Adaptation of Preissmann's scheme for transcritical open channel flows

References

• Alcrudo, F. (2002). A state-of-the-art review on mathematical modelling of flood propagation. 1st project workshop IMPACT, Wallingford, UK.
   Google Scholar
• Baume, J.-P., Malaterre, P.-O., Belaud, G., Le Guennec, B. (2005). SIC: A 1D hydrodynamic model for river and irrigation canal modeling and regulation. Métodos numéricos em recursos hidricos 7, 1–81 (R.C.V. da Silva, ed. Evangraf, Porto Alegre BR).
   Google Scholar
• Burguete , J. and Garcia-Navarro , P. 2004 . Implicit schemes with large time step for non-linear equations: Application to river flow hydraulics . Int. J. Numer. Meth. Fluids , 46 ( 6 ) : 607 – 636 .
   Web of Science ®Google Scholar
• Cunge , J. , Holly , F.M. and Verwey , A. 1980 . Practical aspects of computational river hydraulics , London : Pitman .
   Google Scholar
• Delis , A. I. 2003 . Improved application of the HLLE Riemann solver for the shallow-water equations with source terms . Comm. Num. Meth. Engng. , 19 ( 1 ) : 59 – 83 .
   Web of Science ®Google Scholar
• Djordjevic , S. , Prodanovic , D. and Walters , G. A. 2004 . Simulation of transcritical flow in pipe/channel networks . J. Hydraulic Engng , 130 ( 12 ) : 1167 – 1178 .
   Web of Science ®Google Scholar
• Godlewski , E. and Raviart , P.-A. 1991 . Hyperbolic systems of conservation laws. Mathématiques & Applications , Ellipses, , Paris : SMAI . (3/4)
   Google Scholar
• Guinot , V. 2003 . Godunov-type schemes: An introduction for engineers , Amsterdam, NL : Elsevier .
   Google Scholar
• Harten , A. 1983 . High resolution schemes for hyperbolic conservation laws . J. Comput. Phys. , 49 ( 3 ) : 357 – 393 .
   Web of Science ®Google Scholar
• Jiang , G. and Tadmor , E. 1998 . Non-oscillatory central schemes for multi-dimensional hyperbolic conservation laws . SIAM J. Sci. Comp. , 19 : 1892 – 1917 .
   Web of Science ®Google Scholar
• Johnson , T. , Baines , M. J. and Sweby , P. K. 2002 . A box scheme for transcritical flow . Int. J. Num. Meth. Engng , 55 : 895 – 912 .
   Web of Science ®Google Scholar
• Kutija , V. 1994 . On the numerical modelling of supercritical flows . J. Hydraulic Res , 31 ( 6 ) : 841 – 858 .
   Web of Science ®Google Scholar
• van Leer , B. 1984 . On the relation between the upwind-differencing schemes of Godunov, Engquist-Osher and Roe . SIAM J. Sci. Stat. Comput. , 5 ( 1 ) : 1 – 20 .
   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
• Liu , J. , Glimm , J. and Li , X. 2004 . “ A conservative front tracking method. Proc. 10th Intl. Conf ” . In Hyperbolic Problems: Theory, Numerics and Applications , Osaka, JP : Yokohama Publishers . 57–62
   Google Scholar
• MacDonald , I. 1996 . “ Analysis and computation of steady open channel flow ” . In PhD thesis , Reading, , UK : University of Reading .
   Google Scholar
• Meselhe , E. A. and Holly , F.M. 1997 . Invalidity of Preissmann scheme for transcritical flow . J. Hydraulic Engng , 123 ( 7 ) : 652 – 655 .
   Web of Science ®Google Scholar
• Mignot , E. , Paquier , A. and Rivière , N. 2008 . Experimental and numerical modeling of symmetrical four-branch supercritical cross-junction flow . J. Hydraulic Res , 46 ( 6 ) : 723 – 738 .
   Web of Science ®Google Scholar
• Morton , K. W. , Rudgyard , M. A. and Shaw , G. J. 1994 . Upwind iteration methods for cell vertex scheme in one dimension . J. Comput Phys , 114 ( 2 ) : 209 – 226 .
   Web of Science ®Google Scholar
• Paquier , A. 1996 . “ Validity of 1D model for simulating dam-break wave ” . In Hydroinformatics 96 Zurich 409–416
   Google Scholar
• Roe , P. L. 1981 . Approximate Riemann solvers, parameter vectors, and difference schemes . J. Comput. Phys , 43 ( 2 ) : 357 – 372 .
   Web of Science ®Google Scholar
• Toro , E. F. and Billett , S. J. 2000 . Centered TVD-schemes for hyperbolic conservation laws . IMA J. Numerical Analysis , 20 ( 1 ) : 47 – 79 .
   Web of Science ®Google Scholar
• Toro , E. F. and Garcia-Navarro , P. 2007 . Godunov-type methods for free-surface shallow flows: A review . J. Hydraulic Res. , 45 ( 6 ) : 736 – 751 .
   Web of Science ®Google Scholar
• Ying , X. and Wang , S. S.Y. 2008 . Improved implementation of the HLL approximate Riemann solver for one-dimensional open channel flows . J. Hydraulic Res , 46 ( 1 ) : 21 – 34 .
   Web of Science ®Google Scholar
• Zoppou , C. and Roberts , S. 2003 . Explicit schemes for dam-break simulations . J. Hydraulic Engng , 129 ( 1 ) : 11 – 34 .
   Web of Science ®Google Scholar