A robust two-equation model for transient-mixed flows

References

• Arai , K. and Yamamoto , K. Transient analysis of mixed free-surface-pressurized flows with modified slot model 1: Computational model and experiment . Proc. 4th ASME-JSME Joint Fluids Engrg. Conf. Honolulu, HW (CD-ROM)
   Google Scholar
• Bourdarias , C. and Gerbi , S. 2007 . A finite volume scheme for a model coupling free surface and pressurised flows in pipes . J. Comput. Appl. Math. , 209 ( 1 ) : 109 – 131 .
   Web of Science ®Google Scholar
• Bryson , A. E. 1964 . “ Waves in fluids. Videorecording presented by National Committee for Fluid Mechanics Films ” . Chicago IL Encyclopedia Britannica Educational Corporation . Produced by Educational Services
   Google Scholar
• Capart , H. , Sillen , X. and Zech , Y. 1997 . Numerical and experimental water transients in sewer pipes . J. Hydraulic Res. , 35 ( 5 ) : 659 – 672 .
   Web of Science ®Google Scholar
• Cardle , J. A. 1984 . “ An investigation of hydraulic transients in combination of free surface and pressurized flows ” . Twin Cities, MN : Department of Civil and Mineral Engineering, University of Minnesota . PhD thesis
   Google Scholar
• Cardle , J. A. and Song , C. C.S. 1988 . Mathematical modeling of unsteady flow in storm sewers . Int. J. Eng. Fluid Mech. , 1 ( 4 ) : 495 – 518 .
   Web of Science ®Google Scholar
• Cardle , J. A. , Song , C. C.S. and Yuan , M. 1989 . Measurements of mixed transient flows . J. Hydraul. Eng. , 115 ( 2 ) : 169 – 182 .
   Web of Science ®Google Scholar
• Guinot , V. 2003 . Godunov-type schemes , Amsterdam, NL : Elsevier .
   Google Scholar
• Hamam , M. A. and McCorquodale , J. A. 1982 . Transient conditions in the transition from gravity to surcharged sewer flow . Can. J. Civ. Eng. , 9 ( 2 ) : 189 – 196 .
   Web of Science ®Google Scholar
• León , A. S. 2006 . “ Improved modeling of unsteady free surface, pressurized and mixed flows in storm-sewer systems ” . In PhD thesis , Urbana, IL : Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign .
   Google Scholar
• León , A. S. and Ghidaoui , M. S. 2010 . Discussion of numerical oscillations in pipe-filling bore predictions by shock-capturing models . J. Hydraul. Eng. , in press
   Web of Science ®Google Scholar
• León , A. S. , Ghidaoui , M. S. , Schmidt , A. R. and García , M. H. 2006 . Godunov-type solutions for transient flows in sewers . J. Hydraul. Eng. , 132 ( 8 ) : 800 – 813 .
   Web of Science ®Google Scholar
• León , A. S. , Ghidaoui , M. S. , Schmidt , A. R. and García , M. H. 2007 . “ An efficient finite-volume scheme for modeling water hammer flows ” . In Contemporary modeling of urban water systems 15 , Edited by: James , W. 411 – 430 . Toronto, , Canada : CHI .
   Google Scholar
• León , A. S. , Ghidaoui , M. S. , Schmidt , A. R. and García , M. H. 2008 . An efficient second-order accurate shock capturing scheme for modeling one and two-phase waterhammer flows . J. Hydraul. Eng. , 134 ( 7 ) : 970 – 983 .
   Web of Science ®Google Scholar
• León , A. S. , Ghidaoui , M. S. , Schmidt , A. R. and García , M. H. 2009 . Application of Godunov-type schemes to transient mixed flows . J. Hydraulic Res. , 47 ( 2 ) : 147 – 156 .
   Web of Science ®Google Scholar
• León , A. S. , Liu , X. , Ghidaoui , M. S. and García , M. H. 2010 . A junction and drop-shaft boundary conditions for modeling free surface, pressurized, and mixed free surface-pressurized transient flows . J. Hydraul. Eng. , tentatively accepted
   Web of Science ®Google Scholar
• LeVeque , R. J. 2002 . Finite volume methods for hyperbolic problems , Cambridge, , UK : Cambridge Press .
   Google Scholar
• Martin , C. S. Entrapped air in pipelines . Proc. 2nd Intl. Conf. Pressure Surges . pp. 15 – 28 . British Hydromechanics Research Association Cranfield UK .
   Google Scholar
• Nujic , M. 1995 . Efficient implementation of non-oscillatory schemes for the computation of free-surface flows . J. Hydraulic Res. , 33 ( 1 ) : 101 – 111 .
   Web of Science ®Google Scholar
• Politano , M. , Odgaard , A. J. and Klecan , W. 2007 . Case study: Numerical evaluation of hydraulic transients in a combined sewer overflow tunnel system . J. Hydraul. Eng. , 133 ( 10 ) : 1103 – 1110 .
   Web of Science ®Google Scholar
• Sanders , B. F. 2001 . High-resolution and non-oscillatory solution of the St Venant equations in non-rectangular and non-prismatic channels . J. Hydraulic Res. , 39 ( 3 ) : 321 – 330 .
   Web of Science ®Google Scholar
• Song , C. C.S. , Cardle , J. A. and Leung , K. S. 1983 . Transient mixed-flow models for storm sewers . J. Hydraul. Eng. , 109 ( 11 ) : 1487 – 1503 .
   Web of Science ®Google Scholar
• Toro , E. F. 2001 . Shock-capturing methods for free-surface shallow flows , Chichester, , UK : Wiley .
   Google Scholar
• Trajkovic , B. , Ivetic , M. , Calomino , F. and D'Ippolito , A. 1999 . Investigation of transition from free surface to pressurized flow in a circular pipe . Water Sci. Technol. , 39 ( 9 ) : 105 – 112 .
   Web of Science ®Google Scholar
• Vasconcelos , J. G. 2005 . “ Dynamic approach to the description of flow regime transition in stormwater systems ” . In PhD thesis , Ann Arbor, MI : Department of Civil and Environmental Engineering, University of Michigan .
   Google Scholar
• Vasconcelos , J. G. , Wright , S. J. and Roe , P. L. 2006 . Improved simulation of flow regime transition in sewers: Two-component pressure approach . J. Hydraul. Eng. , 132 ( 6 ) : 553 – 562 .
   Web of Science ®Google Scholar
• Wang , K-H. , Shen , Q. and Zhang , B. 2003 . Modeling propagation of pressure surges with the formation of an air pocket in pipelines . Comput. Fluids. , 32 ( 9 ) : 1179 – 1194 .
   Web of Science ®Google Scholar
• Yen , B. C. 1991 . “ Hydraulic resistance in open channels ” . In Channel flow resistance: Centennial of Manning's formula , 1 – 135 . Littleton CO, , USA : Water Resources Publications .
   Google Scholar
• Yuan , M. 1984 . “ Pressurized surges ” . Twin Cities, MN : Department of Civil and Mineral Engineering, University of Minnesota . MSc thesis
   Google Scholar
• Zhou , F. 2000 . “ Effects of trapped air on flow transients in rapidly filling sewers ” . Edmonton, CA : Department of Civil and Environmental Engineering, University of Alberta . PhD thesis
   Google Scholar
• Zhou , F. , Hick , F. E. and Steffler , P. M. 2002 . Observations of air–water interaction in a rapidly filling horizontal pipe . J. Hydraul. Eng. , 128 ( 6 ) : 635 – 639 .
   Web of Science ®Google Scholar