{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T05:36:16Z","timestamp":1774330576507,"version":"3.50.1"},"reference-count":53,"publisher":"Elsevier BV","content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational Physics"],"published-print":{"date-parts":[[2014,3]]},"DOI":"10.1016\/j.jcp.2013.12.042","type":"journal-article","created":{"date-parts":[[2014,1,3]],"date-time":"2014-01-03T12:44:04Z","timestamp":1388753044000},"page":"83-105","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":181,"special_numbering":"C","title":["A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains"],"prefix":"10.1016","volume":"261","author":[{"given":"S.","family":"Dong","sequence":"first","affiliation":[]},{"given":"G.E.","family":"Karniadakis","sequence":"additional","affiliation":[]},{"given":"C.","family":"Chryssostomidis","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.jcp.2013.12.042_br0010","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1002\/fld.1650120403","article-title":"Vorticity-streamfunction formulation of unsteady incompressible flow past a cylinder sensitivity of the computed flow field to the location of the outflow boundary","volume":"12","author":"Behr","year":"1991","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"10.1016\/j.jcp.2013.12.042_br0020","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1002\/fld.1650190805","article-title":"Effective downstream boundary conditions for incompressible Navier\u2013Stokes equations","volume":"19","author":"Bruneau","year":"1994","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"10.1016\/j.jcp.2013.12.042_br0030","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1146\/annurev.fluid.36.050802.121930","article-title":"Modeling artificial boundary conditions for compressible flow","volume":"36","author":"Colonius","year":"2004","journal-title":"Annu. Rev. Fluid Mech."},{"key":"10.1016\/j.jcp.2013.12.042_br0040","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1017\/S0022112082000561","article-title":"A numerical study of vortex shedding from rectangles","volume":"116","author":"Davis","year":"1982","journal-title":"J. Fluid Mech."},{"key":"10.1016\/j.jcp.2013.12.042_br0050","doi-asserted-by":"crossref","first-page":"3019","DOI":"10.1016\/j.jcp.2009.12.028","article-title":"BDF-like methods for nonlinear dynamic analysis","volume":"229","author":"Dong","year":"2010","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2013.12.042_br0060","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.jfluidstructs.2005.02.004","article-title":"DNS of flow past stationary and oscillating cylinder at Re=10,000","volume":"20","author":"Dong","year":"2005","journal-title":"J. Fluids Struct."},{"key":"10.1016\/j.jcp.2013.12.042_br0070","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1017\/S0022112006002606","article-title":"A combined direct numerical simulation-particle image velocimetry study of the turbulent near wake","volume":"569","author":"Dong","year":"2006","journal-title":"J. Fluid Mech."},{"key":"10.1016\/j.jcp.2013.12.042_br0080","doi-asserted-by":"crossref","first-page":"7013","DOI":"10.1016\/j.jcp.2010.05.037","article-title":"An unconditionally stable rotational velocity-correction scheme for incompressible flows","volume":"229","author":"Dong","year":"2010","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2013.12.042_br0090","doi-asserted-by":"crossref","first-page":"5788","DOI":"10.1016\/j.jcp.2012.04.041","article-title":"A time-stepping scheme involving constant coefficient matrices for phase field simulations of two-phase incompressible flows with large density ratios","volume":"231","author":"Dong","year":"2012","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2013.12.042_br0100","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1002\/fld.1650110706","article-title":"Transient flow past a circular cylinder: A benchmark solution","volume":"11","author":"Engelman","year":"1990","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"10.1016\/j.jcp.2013.12.042_br0110","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/S0168-9274(99)00085-9","article-title":"Spatial development of wakes using a spectral multi-domain method","volume":"33","author":"Forestier","year":"2000","journal-title":"Appl. Numer. Math."