{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T02:08:38Z","timestamp":1775786918057,"version":"3.50.1"},"reference-count":26,"publisher":"Elsevier BV","issue":"1","license":[{"start":{"date-parts":[[2003,2,1]],"date-time":"2003-02-01T00:00:00Z","timestamp":1044057600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Non-Newtonian Fluid Mechanics"],"published-print":{"date-parts":[[2003,2]]},"DOI":"10.1016\/s0377-0257(02)00191-x","type":"journal-article","created":{"date-parts":[[2003,2,17]],"date-time":"2003-02-17T19:46:16Z","timestamp":1045511176000},"page":"45-75","source":"Crossref","is-referenced-by-count":230,"title":["Benchmark solutions for the flow of Oldroyd-B and PTT fluids in planar contractions"],"prefix":"10.1016","volume":"110","author":[{"given":"Manuel A.","family":"Alves","sequence":"first","affiliation":[]},{"given":"Paulo J.","family":"Oliveira","sequence":"additional","affiliation":[]},{"given":"Fernando T.","family":"Pinho","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0377-0257(02)00191-X_BIB1","unstructured":"O. Hassager, Working Group on Numerical Techniques, in: Proceedings of the Vth Workshop on Numerical Methods in Non-Newtonian Flow, J. Non-Newtonian Fluid Mech. 29 (1988) 2\u20135."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB2","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/0377-0257(94)85032-1","article-title":"Report on VIIIth International Workshop on Numerical Methods in Viscoelastic Flows","volume":"52","author":"Brown","year":"1994","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB3","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/S0377-0257(98)00154-2","article-title":"Galerkin\/least square finite-element methods for steady viscoelastic flows","volume":"84","author":"Fan","year":"1999","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB4","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/S0377-0257(00)00198-1","article-title":"The flow of viscoelastic fluids past a cylinder: finite-volume high-resolution methods","volume":"97","author":"Alves","year":"2001","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB5","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/S0377-0257(99)00065-8","article-title":"Viscoelastic flow through a planar contraction using a semi-Lagrangian finite volume method","volume":"87","author":"Phillips","year":"1999","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB6","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/S0377-0257(00)00121-X","article-title":"Effect of a high-resolution differencing scheme on finite-volume predictions of viscoelastic flows","volume":"93","author":"Alves","year":"2000","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB7","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/S0377-0257(00)00196-8","article-title":"A cell-vertex finite volume\/element method on triangles for abrupt contraction viscoelastic flows","volume":"98","author":"Aboubacar","year":"2001","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB8","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/S0377-0257(01)00164-1","article-title":"Highly elastic solutions for Oldroyd-B and Phan-Thien\/Tanner fluids with a finite volume\/element method: planar contraction flows","volume":"103","author":"Aboubacar","year":"2002","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB9","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/0377-0257(95)01358-3","article-title":"The experimental observation and numerical prediction of planar entry flow and die swell for molten polyethylenes","volume":"59","author":"Ahmed","year":"1995","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB10","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.1122\/1.550725","article-title":"Use of coupled birefringence and LDV studies of flow through a planar contraction to test constitutive equations for concentrated polymer solutions","volume":"39","author":"Quinzani","year":"1995","journal-title":"J. Rheol."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB11","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/S0377-0257(97)00129-8","article-title":"Spatially resolved stress birefringence and flow visualization in flow instabilities of a polydimethylsiloxane extruded through a slit die","volume":"77","author":"Legrand","year":"1998","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB12","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/S0377-0257(99)00017-8","article-title":"Plane contraction flows of upper convected Maxwell and Phan-Thien\/Tanner fluids as predicted by a finite-volume method","volume":"88","author":"Oliveira","year":"1999","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB13","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/0377-0257(77)80021-9","article-title":"A new constitutive equation derived from network theory","volume":"2","author":"Phan-Thien","year":"1977","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB14","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1122\/1.549481","article-title":"A nonlinear network viscoelastic model","volume":"22","author":"Phan-Thien","year":"1978","journal-title":"J. Rheol."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0377-0257(98)00082-2","article-title":"Numerical simulation of non-linear elastic flows with a general collocated finite-volume method","volume":"79","author":"Oliveira","year":"1998","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB16","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1002\/fld.428","article-title":"A convergent and universally bounded interpolation scheme for the treatment of advection","volume":"41","author":"Alves","year":"2003","journal-title":"Int. J. Numer. Meth. Fluids"},{"key":"10.1016\/S0377-0257(02)00191-X_BIB17","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1002\/fld.1650080602","article-title":"Curvature-compensated convective transport: SMART, a new boundedness preserving transport algorithm","volume":"8","author":"Gaskell","year":"1988","journal-title":"Int. J. Numer. Meth. Fluids"},{"key":"10.1016\/S0377-0257(02)00191-X_BIB18","doi-asserted-by":"crossref","first-page":"940","DOI":"10.1115\/1.2791802","article-title":"Representation of Stokes flow through a planar contraction by Papkovich\u2013Fadle eigenfunctions","volume":"66","author":"Rogerson","year":"1999","journal-title":"J. Appl. Mech."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB19","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/0377-0257(93)80029-B","article-title":"The flow of an Oldroyd-B fluid around a sharp corner","volume":"50","author":"Hinch","year":"1993","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB20","doi-asserted-by":"crossref","unstructured":"M.A. Alves, P.J. Oliveira, F.T. Pinho, Numerical simulations of viscoelastic flow around sharp corners, in: Computational Fluid and Solid Mechanics, Elsevier, Amsterdam, 2001, pp. 772\u2013775.","DOI":"10.1016\/B978-008043944-0\/50766-6"},{"key":"10.1016\/S0377-0257(02)00191-X_BIB21","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/S0377-0257(01)00186-0","article-title":"Viscoelastic contraction flows: comparison of axisymmetric and planar configurations","volume":"102","author":"Nigen","year":"2002","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB22","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/S0377-0257(96)01506-6","article-title":"Re-entrant corner behavior of the PTT fluid","volume":"69","author":"Renardy","year":"1997","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB23","unstructured":"R.I. Tanner, A. Jabbarzadeh, S.-C. Xue, Computations at sharp corners, in: proceedings of the XIIIth International Congress on Rheology, vol. 2, Cambridge, 2000, pp. 181\u2013183."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB24","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/0377-0257(94)80055-3","article-title":"Flow characteristics of viscoelastic fluids in an abrupt contraction by using numerical modeling","volume":"52","author":"Saramito","year":"1994","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB25","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/0377-0257(84)80049-X","article-title":"Numerical simulation of the flow of a viscoelastic fluid through an abrupt contraction","volume":"14","author":"Keunings","year":"1984","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"10.1016\/S0377-0257(02)00191-X_BIB26","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1017\/S002211209900453X","article-title":"Analytical solution for fully developed channel and pipe flow of Phan-Thien\u2013Tanner fluids","volume":"387","author":"Oliveira","year":"1999","journal-title":"J. Fluid Mech."}],"container-title":["Journal of Non-Newtonian Fluid Mechanics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S037702570200191X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S037702570200191X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,3,27]],"date-time":"2019-03-27T10:52:33Z","timestamp":1553683953000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S037702570200191X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,2]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2003,2]]}},"alternative-id":["S037702570200191X"],"URL":"https:\/\/doi.org\/10.1016\/s0377-0257(02)00191-x","relation":{},"ISSN":["0377-0257"],"issn-type":[{"value":"0377-0257","type":"print"}],"subject":[],"published":{"date-parts":[[2003,2]]}}}