Abstract
We consider the seven-equation model for compressible two-phase flows and propose a large time-step numerical scheme based on a time implicit-explicit Lagrange-Projection strategy introduced in Coquel et al. [6] for Euler equations. The main objective is to get a Courant-Friedrichs-Lewy (CFL) condition driven by (slow) contact waves instead of (fast) acoustic waves.
MSC2010: 76T99, 74S10
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References
A. Ambroso, C. Chalons, F. Coquel, T. Galié. Relaxation and numerical approximation of a two fluid two pressure diphasic model. M2AN, vol. 43, pp. 1063-1097, (2009).
A. Ambroso, C. Chalons and P.-A. Raviart. A Godunov-type method for the seven-equation model of compressible two-phase flow. LJLL report number R10020, http://www.ljll.math.upmc.fr/publications/2010/R10020.php, (2010).
N. Andrianov and G. Warnecke. The Riemann problem for the Baer-Nunziato two-phase flow model. Journal of Computational Physics, vol. 195, pp. 434-464, (2004).
M.R. Baer and J.W. Nunziato, A two phase mixture theory for the deflagration to detonation transition in reactive granular materials. Int. J. Mult. Flows, vol. 12(6), pp. 861-889, (1986).
C. Chalons and J.-F. Coulombel, Relaxation approximation of the Euler equations. J. Math. Anal. Appl., vol. 348(2), pp. 872-893, (2008).
F. Coquel, Q.-L. Nguyen, M. Postel and Q.-H. Tran, Entropy-satisfying relaxation method with large time-steps for Euler IBVPs. Math. Comp, vol. 79, pp. 1493-1533, (2010).
P. Embid and M. Baer, Mathematical analysis of a two-phase continuum mixture theory, Contin. Mech. Thermodyn. vol. 4(4), pp. 279-312, (1992).
T. Gallouët, J.-M. Hérard and N. Seguin. Numerical modeling of two-phase flows using the two-fluid two-pressure approach. M3AS, vol. 14(5), pp. 663-700, (2004).
S. Karni, E. Kirr, A. Kurganov and G. Petrova, Compressible two-phase flows by central and upwind schemes, M2AN, vol. 38(3), pp. 477-493, (2004).
S.T. Munkejord, Comparison of Roe-type methods for solving the two-fluid model with and without pressure relaxation, Computers and Fluids, vol. 36, pp. 1061-1080, (2007).
R. Saurel and R. Abgrall, A multiphase Godunov method for compressible multifluid and multiphase flows, J. Comput. Phys., vol. 150, pp. 425-467, (1999).
D.-W. Schwendeman, C.-W. Wahle and A.-K. Kapila. The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow. Journal of Computational Physics, vol. 212, pp. 490-526, (2006).
B. Stewart and B. Wendroff, Two-phase flow : models and methods, J. Comput. Phys., vol. 56, pp. 363-409, (1984).
S.-A. Tokareva and E.-F. Toro, HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow, J. Comput. Phys., to appear, (2010).
Acknowledgements
Part of this work has been achieved within the framework of the NEPTUNE project, supported by CEA, EDF, IRSN, AREVA-NP.
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Chalons, C., Coquel, F., Kokh, S., Spillane, N. (2011). Large Time-Step Numerical Scheme for the Seven-Equation Model of Compressible Two-Phase Flows. In: Fořt, J., Fürst, J., Halama, J., Herbin, R., Hubert, F. (eds) Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Proceedings in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20671-9_24
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DOI: https://doi.org/10.1007/978-3-642-20671-9_24
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