},{"key":"10.1016\/j.jcp.2013.12.042_br0120","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1137\/S003614290038296X","article-title":"Numerical treatment of defective boundary conditions for the Navier\u2013Stokes equations","volume":"40","author":"Formaggia","year":"2002","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.jcp.2013.12.042_br0130","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/0167-6105(90)90219-3","article-title":"Numerical calculation of laminar vortex shedding flow past cylinders","volume":"35","author":"Franke","year":"1990","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"10.1016\/j.jcp.2013.12.042_br0140","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1002\/fld.1650110704","article-title":"A test problem for outflow boundary conditions \u2013 flow over a backward-facing step","volume":"11","author":"Gartling","year":"1990","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"10.1016\/j.jcp.2013.12.042_br0150","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.wavemoti.2003.12.004","article-title":"High-order local non-reflecting boundary conditions: a review","volume":"39","author":"Givoli","year":"2004","journal-title":"Wave Motion"},{"key":"10.1016\/j.jcp.2013.12.042_br0160","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1017\/S002211209300031X","article-title":"Vorticity measurements in the near wake of a circular cylinder at low Reynolds numbers","volume":"246","author":"Green","year":"1993","journal-title":"J. Fluid Mech."},{"key":"10.1016\/j.jcp.2013.12.042_br0170","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1146\/annurev.fl.23.010191.002213","article-title":"Incompressible fluid dynamics: some fundamental formulation issues","volume":"23","author":"Gresho","year":"1991","journal-title":"Annu. Rev. Fluid Mech."},{"key":"10.1016\/j.jcp.2013.12.042_br0180","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1017\/S0022112095000322","article-title":"A note on bluff body vortex formation","volume":"284","author":"Griffin","year":"1995","journal-title":"J. Fluid Mech."},{"key":"10.1016\/j.jcp.2013.12.042_br0190","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1002\/(SICI)1097-0363(19970228)24:4<393::AID-FLD505>3.0.CO;2-O","article-title":"The \u2018no boundary condition\u2019 outflow boundary condition","volume":"24","author":"Griffiths","year":"1997","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"10.1016\/j.jcp.2013.12.042_br0200","doi-asserted-by":"crossref","first-page":"1496","DOI":"10.1007\/s10439-008-9527-7","article-title":"Outflow boundary conditions for arterial networks with multiple outlets","volume":"36","author":"Grinberg","year":"2008","journal-title":"Ann. Biomed. Eng."},{"key":"10.1016\/j.jcp.2013.12.042_br0210","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1137\/040604418","article-title":"Error analysis of pressure-correction schemes for the time-dependent Stokes equations with open boundary conditions","volume":"43","author":"Guermond","year":"2005","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.jcp.2013.12.042_br0220","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1137\/S0036142901395400","article-title":"Velocity-correction projection methods for incompressible flows","volume":"41","author":"Guermond","year":"2003","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.jcp.2013.12.042_br0230","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1016\/j.jcp.2004.12.025","article-title":"On the outflow boundary condition for external incompressible flows: a new approach","volume":"206","author":"Hasan","year":"2005","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2013.12.042_br0240","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1002\/(SICI)1097-0363(19960315)22:5<325::AID-FLD307>3.0.CO;2-Y","article-title":"Artificial boundaries and flux and pressure: conditions for the incompressible Navier\u2013Stokes equations","volume":"22","author":"Heywood","year":"1996","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"10.1016\/j.jcp.2013.12.042_br0250","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1146\/annurev.fl.22.010190.002353","article-title":"Local and global instabilities in spatially developing flows","volume":"22","author":"Huerre","year":"1990","journal-title":"Annu. Rev. Fluid Mech."