Relaxation models of phase transition flows
Philippe Helluy; Nicolas Seguin
ESAIM: Mathematical Modelling and Numerical Analysis (2006)
- Volume: 40, Issue: 2, page 331-352
- ISSN: 0764-583X
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top- 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.
- T. Barberon and P. Helluy, Finite volume simulations of cavitating flows. In Finite volumes for complex applications, III (Porquerolles, 2002), Lab. Anal. Topol. Probab. CNRS, Marseille (2002) 441–448 (electronic).
- T. Barberon and P. Helluy, Finite volume simulation of cavitating flows. Comput. Fluids34 (2005) 832–858.
- T. Barberon, P. Helluy and S. Rouy, Practical computation of axisymmetrical multifluid flows. Int. J. on Finite Volumes1 (2003) 1–34. URIhttp://averoes.math.univ-paris13.fr/IJFV
- F. Bouchut, A reduced stability condition for nonlinear relaxation to conservation laws. J. Hyper. Diff. Eqns1 (2004) 149–170.
- Y. Brenier, Averaged multivalued solutions for scalar conservation laws. SIAM J. Numer. Anal.21 (1984) 1013–1037.
- Y. Brenier, Un algorithme rapide pour le calcul de transformées de Legendre-Fenchel discrètes. C.R. Acad. Sci. Paris Sér. I Math.308 (1989) 587–589.
- H.B. Callen, Thermodynamics and an introduction to thermostatistics, second edition. Wiley and Sons (1985).
- F. Caro, Modélisation et simulation numérique des transitions de phase liquide-vapeur. Ph.D. thesis, École Polytechnique, Paris, France (November 2004).
- G. Chanteperdrix, P. Villedieu, J.-P. Vila, A compressible model for separated two-phase flows computations. In ASME Fluids Engineering Division Summer Meeting. ASME, Montreal, Canada (July 2002).
- G.Q. Chen, C. David Levermore and T.-P. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy. Comm. Pure Appl. Math.47 (1994) 787–830.
- J.-P. Croisille, Contribution à l'étude théorique et à l'approximation par éléments finis du système hyperbolique de la dynamique des gaz multidimensionnelle et multiespèces. Ph.D. thesis, Université Paris VI, France (1991).
- S. Dellacherie, Relaxation schemes for the multicomponent Euler system. ESAIM: M2AN37 (2003) 909–936.
- L.C. Evans, Entropy and partial differential equations (2004). URIhttp://math.berkeley.edu/~evans/entropy.and.PDE.pdf
- A. Harten, P.D. Lax and B. Van Leer, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev.25 (1983) 35–61.
- B.T. Hayes and P.G. LeFloch, Nonclassical shocks and kinetic relations: strictly hyperbolic systems. SIAM J. Math. Anal.31 (2000) 941–991 (electronic).
- J.-B. Hiriart-Urruty, Optimisation et analyse convexe. Mathématiques, Presses Universitaires de France, Paris (1998).
- J.-B. Hiriart-Urruty and C. Lemaréchal, Fundamentals of convex analysis. Grundlehren Text Editions, Springer-Verlag, Berlin (2001).
- S. Jaouen, Étude mathématique et numérique de stabilité pour des modèles hydrodynamiques avec transition de phase. Ph.D. thesis, Université Paris VI (November 2001).
- L. Landau and E. Lifchitz, Physique statistique. Physique théorique, Ellipses, Paris (1994).
- P.D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, in CBMS Regional Conf. Ser. In Appl. Math. 11, Philadelphia, SIAM (1972).
- P.G. LeFloch and C. Rohde, High-order schemes, entropy inequalities, and nonclassical shocks. SIAM J. Numer. Anal.37 (2000) 2023–2060.
- R.J. LeVeque and M. Pelanti, A class of approximate Riemann solvers and their relation to relaxation schemes. J. Comput. Phys.172 (2001) 572–591.
- T.P. Liu, The Riemann problem for general systems of conservation laws. J. Differ. Equations56 (1975) 218–234.
- Y. Lucet, A fast computational algorithm for the Legendre-Fenchel transform. Comput. Optim. Appl.6 (1996) 27–57.
- Y. Lucet, Faster than the fast Legendre transform, the linear-time Legendre transform. Numer. Algorithms16 (1998) 171–185.
- P.-A. Mazet and F. Bourdel, Multidimensional case of an entropic variational formulation of conservative hyperbolic systems. Rech. Aérospatiale5 (1984) 369–378.
- R. Menikoff and B.J. Plohr, The Riemann problem for fluid flow of real materials. Rev. Mod. Phys.61 (1989) 75–130.
- B. Perthame, Boltzmann type schemes for gas dynamics and the entropy property. SIAM J. Numer. Anal.27 (1990) 1405–1421.
- R. Saurel and R. Abgrall, A multiphase Godunov method for compressible multifluid and multiphase flows. J. Comput. Phys.150 (1999) 425–467.
Citations in EuDML Documents
top- Gloria Faccanoni, Samuel Kokh, Grégoire Allaire, Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium
- Gloria Faccanoni, Samuel Kokh, Grégoire Allaire, Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium