References
- Bresch D, Hillairet M. A compressible multifluid system with new physical relaxation terms. Ann l'ENS. 2019;52:255–295.
- Baer MR, Nunziato JW. A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials. Int J Multiph Flow. 1986;12:861–889.
- Gavryliuk S. The structure of pressure relaxation terms: one-velocity case. EDF report H-183-2014-0276-EN. 2014.
- Drew D, Passman SL. Theory of multicomponent fluids. Springer Verlag; 1999. (Applied mathematical sciences; vol. 13)
- Ishii M, Hibiki T. Thermo-fluid dynamics of two-phase flow. Springer Verlag; 2006.
- Hillairet M, Mathis H, Seguin N. Analysis of compressible bubbly flows. Parti I: construction of a microscopic model. Forthcoming paper 2021.
- Hillairet M, Mathis H, Seguin N. Analysis of compressible bubbly flows. Part II: Derivation of a macroscopic model. Forthcoming paper 2021.
- Bresch D, Burtea C, Lagoutiere F. Mathematical justification of a compressible bi-fluid system with different pressure laws: a semi-discrete approach and numerical illustrations. Submitted 2021.
- Allaire G, Clerc S, Kokh S. A five-equation model for the simulation of internaces between compressible fluids. J Comput Phys. 2002;181:577–616.
- Crouzet F, Daude F, Gedon P, et al. Validation of a two-fluid model on unsteady liquid-vapor water flows. Comput Fluids. 2015;119:131–142.
- Després B, Lagoutière F. Numerical resolution of a two-component compressible fluid model with interfaces. Prog Comput Fluid Dyn. 2007;7:295–310.
- Lagoutière F. Modélisation mathématique et résolution numérique de problèmes de fluides compressible à plusieurs constituants. Thèse de doctorat, université Pierre et Marie Curie. 2000.
- Weinan E. Propagation of oscillations in the solutions of 1D compressible fluid equations. Commun Partial Differ Equ. 1992;17(3–4):545–552.
- Serre D. Variations de grande amplitude pour la densité d'un fluide compressiible. Phys D. 1991;48:113–128.
- Amosov AA, Zlotnikov AA. On the error of quasi-averaging of the equations of motion of viscous barotropic medium with rapidly oscillating data. Comput Math Phys. 1996;36:1415–1428.
- Plotnikov P, Skolowski J. Compressible Navier–Stokes equations, theory and shape optimization. Basel: Birkhäuser; 2012. (Series: monografie matematyczne).
- Bresch D, Hillairet M. Note on the derivation of multi-component flow systems. Proc Am Math Soc. 2015;143:3429–3443.
- Lions P-L, Perthame B, Tadmor E. A kinetic formulation of multidimensional scalar conservation laws and related equations. J Am Math Soc. 1994;7(1):169–191.
- Bresch D, Huang X. A multi-fluid compressible system as the limit of weak solutions of the isentropic compressible Navier–Stokes equations. Arch Ration Mech Anal. 2011;201:647–680.
- Hillairet M. Propagation of density-oscillations in solutions to barotropic compressible Navier–Stokes system. J Math Fluid Mech. 2007;9:343–376.
- Hillairet M. On Baer–Nunziato multiphase flow models. ESAIM Proc Surv. 2019;66:61–83.
- Hoff D. Global existence of the Navier–Stokes equation for multidimensional compressible flow with discontinuous initial data. J Differ Equ. 2005;120:215–254.
- Desjardins B. Regularity of weak solutions of the compressible isentropic Navier–Stokes equations. Commun Partial Differ Equ. 1997;22:977–1008.
- Burtea C, Crin-Barat T, Tan J. Relaxation limit for a damped one-velocity Baer–Nunziato model to a Kapila model. Submitted 2021. See arXiv:2109.07746v1.
- Michoski C, Vasseur A. Existence and uniqueness of strong solutions for a compressible multiphase Navier–Stokes miscible fluid-flow problem in dimension n = 1. Math Models Methods Appl Sci. 2009;19:443–476.
- Novotny A. Weak solutions for a bi-fluid model for a mixture of two compressible non interacting fluid. Sci China Math. 2020;63(12):2399–2414.
- Vasseur A, Wen H, Yu C. Global weak solution to the viscous two-fluid model with finite energy. J Math Pures Appl. 2019;125:247–282.
- Lions P-L. Mathematical topics in fluid dynamics, vol. 2, compressible models. Oxford: Oxford Science Publication; 1998.
- Novotny A, Straškraba I. Introduction to the mathematical theory of compressible flow, vol. 27. Oxford: Oxford University Press; 2004.