},{"key":"10.1016\/j.jcp.2013.12.042_br0260","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1006\/jcph.1993.1140","article-title":"A nonreflecting outlet boundary condition for incompressible unsteady Navier\u2013Stokes calculations","volume":"107","author":"Jin","year":"1993","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2013.12.042_br0270","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1006\/jcph.1993.1071","article-title":"Boundary conditions for open boundaries for the incompressible Navier\u2013Stokes equation","volume":"105","author":"Johansson","year":"1993","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2013.12.042_br0280","series-title":"Spectral\/hp Element Methods for Computational Fluid Dynamics","author":"Karniadakis","year":"2005"},{"key":"10.1016\/j.jcp.2013.12.042_br0290","article-title":"Numerical prediction of vortex shedding behind a square cylinder","author":"Kelkar","year":"2013","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"10.1016\/j.jcp.2013.12.042_br0300","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1002\/(SICI)1097-0363(19990228)29:4<411::AID-FLD794>3.0.CO;2-6","article-title":"Computations of a laminar backward-facing step flow at Re=800 with a spectral domain decomposition method","volume":"29","author":"Keskar","year":"1999","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"10.1016\/j.jcp.2013.12.042_br0310","doi-asserted-by":"crossref","first-page":"3551","DOI":"10.1016\/j.cma.2009.02.012","article-title":"Segmented langrangian method for constraining the shape of velocity profiles at outlet boundaries for three-dimensional finite element simulations of blood flow","volume":"198","author":"Kim","year":"2009","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"10.1016\/j.jcp.2013.12.042_br0320","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1017\/S0305004100023999","article-title":"Laminar flow behind a two-dimensional grid","volume":"44","author":"Kovasznay","year":"1948","journal-title":"Proc. Camb. Philol. Soc."},{"key":"10.1016\/j.jcp.2013.12.042_br0330","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1002\/fld.1650110705","article-title":"Open boundary condition symposium benchmark solution: stratified flow over a backward-facing step","volume":"11","author":"Leone","year":"1990","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"10.1016\/j.jcp.2013.12.042_br0340","doi-asserted-by":"crossref","first-page":"7250","DOI":"10.1016\/j.jcp.2009.06.021","article-title":"Open and traction boundary conditions for the incompressible Navier\u2013Stokes equations","volume":"228","author":"Liu","year":"2009","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2013.12.042_br0350","doi-asserted-by":"crossref","first-page":"874","DOI":"10.1016\/j.jcp.2007.01.010","article-title":"Boundary conditions for a divergence free velocity-free formulation of the Navier\u2013Stokes equations","author":"Nordstrom","year":"2007","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2013.12.042_br0360","doi-asserted-by":"crossref","first-page":"1231","DOI":"10.1137\/040604972","article-title":"Well-posed boundary conditions for the Navier\u2013Stokes equations","volume":"43","author":"Nordstrom","year":"2005","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.jcp.2013.12.042_br0370","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1017\/S0022112082003115","article-title":"Strouhal numbers of rectangular cylinders","volume":"123","author":"Okajima","year":"1982","journal-title":"J. Fluid Mech."},{"key":"10.1016\/j.jcp.2013.12.042_br0380","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1002\/1097-0363(20000630)33:4<499::AID-FLD19>3.0.CO;2-7","article-title":"On simulation of outflow boundary conditions in finite difference calculations for incompressible fluid","volume":"33","author":"Olshanskii","year":"2000","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"10.1016\/j.jcp.2013.12.042_br0390","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/0021-9991(76)90023-1","article-title":"A simple boundary condition for unbounded hyperbolic flows","volume":"21","author":"Orlanski","year":"1976","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2013.12.042_br0400","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1002\/fld.1650140506","article-title":"A new outflow boundary condition","volume":"14","author":"Papanastasiou","year":"1992","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"10.1016\/j.jcp.2013.12.042_br0410","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.compfluid.2012.08.028","article-title":"Open boundary conditions for the velocity-correction scheme of the Navier\u2013Stokes equations","volume":"70","author":"Poux","year":"2012","journal-title":"Comput. Fluids"},{"key":"10.1016\/j.jcp.2013.12.042_br0420","doi-asserted-by":"crossref","first-page":"4011","DOI":"10.1016\/j.jcp.2011.02.024","article-title":"Improvements on open and traction boundary conditions for