journal-title":"Geochem. Geophys. Geosyst."},{"issue":"3","key":"10.1016\/j.camwa.2018.02.010_b75","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1016\/j.camwa.2015.12.043","article-title":"Adjoint Lattice Boltzmann for topology optimization on multi-GPU architecture","volume":"71","author":"\u0141aniewski-Wo\u0142\u0142k","year":"2016","journal-title":"Comput. Math. Appl."},{"issue":"04","key":"10.1016\/j.camwa.2018.02.010_b76","doi-asserted-by":"crossref","first-page":"1042","DOI":"10.4208\/cicp.220115.110915a","article-title":"Single component multiphase lattice Boltzmann method for taylor\/bretherton bubble train flow simulations","volume":"19","author":"Dzikowski","year":"2016","journal-title":"Commun. Comput. Phys."},{"issue":"2","key":"10.1016\/j.camwa.2018.02.010_b77","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/0022-5193(80)90358-6","article-title":"Random sequential adsorption","volume":"87","author":"Feder","year":"1980","journal-title":"J. Theoret. Biol."},{"issue":"04","key":"10.1016\/j.camwa.2018.02.010_b78","doi-asserted-by":"crossref","first-page":"1650037","DOI":"10.1142\/S0129183116500376","article-title":"Reassessing the single relaxation time Lattice Boltzmann method for the simulation of Darcy\u2019s flows","volume":"27","author":"Prestininzi","year":"2016","journal-title":"Internat. J. Modern Phys. C"},{"key":"10.1016\/j.camwa.2018.02.010_b79","series-title":"Applied Computational Geometry Towards Geometric Engineering","first-page":"203","article-title":"Triangle: Engineering a 2d quality mesh generator and Delaunay triangulator","volume":"no. 1148","author":"Shewchuk","year":"1996"},{"issue":"2","key":"10.1016\/j.camwa.2018.02.010_b80","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1145\/2629697","article-title":"Tetgen, a Delaunay-based quality tetrahedral mesh generator","volume":"41","author":"Si","year":"2015","journal-title":"ACM Trans. Math. Software (TOMS)"},{"key":"10.1016\/j.camwa.2018.02.010_b81","unstructured":"M. Krotkiewski, M. Dabrowski, MUTILS - a set of efficient modeling tools for multi-core CPUs implemented in MEX, in: EGU General Assembly Conference Abstracts, Vol. 15 of EGU General Assembly Conference Abstracts, 2013, pp. EGU2013\u20137877."},{"issue":"4","key":"10.1016\/j.camwa.2018.02.010_b82","doi-asserted-by":"crossref","first-page":"Q04030","DOI":"10.1029\/2007GC001719","article-title":"MILAMIN: MATLAB-based finite element method solver for large problems","volume":"9","author":"Dabrowski","year":"2008","journal-title":"Geochem. Geophys. Geosyst."},{"issue":"3","key":"10.1016\/j.camwa.2018.02.010_b83","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1103\/PhysRev.94.511","article-title":"A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems","volume":"94","author":"Bhatnagar","year":"1954","journal-title":"Phys. Rev."},{"key":"10.1016\/j.camwa.2018.02.010_b84","series-title":"Lattice Boltzmann Method and its Applications in Engineering","volume":"vol. 3","author":"Guo","year":"2013"},{"issue":"1792","key":"10.1016\/j.camwa.2018.02.010_b85","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1098\/rsta.2001.0955","article-title":"Multiple-relaxation-time lattice Boltzmann models in three dimensions","volume":"360","author":"D\u2019Humi\u00e8res","year":"2002","journal-title":"Phil. Trans. R. Soc. A"},{"issue":"2","key":"10.1016\/j.camwa.2018.02.010_b86","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1023\/A:1012230722915","article-title":"Accelerated lattice Boltzmann schemes for steady-state flow simulations","volume":"16","author":"Bernaschi","year":"2001","journal-title":"J. Sci. Comput."},{"issue":"3","key":"10.1016\/j.camwa.2018.02.010_b87","doi-asserted-by":"crossref","first-page":"3366","DOI":"10.1103\/PhysRevE.60.3366","article-title":"Simulation of low-Reynolds-number flow via a time-independent lattice-Boltzmann method","volume":"60","author":"Verberg","year":"1999","journal-title":"Phys. Rev. E"},{"issue":"4","key":"10.1016\/j.camwa.2018.02.010_b88","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1016\/j.camwa.2015.05.001","article-title":"The cumulant lattice Boltzmann equation in three dimensions: Theory and validation","volume":"70","author":"Geier","year":"2015","journal-title":"Comput. Math. Appl."},{"issue":"2","key":"10.1016\/j.camwa.2018.02.010_b89","first-page":"75","article-title":"Incorporating a body force term into the lattice Boltzmann equation","volume":"4","author":"Kupershtokh","year":"2004","journal-title":"Vestn. NGU Ser.: Math. Mech. Inform."},{"issue":"5","key":"10.1016\/j.camwa.2018.02.010_b90","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1016\/j.camwa.2009.02.024","article-title":"On equations of state in a lattice Boltzmann method","volume":"58","author":"Kupershtokh","year":"2009","journal-title":"Comput. Math. Appl."