Résolution des équations de Saint-Venant par la méthode des volumes finis non structurés

Authors

  • Yu-e Shi Research Institute for Knowledge Systems P.O. Box 463 6200 AL, Maastricht The Netherlands
  • Kim Dan Nguyen UMR CNRS 6143 « Morphodynamique Continentale et Côtière » Département de Mathématiques et Mécanique Université de Caen, Campus II, Bd. Maréchal Juin BP 5186, F-14032 Caen cedex
  • The Hung Nguyen Institut de Mécanique, 264 Doi Can, Hanoi, Vietnam

DOI:

https://doi.org/10.13052/REMN.16.723-747

Keywords:

Saint-Venant equations, numerical models, unstructured finite-volumes, projection technique

Abstract

This paper presents a resolution of the Saint-Venant equations by a projection method. Using unstructured finite-volumes methods, a 2-D horizontal shallow water numerical model is developed. Two applications with complex bathymetries are reported in this article. The model can be applied to the calculation of river, estuarine and coastal flows.

Downloads

Download data is not yet available.

References

Alcrudo F., Garcia-Navarro P., “A high-resolution Godunov-type scheme in finite volumes

for the 2D shallow-water equations”, Int. J. Numer. Meth. Fluids, vol. 16, n° 6, 1993,

p. 489-505.

Alcrudo F., Gil E., “The malpasset dam break case study”, The Proceeding of the 4th CADAM

meeting, Zaragoza, Spain, 1999. p. 95-109.

Borthwick A.G.L., Karr E.T., “Shallow flow modeling using curvilinear depth-averaged

stream function and vorticity transport equations”, Int. J. Numer. Meth. Fluids, vol. 17,

p. 417-445.

Brufau P., Garcia-Navarro P., Vázquez-Cendón M.E., “Zero mass error using unsteady

wetting-drying conditions in shallow flows over dry irregular topography”, Int. J. Numer.

Meth. Fluids, vol. 45, 2004, p. 1047-1082.

Brufau P., Vázquez-Cendón M.E., García-Navarro P., “A numerical model for the flooding

and drying of irregular domains”, Int. J. Numer. Meth. Fluids, vol. 39, 2002, p. 247-275.

Caleffi V., Valiani A., Bernini A., “Fourth-rder balanced source term treatment in central

WENO schemes for shallow water equations”, J. Comp. Phys, vol. 218, 2006, p. 228-245.

Chan C.T., Anastasiou K., “Solution of incompressible flows with or without a free surface

using the finite volume method on unstructured triangular meshes”, Int. J. Numer. Meth.

Fluids, vol. 29, 1999, p. 35-57.

Chorin A. J., “Numerical solution of the Navier-, n° 1, 2000, p. 35-58, “Stokes equations”.

Math. Comput., vol. 22, n° 104, 1968, p. 745-762.

Chorin A.J., “On the convergence of discrete approximations to the Navier-Stokes equations”

Math. Comput., vol. 23, 1969, p. 341-353.

Fennema R., Chaudry M., “Explicit methods for 2-D transient free-surface flows”,

J. Hydraul. Eng., ASCE, vol. 116, n° 8, 1990, p. 1013-1034.

Garcia-Navarro P., Alcrudo F., “Saviron J.M. 1-D open-channel flow simulation using TVDMcCormack

scheme”, J. Hydraul. Eng., ASCE, vol. 118, n° 10, 1992, p. 1359-1372.

Guillou S., Modélisation des écoulement côtiers et estuariens : étude mathématique et

applications en coordonnes généralisées, Thèse de doctorat, Université Paris VI, 1996.

Guillou S., Nguyen K.D., “An improved technique for solving two-dimensional shallow water

problems”, Int. J. Numer. Meth. Fluids, vol. 29, n° 4, 1999, p. 465-483.

Hanich L., Résolution des équations de la mécanique des fluides par des méthodes TVD en

coordonnées généralisées, Thèse doctorale, Université de Caen, 1996.

Harten A., Engquist B., Osher S., “Chakravarthy S.R. Uniformly high order accurate nonoscillatory

schemes”, J. Comp. Phys, vol. 71, 1987, p. 231.

Hervouet J.M., Petitjean A., “Malpasset dam break revisited with two-dimensional

computations”, Journal of Hydraulic Research, vol. 37, n° 6, 1999, p. 777-788.

Hervouet J.M., “A high resolution 2-D dam-break model using parallelization”, Hydrological

Processes, vol. 14, n° 13, 2000, p. 2211-2230.

