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Kerger, F.; Archambeau, P.; Erpicum, S.; Dewals, B. J.; Pirotton, M.

An exact Riemann solver and a Godunov scheme for simulating highly transient mixed flows. (English) Zbl 1350.76038

J. Comput. Appl. Math. 235, No. 8, 2030-2040 (2011).
Summary: The current research aims at deriving a one-dimensional numerical model for describing highly transient mixed flows. In particular, this paper focuses on the development and assessment of a unified numerical scheme adapted to describe free-surface flow, pressurized flow and mixed flow (characterized by the simultaneous occurrence of free-surface and pressurized flows). The methodology includes three steps. First, the authors derived a unified mathematical model based on the Preissmann slot model. Second, a first-order explicit finite volume Godunov-type scheme is used to solve the set of equations. Third, the numerical model is assessed by comparison with analytical, experimental and numerical results. The key results of the paper are the development of an original negative Preissmann slot for simulating sub-atmospheric pressurized flow and the derivation of an exact Riemann solver for the Saint-Venant equations coupled with the Preissmann slot.

Cited in 8 Documents

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs

Keywords:

hydraulics; finite volume method; negative preissmann slot; Saint-Venant equations; transient flow; water hammer
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References:

[1] Guo, Q.; Song, C., Surging in urban storm drainage systems, Journal of Hydraulic Engineering, 116, 12, 1523-1537 (1990)
[2] Zhou, F.; Hicks, F. E.; Steffler, P. M., Transient flow in a rapidly filling horizontal pipe containing trapped air, Journal of Hydraulic Engineering, 128, 6, 625-634 (2002)
[3] Guo, Q.; Song, C., Dropshaft hydrodynamics under transient conditions, Journal of Hydraulic Engineering, 117, 8, 1042-1055 (1991)
[4] Vasconcelos, J.; Wright, S., Experimental investigation of surges in a stormwater storage tunnel, Journal of Hydraulic Engineering, 131, 10, 853-861 (2005)
[5] Wiggert, D., Transient flow in free-surface, pressurized systems, Journal of the Hydraulics Division, Proceedings of the American Society of Civil Engineers, 98, 1, 11-26 (1972)
[6] Cardle, J.; Song, C., Mathematical modeling of unsteady flow in storm sewers, International Journal of Engineering Fluid Mechanics, 1, 4, 495-518 (1988)
[7] Politano, M.; Odgaard, A. J.; Klecan, W., Numerical evaluation of hydraulic transients in a combined sewer overflow tunnel system, Journal of Hydraulic Research, 133, 10, 1103-1110 (2007)
[8] Li, J.; McCorquodale, A., Modeling mixed flow in storm sewers, Journal of Hydraulic Engineering, 125, 11, 1170-1180 (1999)
[9] A. Preismann, Propagation des intumescences dans les canaux et rivieres, in: First Congress of the French Association for Computation, Grenoble, France, 1961.; A. Preismann, Propagation des intumescences dans les canaux et rivieres, in: First Congress of the French Association for Computation, Grenoble, France, 1961.
[10] Vasconcelos, J.; Wright, S.; Roe, P. L., Improved simulation of flow regime transition in sewers: the two-component pressure approach, Journal of Hydraulic Engineering, 132, 6, 553-562 (2006)
[11] Bourdarias, C.; Gerbi, S., A finite volume scheme for a model coupling free surface and pressurized flows in pipes, Journal of Computational and Applied Mathematics, 209, 109-131 (2007) · Zbl 1135.76036
[12] Bourdarias, C.; Gerbi, S.; Gisclon, M., A kinetic formulation for a model coupling free surface and pressurized flows in closed pipes, Journal of Computational and Applied Mathematics, 218, 2, 522 (2008) · Zbl 1152.76020
[13] Arora, M.; Roe, P. L., On postshock oscillations due to shock capturing schemes in unsteady flows, Journal of Computational Physics, 130, 25-40 (1997) · Zbl 0869.76050
[14] Garcia-Navarro, P.; Alcrudo, F.; Priestley, A., An implicit method for water flow modelling in channels and pipes, Journal of Hydraulic Research, 32, 5, 721-742 (1994)
[15] Leon, A.; Ghidaoui, M.; Schmidt, A.; Garcia, M., Godunov-type solutions for transient flows in sewers, Journal of Hydraulic Engineering, 132, 8, 800-813 (2006)
[16] Cunge, J. A.; Holly, F. M.; Verwey, A., (Practical Aspects of Computational River Hydraulics. Practical Aspects of Computational River Hydraulics, Monographs and Surveys in Water Resources Engineering, vol. 3 (1980), Pitman Advanced Pub. Program: Pitman Advanced Pub. Program Boston)
[17] Wylie, E. B.; Streeter, V. L., Fluid Transients (1978), M.-H. Inc., p. 385
[18] Toro, F. E., Shock-Capturing Methods for Free-Surface Shallow Flows (2000), John Wiley and Sons Ltd.: John Wiley and Sons Ltd. Chichester, NY, Weinheim, Brisbane, Singapore, Toronto, p. 310
[19] Leveque, R. J., (Finite Volume Methods for Hyperbolic Problems. Finite Volume Methods for Hyperbolic Problems, Cambridge Texts in Applied Mathematics (2002), Cambridge University Press: Cambridge University Press Cambridge), 540 · Zbl 1010.65040
[20] Glaister, P., Approximate Riemann solutions of the shallow water equations, Journal of Hydraulic Research, 26, 3, 293-306 (1988)
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