Free Access
Issue |
ESAIM: M2AN
Volume 49, Number 2, March-April 2015
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Page(s) | 601 - 619 | |
DOI | https://doi.org/10.1051/m2an/2014048 | |
Published online | 17 March 2015 |
- R. Abgrall, An extension of Roe’s upwind scheme to algebraic equilibrium real gas models. Comput. Fluids 19 (1991) 171–182. [CrossRef] [Google Scholar]
- R. Abgrall and R. Saurel, Discrete equations for physical and numerical compressible multiphase mixtures. J. Comput. Phys. 186 (2003) 361–396. [CrossRef] [MathSciNet] [Google Scholar]
- G. Allaire, S. Clerc and S. Kokh, A five-equation model for the simulation of interfaces between compressible fluids. J. Comput. Phys. 181 (2002) 577–616. [CrossRef] [MathSciNet] [Google Scholar]
- P. Aursand and T. Flåtten, On the dispersive wave-dynamics of 2 × 2 relaxation systems. J. Hyperbolic Diff. Eq. 9 (2012) 641–659. [CrossRef] [Google Scholar]
- M.R. Baer and J.W. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials. Int. J. Multiphase Flow 12 (1986) 861–889. [Google Scholar]
- F. Bouchut, A reduced stability condition for nonlinear relaxation to conservation laws. J. Hyperbolic Diff. Eq. 1 (2004) 149–170. [Google Scholar]
- F. Caro, F. Coquel, D. Jamet and S. Kokh, A simple finite-volume method for compressible isothermal two-phase flows simulation. Int. J. Finite 3 (2006). [Google Scholar]
- G.-Q. Chen, C.D. Levermore and T.-P. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy. Commun. Pure Appl. Math. 47 (1994) 787–830. [CrossRef] [MathSciNet] [Google Scholar]
- S. Dellacherie, Relaxation schemes for the multicomponent Euler system. ESAIM: M2AN 37 (2003) 909–936. [CrossRef] [EDP Sciences] [Google Scholar]
- G. Faccanoni, S. Kokh and G. Allaire, Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium. ESAIM: M2AN 46 (2012) 1029–1054. [CrossRef] [EDP Sciences] [Google Scholar]
- T. Flåtten and H. Lund, Relaxation two-phase flow models and the subcharacteristic condition. Math. Models Methods Appl. Sci. 21 (2011) 2379–2407. [CrossRef] [MathSciNet] [Google Scholar]
- T. Flåtten, A. Morin and S.T. Munkejord, Wave propagation in multicomponent flow models. SIAM J. Appl. Math. 70 (2010) 2861–2882. [CrossRef] [MathSciNet] [Google Scholar]
- T. Flåtten, A. Morin and S.T. Munkejord, On solutions to equilibrium problems for systems of stiffened gases. SIAM J. Appl. Math. 71 (2011) 41–67. [CrossRef] [MathSciNet] [Google Scholar]
- P. Helluy and N. Seguin, Relaxation models of phase transition flows. ESAIM: M2AN 40 (2006) 331–352. [CrossRef] [EDP Sciences] [Google Scholar]
- H.-O. Kreiss and J. Lorenz, Initial-boundary value problems and the Navier-Stokes equations. Academic Press (1989). [Google Scholar]
- T.-P. Liu, Hyperbolic conservation laws with relaxation. Commun. Math. Phys. 108 (1987) 153–175. [CrossRef] [MathSciNet] [Google Scholar]
- H. Lund, A hierarchy of relaxation models for two-phase flow. SIAM J. Appl. Math. 72 (2012) 1713–1741. [CrossRef] [MathSciNet] [Google Scholar]
- H. Lund and P. Aursand, Two-phase flow of CO2 with phase transfer. Energy Procedia 23 (2012) 246–255. [CrossRef] [Google Scholar]
- A. Morin, P.K. Aursand, T. Flåtten and S.T. Munkejord, Numerical resolution of CO2 transport dynamics. In Proc. of SIAM Conference on Mathematics for Industry: Challenges and Frontiers (MI09). SIAM, Philadelphia (2009) 108–119. [Google Scholar]
- A. Morin and T. Flåtten, A two-fluid four-equation model with instantaneous thermodynamical equilibrium. Submitted. [Google Scholar]
- A. Murrone and H. Guillard, A five equation reduced model for compressible two phase flow problems. J. Comput. Phys. 202 (2005) 664–698. [Google Scholar]
- R. Natalini, Convergence to equilibrium for the relaxation approximation of conservation laws. Commun. Pure Appl. Math. 49 (1996) 795–823. [CrossRef] [Google Scholar]
- R. Natalini, Recent results on hyperbolic relaxation problems. Analysis of systems of conservation laws. In vol. 99 of Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math. Chapman & Hall/CRC, Boca Raton, FL (1999) 128–198. [Google Scholar]
- M. Pelanti and K.-M. Shyue, A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves. J. Comput. Phys. 259 (2014) 331–357. [CrossRef] [MathSciNet] [Google Scholar]
- R. Saurel and R. Abgrall, A multiphase Godunov method for compressible multifluid and multiphase flows. J. Comput. Phys. 150 (1999) 425–467. [Google Scholar]
- R. Saurel, F. Petitpas and R. Abgrall, Modelling phase transition in metastable liquids: application to cavitating and flashing flows. J. Fluid Mech. 607 (2008) 313–350. [CrossRef] [MathSciNet] [Google Scholar]
- R. Saurel, F. Petitpas and R.A. Berry, Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures. J. Comput. Phys. 228 (2009) 1678–1712. [CrossRef] [Google Scholar]
- C.A. Ward and G. Fang, Expression for predicting liquid evaporation flux: Statistical rate theory approach. Phys. Rev. E 59 (1999) 429–440. [CrossRef] [Google Scholar]
- W.-A. Yong, Basic aspects of hyperbolic relaxation systems, in Advances in the Theory of Shock Waves. Vol. 47 of Progr. Nonlin. Differ. Eq. Appl. Birkhäuser Boston, Boston (2001) 259–305. [Google Scholar]
- A. Zein, M. Hantke and G. Warnecke, Modeling phase transition for compressible two-phase flows applied to metastable liquids. J. Comput. Phys. 229 (2010) 2964–2998. [CrossRef] [MathSciNet] [Google Scholar]
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