Navier\u2013Stokes time-splitting methods","volume":"230","author":"Poux","year":"2011","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2013.12.042_br0430","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1002\/(SICI)1097-0363(19970228)24:4<413::AID-FLD507>3.0.CO;2-N","article-title":"Imposing \u2018no\u2019 boundary condition at outflow: why does it work?","volume":"24","author":"Renardy","year":"1997","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"10.1016\/j.jcp.2013.12.042_br0440","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1063\/1.869930","article-title":"Three-dimensional Floquet instability of the wake of square cylinder","volume":"11","author":"Robichaux","year":"1999","journal-title":"Phys. Fluids"},{"key":"10.1016\/j.jcp.2013.12.042_br0450","doi-asserted-by":"crossref","first-page":"1225","DOI":"10.1016\/j.compfluid.2003.04.001","article-title":"Development of boundary conditions for direct numerical simulations of three-dimensional vortex breakdown phenomena in semi-infinite domains","volume":"33","author":"Ruith","year":"2004","journal-title":"Comput. Fluids"},{"key":"10.1016\/j.jcp.2013.12.042_br0460","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1002\/fld.1650181006","article-title":"Resume and remarks on the open boundary condition minisymposium","volume":"18","author":"Sani","year":"1994","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"10.1016\/j.jcp.2013.12.042_br0470","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1017\/S0022112094001679","article-title":"Self-excited oscillations in the wake of two-dimensional bluff bodies and their control","volume":"271","author":"Schumm","year":"1994","journal-title":"J. Fluid Mech."},{"key":"10.1016\/j.jcp.2013.12.042_br0480","first-page":"44","article-title":"Fluid forces acting on cylinders of rectangular cross-section","author":"Shimizu","year":"2013","journal-title":"Trans. Jpn. Soc. Mech. Eng. B"},{"key":"10.1016\/j.jcp.2013.12.042_br0490","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1002\/(SICI)1097-0363(19980115)26:1<39::AID-FLD623>3.0.CO;2-P","article-title":"Low Reynolds number flow around a square cylinder at incidence: study of blockage, onset of vortex shedding, and open boundary conditions","volume":"26","author":"Sohankar","year":"1998","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"10.1016\/j.jcp.2013.12.042_br0500","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1002\/cnm.1630010305","article-title":"A note on the imposition of traction boundary conditions when using the FEM for solving incompressible flow problems","volume":"1","author":"Taylor","year":"1985","journal-title":"Commun. Appl. Numer. Methods"},{"key":"10.1016\/j.jcp.2013.12.042_br0510","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1017\/S0022112086000976","article-title":"On the formation of vortex streets behind stationary cylinders","volume":"170","author":"Triantafyllou","year":"1986","journal-title":"J. Fluid Mech."},{"key":"10.1016\/j.jcp.2013.12.042_br0520","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/S0168-9274(98)00025-7","article-title":"Numerical solution of problems on unbounded domains: A review","volume":"27","author":"Tsynkov","year":"1998","journal-title":"Appl. Numer. Math."},{"key":"10.1016\/j.jcp.2013.12.042_br0530","doi-asserted-by":"crossref","first-page":"8573","DOI":"10.1016\/j.jcp.2011.08.009","article-title":"An eigen-based high-order expansion basis for structured spectral elements","volume":"230","author":"Zheng","year":"2011","journal-title":"J. Comput. Phys."}],"container-title":["Journal of Computational Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021999113008504?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021999113008504?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2018,10,7]],"date-time":"2018-10-07T19:22:24Z","timestamp":1538940144000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0021999113008504"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,3]]},"references-count":53,"alternative-id":["S0021999113008504"],"URL":"https:\/\/doi.org\/10.1016\/j.jcp.2013.12.042","relation":{},"ISSN":["0021-9991"],"issn-type":[{"value":"0021-9991","type":"print"}],"subject":[],"published":{"date-parts":[[2014,3]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational Physics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jcp.2013.12.042","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2013 Elsevier Inc. All rights reserved.","name":"copyright","label":"Copyright"}]}}