The computation unsteady flow in a pressurized hydraulic systempresents many difficulties as well on the practical level as theoretical. In this work, a numerical approach based on the finite volumes method is presented for the simulation of water hammer problems. After having presented the hyperbolic differential equations governing the elastic wave propagation, the discretization details of the mathematical model meaning Godunov scheme are given as well as the integration of the source term and the implementation of the boundary conditions where an approach in excentred grid is introduced. The application treats a case of pumping station protected by a throttled air vessel. The results are analyzed and compared with those obtained in experiments and also numerically by the method of the characteristics. The finite volume numerical model gave very satisfactory results compared to the method of the characteristics and where congruence with experimental measurements is appreciable.



water hammer, numerical computation, finite volume method, Godunov scheme, air vessel

Full Text:

PDF (Français)


AFSHAR M. H., ROHANI M. (2008): "Water hammer simulation by implicit method of characteristic". International Journal of Pressure vessels and piping, 85: 851-859.

AMARA, L., ACHOUR, B., BERREKSI, A. (2013): "Approche numérique aux volumes finis pour le calcul de la réponse dynamique des cheminées d’équilibre". LARHYSS Journal, 14 : 7-19.

BERGERON, L. (1949) : "Du coup de bélier en hydraulique au coup de foudre en électricité. Méthode graphique générale". Dunod, Paris.

CHAUDHRY, M. H. (1979) : "Applied hydraulic transients". Van Nostrand.

CHAUDHRY, M. H., BHALLAMUDI, S.M., MARTIN, C.S., NAGHASH, M. (1990): "Analysis of Transient Pressures in Bubbly, Homogeneous, Gas-Liquid Mixtures". Journal of Fluids Engineering, ASME 112: 225–231.

CHAUDHRY, M. H., HUSSAINI, M. Y. (1985): "Second-Order Accurate Explicit Finite-Difference Schemes for Water Hammer Analysis". Journal of Fluids Engineering, ASME 107: 523–529.

DE ALMEIDA, B., KOELLE, E. (1992) : "Fluid transients in pipe networks". Computational Mechanics Publications, Elsevier Applied Science, Glasgow.

GHIDAOUI, M. S., ZHAO, M., MCLNNIS, D. A., AXWORTH, D. H. (2005): "A review of Water hammer Theory and Practice". Transactions of the ASME 58: 49-76.

GUINOT, V. (2003): "Godunov-type schemes: an introduction for engineers". Elsevier Science B.V.

GUINOT, V. (2008): "Wave Propagation in Fluids : Models and numerical techniques". ISTE Ltd and John Wiley & Sons, Inc.

LEÓN S. A. (2007): "Improved modeling of unsteady free surface, pressurized and mixed flows in storm-sewer systems". Thèse de Doctorat de Philosophie (Ph.D) en Génie civil, Université d’Illinois.

LEVEQUE, J. (2002): "Finite Volume Methods for Hyperbolic Problems". Cambridge University Press, Cambridge.

PURCELL, P. J. (1997): "Case Study of Check-Valve Slam in Rising Main Protected by Air Vessel". Journal of Hydraulic Engineering, ASCE, 123(12): 1166-1168.

TORO ELEUTERIO, F., GARCIA-NAVARRO, P. (2007): "Godunov-type methods for free-surface shallow flows: A review". Journal of Hydraulic Research, 45(6): 736-751.

TORO, E. F. (2009): "Riemann Solvers and Numerical Methods for Fluid Dynamics, A Pratical Introduction". Troisième édition, Springer-Verlag.

WANG, C. ET YANG, J.D. 2014: "Water Hammer Simulation Using Explicit–Implicit Coupling Methods". Journal of Hydraulic Engineering, ASCE, (11) : 1-11.

WYLIE, E. B., STREETER, V. L. (1978): "Fluid transients". MacGraw-Hill.

ZHAO, M., GHIDAOUI, M. S. (2004): "Godunov-type solutions for water hammer flows". Journal of Hydraulic Engineering, ASCE 130(4): 341-348.


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.