Abstract
The so-called mixed flows in pipes include two-phase stratified regimes as well as single-phase pressurized regimes with transitions. It is proposed to handle those configurations numerically with the compressible two-layer model developed in [7]. Thus, a fractional step method is proposed to deal explicitly with the slow propagation phenomena and implicitly with the fast ones. It results in a large time-step scheme accurate in both regimes. Numerical experiments are performed including convergence results and academical test cases.
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References
Bourdarias, C., Gerbi, S.: A finite volume scheme for a model coupling free surface and pressurised flows in pipes. J. Comput. Appl. Math. 209, 1–47 (2007)
Chalons, C., Coquel, F., Kokh, S., Spillane, N.: Large time-step numerical scheme for the seven-equation model of compressible two-phase flows. Springer Proc. Math. Stat. 4, 225–233 (2011)
Coquel, F., Gallouët, T., Hérard, J.M., Seguin, N.: Closure laws for a two-fluid two-pressure model. C. R. Acad. Sci. Paris 334(I), 927–932 (2002)
Coquel, F., Godlewski, E., Seguin, N.: Relaxation of fluid systems. Math. Models Methods Appl. Sci. 22(8) (2012)
Coquel, F., Hérard, J.M., Saleh, K.: A splitting method for the isentropic Baer-Nunziato two-phase flow model. ESAIM: Proc. 38(3), 241–256 (2012)
Demay, C., Bourdarias, C., de Laage de Meux, B., Gerbi, S., Hérard, J.M.: Numerical simulation of a compressible two-layer model: a first attempt with an implicit-explicit splitting scheme. Submitted (2016). https://hal.archives-ouvertes.fr/hal-01421889
Demay, C., Hérard, J.M.: A compressible two-layer model for transient gas-liquid flows in pipes. Contin. Mech. Thermodyn. 29(2), 385–410 (2017)
Gerbeau, J.F., Perthame, B.: Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation. Discret. Contin. Dyn. Syst. Ser. B 1, 89–102 (2001)
Acknowledgements
C. Demay received a financial support by ANRT through an EDF-CIFRE contract 2014/749. Numerical facilities were provided by EDF.
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Demay, C., Bourdarias, C., de Laage de Meux, B., Gerbi, S., Hérard, JM. (2017). A Fractional Step Method to Simulate Mixed Flows in Pipes with a Compressible Two-Layer Model. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems. FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-319-57394-6_4
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DOI: https://doi.org/10.1007/978-3-319-57394-6_4
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