Hervouet J.M., Hydrodynamique des écoulements à surface libre: Modélisation numérique

avec la méthode des éléments finis, Paris, Presses de l’Ecole Nationale des Ponts et

Chaussées, 2003.

Kobayashi M.H., Pereira J.M.C., Pereira J.C.F., “A conservative finite-volume second-order

accurate projection method on hybrid unstructured grids”, J. Comp. Phys, vol. 150, n° 1,

, p. 40-75.

Lien F.S., “A pressure-based unstructured grid method for all-speed flows”, Int. J. Numer.

Meth. Fluids, vol. 33, n° 3, 2000, p. 355-374.

Murillo J., Garcia-Navarro P., Brufau P., Burguete J., “Extension of an explicit finite volume

method to large time steps (CFL>1), application to shallow water flows”, Int. J. Numer.

Meth. Fluids, vol. 50, 2005, p. 63-102.

Nguyen V.H., Nguyen V.D., Ngo, H. C., “On some numerical methods for solving the 1-D

Saint-Venant Equations of general flow regime, Part 2: Verification and Application”,

Vietnam Journal of Mechanics, NCST de Vietnam, vol. 25, n° 1, 2003, p. 26-38.

Rhie C.M., Chow W.L, “Numerical study of the turbulent flow past an airfoil with trailing

edge separation”, AIAA J., vol. 21, n° 11, 1983, p. 1525-1532.

Roe P.L., “Approximate Riemann solvers, parameter vectors and difference schemes”,

J. Comp. Phys., vol. 43, n° 2, 1981, p. 357-372.

Ryhming I.L., Dynamique des fluides, Presses Polytechniques et Universitaires Romandes,

Saint-Venant, A.J.C., Théorie du mouvement non-permanent des eaux, avec application aux

crues des rivières et à l’introduction des marées dans leur lit, Compte-Rendu à l’Académie

des Sciences de Paris, vol. 73, 1871, p. 147-154.

Sleigh P.A, Gaskell P.H., Berzins M., Wright N.G., “An unstructured finite-volume algorithm

for predicting flow in rivers and estuaries”, Comput. Fluids, vol. 27, n° 4, 1998, p. 479-508.

Stevens D.E, Chan S. T., Gresho P., “An approximate projection method for incompressible

flow”, Int. J. Numer. Meth. Fluids, vol. 40, 2002, p. 1303-1325.

Tan W., Shallow water hydrodynamics, Amstrerdam, The Netherlands, Elsevier, 1992.

Tannehill J.C., Anderson D.A., Pletcher R.H., Computational Fluid Mechanics and Heat

Transfer, Chapter IV “Application of Numerical Methods to Selected Model Equations”,

nd Edition, Taylor & Francis, Washington D.C., p. 156-158, 1997.

Temam R., “Une méthode d’approximation de la solution des équations Navier-Stokes”, Bull.

Soc. Math. France, vol. 98, n° 4, 1968, p. 115-152.

Temam R., Navier-Stokes Equations, North-Holland, Amsterdam, 1977.

Valiani A., Caleffi V., Zanni A., “Case study: Malpasset dam-break simulation using a twodimensional

finite volume method”, J. Hydraul. Eng., ASCE, vol. 128, n° 5, 2002, p. 460-

Van Leer B., “Towards the ultimate conservative difference scheme, IV, A new approach to

numerical convection”, J. Comp. Phys, vol. 23, n° 3, 1977, p. 276-299.

Vukovic S, Sopta L., “ENO and WENO schemes with the exact conservation property for

one-dimensional shallow water equations”, J. Comp. Phys, vol. 179, n° 2, 2002, p. 593-

Zhao D.H., Shen H.W., Tabious G.Q., Lai J.S., Tan W.Y., “Finite-volume two-dimensional

unsteady-flow model for river basin”, J. Hydraul. Eng., ASCE, vol. 120, n° 7, 1994,

p. 864-883.

Zhou J.G., Causon D.M., Mingham C.G., Ingram D.M., “The surface gradient method for the

treatment of source terms in the shallow-water equations”, J. Comp. Phys, vol. 168, n° 1,

, p. 1-25.

Downloads

Published

2007-10-18

How to Cite

Shi, Y.- e ., Nguyen, K. D. ., & Nguyen, T. H. . (2007). Résolution des équations de Saint-Venant par la méthode des volumes finis non structurés. European Journal of Computational Mechanics, 16(6-7), 723–747. https://doi.org/10.13052/REMN.16.723-747

Issue

Section

Original Article