},{"issue":"18","key":"10.1016\/j.camwa.2018.02.010_b91","doi-asserted-by":"crossref","first-page":"4357","DOI":"10.1039\/c002974b","article-title":"Lattice Boltzmann simulations of phase-separating flows at large density ratios: the case of doubly-attractive pseudo-potentials","volume":"6","author":"Falcucci","year":"2010","journal-title":"Soft Matter"},{"issue":"5","key":"10.1016\/j.camwa.2018.02.010_b92","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1093\/imamat\/hxr014","article-title":"Modern lattice Boltzmann methods for multiphase microflows","volume":"76","author":"Falcucci","year":"2011","journal-title":"IMA J. Appl. Math."},{"issue":"6","key":"10.1016\/j.camwa.2018.02.010_b93","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.1063\/1.869307","article-title":"On pressure and velocity boundary conditions for the lattice Boltzmann BGK model","volume":"9","author":"Zou","year":"1997","journal-title":"Phys. Fluids"},{"issue":"1","key":"10.1016\/j.camwa.2018.02.010_b94","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/BF02120313","article-title":"A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles","volume":"1","author":"Brinkman","year":"1947","journal-title":"Appl. Sci. Res."},{"issue":"1","key":"10.1016\/j.camwa.2018.02.010_b95","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/BF02120313","article-title":"A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles","volume":"1","author":"Brinkman","year":"1949","journal-title":"Flow Turbul. Combust."},{"issue":"5","key":"10.1016\/j.camwa.2018.02.010_b96","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.4208\/cicp.290610.020211a","article-title":"On the importance of the stokes-brinkman equations for computing effective permeability in karst reservoirs","volume":"10","author":"Krotkiewski","year":"2011","journal-title":"Commun. Comput. Phys."},{"issue":"4","key":"10.1016\/j.camwa.2018.02.010_b97","doi-asserted-by":"crossref","first-page":"1434","DOI":"10.1063\/1.868258","article-title":"Computer simulation study of the effective viscosity in brinkman\u2019s equation","volume":"6","author":"Martys","year":"1994","journal-title":"Phys. Fluids (1994-Present)"},{"issue":"2","key":"10.1016\/j.camwa.2018.02.010_b98","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/0020-7225(92)90058-O","article-title":"Flow past a circular cylinder embedded in a porous medium based on the Brinkman model","volume":"30","author":"Pop","year":"1992","journal-title":"Internat. J. Engrg. Sci."},{"key":"10.1016\/j.camwa.2018.02.010_b99","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1017\/S0022112068000212","article-title":"Secondary flow in a Hele-Shaw cell","volume":"31","author":"Thompson","year":"1968","journal-title":"J. Fluid Mech."},{"issue":"4","key":"10.1016\/j.camwa.2018.02.010_b100","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1021\/es60016a003","article-title":"Model for predicting pressure drop and filtration efficiency in fibrous media","volume":"2","author":"Spielman","year":"1968","journal-title":"Environ. Sci. Technol."},{"issue":"4","key":"10.1016\/j.camwa.2018.02.010_b101","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1023\/A:1016770308900","article-title":"The viscous drag of a rough cylinder in a liquid flow in a porous medium","volume":"63","author":"Chernyakov","year":"2001","journal-title":"Colloid J."},{"issue":"3","key":"10.1016\/j.camwa.2018.02.010_b102","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1080\/00986440903088603","article-title":"Darcy-brinkman flow with solid inclusions","volume":"197","author":"Wang","year":"2010","journal-title":"Chem. Eng. Commun."},{"issue":"4","key":"10.1016\/j.camwa.2018.02.010_b103","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1017\/S0022112069000796","article-title":"Stokes flow around a circular cylindrical post confined between two parallel plates","volume":"37","author":"Lee","year":"1969","journal-title":"J. Fluid Mech."}],"container-title":["Computers & Mathematics with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S089812211830083X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S089812211830083X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T14:47:53Z","timestamp":1719845273000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S089812211830083X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5]]},"references-count":103,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2018,5]]}},"alternative-id":["S089812211830083X"],"URL":"https:\/\/doi.org\/10.1016\/j.camwa.2018.02.010","relation":{},"ISSN":["0898-1221"],"issn-type":[{"type":"print","value":"0898-1221"}],"subject":[],"published":{"date-parts":[[2018,5]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Depth-averaged Lattice Boltzmann and Finite Element methods for single-phase flows in fractures with obstacles","name":"articletitle","label":"Article Title"},{"value":"Computers & Mathematics with Applications","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.camwa.2018.02.010","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2018 Elsevier Ltd.","name":"copyright","label":"Copyright"}]}}