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A fractional step method to simulate mixed flows in pipes with a compressible two-layer model. (English) Zbl 1366.76070

Cancès, Clément (ed.) et al., Finite volumes for complex applications VIII – hyperbolic, elliptic and parabolic problems. FVCA 8, Lille, France, June 12–16, 2017. Cham: Springer (ISBN 978-3-319-57393-9/hbk; 978-3-319-57394-6/ebook; 978-3-319-58818-6/set). Springer Proceedings in Mathematics & Statistics 200, 33-41 (2017).
Summary: 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 [the first and last authors, “A compressible two-layer model for transient gas-liquid flows in pipes”, Contin. Mech. Thermodyn. 29, No. 2, 385–410 (2016; doi:10.1007/s00161-016-0531-0)]. 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.
For the entire collection see [Zbl 1371.65001].

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76Txx Multiphase and multicomponent flows
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References:

[1] 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) · Zbl 1135.76036 · doi:10.1016/j.cam.2006.10.086
[2] 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) · Zbl 1246.76071 · doi:10.1007/978-3-642-20671-9_24
[3] 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) · Zbl 0999.35057
[4] Coquel, F., Godlewski, E., Seguin, N.: Relaxation of fluid systems. Math. Models Methods Appl. Sci. 22(8) (2012) · Zbl 1248.35008 · doi:10.1142/S0218202512500145
[5] 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) · Zbl 1329.76253
[6] 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 · Zbl 1366.76070
[7] 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) · Zbl 1365.76317 · doi:10.1007/s00161-016-0531-0
[8] 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) · Zbl 0997.76023 · doi:10.3934/dcdsb.2001.1.89
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