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RESEARCH PAPERS

Analytical treatment of source terms for complex channel geometry

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Pages 753-763 | Received 13 May 2008, Published online: 26 Apr 2010

References

  • Aureli , F. , Mignosa , P. and Tomirotti , M. 2000 . Numerical simulation and experimental verification of dam-break flows with shocks . J. Hydr. Res. , 38 ( 3 ) : 197 – 206 .
  • Capart , H. , Eldho , T. I. , Huang , S. Y. , Young , S. Y. and Zech , Y. 2003 . Treatment of natural geometry in finite volume river flow computations . J. Hydr. Engng. , 129 ( 5 ) : 385 – 393 .
  • Cunge , J. A. , Holly , F. M. Jr. and Verwey , A. 1980 . Practical Aspects of Computational River Hydraulics , London, , UK : Pitman .
  • Delis , A. I. , Skeels , A. I. and Ryrie , S. C. 2000 . Evaluation of some approximate Riemann solvers for transient open channel flows . J. Hydr. Res. , 38 ( 3 ) : 217 – 231 .
  • de Saint-Venant , B. 1871 . Theorie du movement non permanent des eaux, avec application aux crues de rivieras et a l'introduction des marces dans leur lit . Comptes Rendus de l'Academic des Sciences , 73 : 147 – 154 . 237 – 240 .
  • Einstein , H. A. 1934 . Der hydraulische oder Profil-Radius . Schweizerische Bauzeitung , 103 ( 8 ) : 89 – 91 . [in German]
  • Engelund , F. Flow resistance and hydraulic radius . Tech. Univ. Denmark, Basic Research Report 6 . pp. 3 – 4 .
  • Fennema , R. J. and Chaudhry , M. H. 1986 . Explicit numerical schemes for unsteady free-surface flows with shocks . Water Resour. Res. , 22 ( 13 ) : 1923 – 1930 .
  • Garcia-Navarro , P. , Alcrudo , F. and Savirón , J. M. 1992 . 1-D openchannel flow simulation using TVD-McCormack scheme . J. Hydr. Engng. , 118 ( 10 ) : 1359 – 1371 .
  • Garcia-Navarro , P. and Vazquez-Cendon , M. E. 2000 . On numerical treatment of the source terms in the shallow water equations . Comput. Fluids , 29 ( 8 ) : 951 – 979 .
  • Glaister , P. 1993 . Flux difference splitting for open-channel flows . Intl. J. Numer. Meth. Fluids , 16 : 629 – 654 .
  • Goutal , N. and Maurel , F. 1997 . “ Dam-break wave simulation ” . In Direction des études et recherches , Paris, , France : Electricité de France . Rep. HE43/97/016/B
  • Hirsch , C. 1990 . Numerical Computation of Internal and External Flows Wiley, New York
  • Horton , R. A. 1933 . Separate roughness coefficients for channel bottom and sides . Engng. News Record , 111 ( 22 ) : 652 – 653 .
  • Jaeger , C. 1961 . Engineering Fluid Mechanics , London, , UK : Blackie and Sons .
  • Keulegan , G. H. 1938 . Laws of turbulent flow in open channels . J. Res. National Bureau of Standards , 21 : 707 – 741 .
  • Lai , C. 1986 . “ Numerical modelling of unsteady open-channel flow ” . In Advances in Hydroscience , Vol. 14 , 161 – 333 . New York, NY : Academic Press .
  • Lai , C. , Baltzer , R. A. and Schaffranek , R. W. 2002 . Conservationform equations of unsteady open-channel flow . J. Hydr. Res. , 40 ( 5 ) : 567 – 578 .
  • Lax , P. D. and Wendroff , B. 1960 . System of conservation laws . Com. Pure Applied Math. , 13 : 217 – 237 .
  • LeVeque , R. J. 1990 . Numerical methods for conservation laws , EHT Lectures in Mathematics Series Basel
  • MacCormack , R. W. 1969 . The effect of viscosity in hypervelocity impact cratering , 69 – 354 . Cincinnati, Ohio : Amer. Institute of Aeronautics and Astronautics paper .
  • Manning , R. 1891 . On the flow of water in open channels and pipes . Trans. Inst. of Civil Engrs. Ireland , 20 : 161 – 207 .
  • Marchi , E. 1961 . Il moto uniforme delle correnti liquide nei condotti chiusi e aperti . L–Energia Elettrica , 38 ( 4–5 ) : 289 – 301 . [in Italian]
  • Meselhe , E. A. , Sotiropoulos , F. and Holly , F. M. Jr. 1997 . Numerical simulation of transcritical flow in open channels . J. Hydr. Engng. , 123 ( 9 ) : 774 – 783 .
  • Moretti , G. 1979 . The lambda scheme . Comput. Fluids , 7 : 191 – 205 .
  • Nujić , M. 1995 . Efficient implementation of non-oscillatory schemes for the computation of free-surface flows . J. Hydr. Res. , 33 ( 1 ) : 101 – 111 .
  • Preissmann , A. and Cunge , J. 1961 . Calcul du mascaret sur machines électroniques . La Houille Blanche , 16 ( 5 ) : 588 – 596 . [in French]
  • Sanders , B. F. 2001 . High-resolution and non-oscillatory solution of the St. Venant equations in non-rectangular and non-prismatic channels . J. Hydr. Res. , 39 ( 3 ) : 321 – 330 .
  • Strickler , A. 1923 . Beiträge zur Frage der Geschwindigkeitsformel und der Rauhigkeitszahlen für Ströme, Kanäle und geschlossene Leitungen , Mitteilung 16 Bern, , Switzerland : Eidgenössisches Amt für Wasserwirtschaft . [in German]
  • 1984 . High resolution schemes using flux limiters for hyperbolic conservation laws . SIAM J. Numer. Anal. , 21 ( 5 ) : 995 – 1011 .
  • Toro , E. F. 1999 . Riemann Solvers and Numerical Methods for Fluid Dynamics , Berlin : Springer .
  • Toro , E. F. 2001 . Shock-Capturing Methods for Free-Surface Shallow Flows , New York : Wiley .
  • Valiani , A. , Schippa , L. and Bondoli , L. On the source terms treatment in 1D natural rivers simulation . Proc. 3rd Intl. ISEH and IAHR Symp. Environmental Hydraulics, Paper 454 . pp. 1 – 6 . Tempe, , USA : Arizona State University .
  • Valiani , A. , Caleffi , V. and Zanni , A. 2002 . Case study: Malpasset dam-break simulation using a 2D finite volume method . J. Hydr. Engng. , 128 ( 5 ) : 460 – 472 .

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