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Boundary layers and shock profiles for the discrete Boltzmann equation for mixtures
Ghost effect for a vapor-vapor mixture
1. | Institut Polytechnique de Bordeaux, 351, cours de la Libération, 33405 TALENCE Cedex, France |
References:
[1] |
K. Aoki, The behaviour of a vapor-gas mixture in the continuum limit: Asymptotic analysis based on the Boltzman equation, in "Rarefied Gas Dynamic" (eds. T. J. Bartel and M. A. Gallis), AIP, Melville, (2001), 565-574. |
[2] |
K. Aoki, C. Bardos and S. Takata, Knudsen layer for a gas mixture, Journ. Stat. Phys., 112 (2003), 629-655.
doi: 10.1023/A:1023876025363. |
[3] |
K. Aoki, S. Takata and S. Kosuge, Vapor flows caused by evaporation and condensation on two parallel plane surfaces: Effect of the presence of a noncondensable gas, Physics of Fluids, 10 (1998), 1519-1532.
doi: 10.1063/1.869671. |
[4] |
K. Aoki, S. Takata and S. Taguchi, Vapor flows with evaporation and condensation in the continuum limit: Effect of a trace of non condensable gas, European Journal of Mechanics B Fluids, 22 (2003), 51-71.
doi: 10.1016/S0997-7546(02)00008-0. |
[5] |
L. Arkeryd, R. Esposito, R. Marra and A. Nouri, Stability of the laminar solution of the Boltzmann equation for the Benard problem, Bull. Inst. Math. Academia Sinica (N.S.), 3 (2008), 51-97. |
[6] |
L. Arkeryd, R. Esposito, R. Marra and A. Nouri, Stability for Rayleigh-Benard convective solutions of the Boltzmann equation, Arch. Ration. Mech. Anal., 198 (2010), 125-187.
doi: 10.1007/s00205-010-0292-z. |
[7] |
L. Arkeryd, R. Esposito, R. Marra and A. Nouri, Ghost effect by curvature in planar Couette flow, to appear in Kinetic and Related Models. |
[8] |
L. Arkeryd and A. Nouri, The stationary nonlinear Boltzmann equation in a Couette setting with multiple, isolated $L^q$-solutions and hydrodynamic limits, Journ. Stat. Phys., 118 (2005), 849-881.
doi: 10.1007/s10955-004-2708-3. |
[9] |
L. Arkeryd and A. Nouri, On a Taylor-Couette type bifurcation for the stationary nonlinear Boltzmann equation, Journ. Stat. Phys., 124 (2006), 401-443.
doi: 10.1007/s10955-005-8008-8. |
[10] |
C. Bardos, R. E. Caflisch and B. Nicolaenko, The Milne and Kramer problems for the Boltzmann Equation of a hard sphere gas, Commun. Pure and Applied Math., 39 (1986), 323-352. |
[11] |
S. Brull, "Etude Cinétique d'un Gaz à Plusieurs Composantes," Ph.D thesis, Université de Provence, 2006. |
[12] |
S. Brull, The stationary Boltzmann equation for a two-component gas in the slab, Math. Meth. Appl. Sci., 31 (2008), 153-178.
doi: 10.1002/mma.897. |
[13] |
S. Brull, The stationary Boltzmann equation for a two-component gas for soft forces in the slab, Math. Meth. Appl. Sci., 31 (2008), 1653-1666.
doi: 10.1002/mma.991. |
[14] |
S. Brull, Problem of evaporation-condensation for a two component gas in the slab, Kinetic and Related Models, 1 (2008), 185-221.
doi: 10.3934/krm.2008.1.185. |
[15] |
S. Brull, The stationary Boltzmann equation for a two-component gas in the slab for different molecular masses, Adv. in Diff. Eq., 15 (2010), 1103-1124. |
[16] |
R. E. Caflisch, The fluid dynamic limit of the nonlinear Boltzmann equation, Commun. Pure and Applied Math., 33 (1980), 651-666.
doi: 10.1002/cpa.3160330506. |
[17] |
C. Cercignani, "The Boltzman Equation and its Applications," Applied Mathematical Sciences, 67, Springer-Verlag, New York, 1988. |
[18] |
C. Cercignani, R. Illner and M. Pulvirenti, "The Mathematical Theory of Dilute Gases," Applied Mathematical Sciences, 106, Springer-Verlag, New York, 1994. |
[19] |
L. Desvillettes, Sur quelques hypothèses nécessaires à l'obtention du développement de Chapman-Enskog, preprint, 1994. |
[20] |
R. Esposito, J. L. Lebowitz and R. Marra, Hydrodynamic limit of the stationary Boltzmann Equation in a slab, Comm. Math. Phys., 160 (1994), 49-80.
doi: 10.1007/BF02099789. |
[21] |
R. Esposito, J. L. Lebowitz and R. Marra, The Navier-Stokes limit of stationary solutions of the nonlinear Boltzmann equation, Journ. Stat. Phys., 78 (1995), 389-412.
doi: 10.1007/BF02183355. |
[22] |
H. Grad, Asymptotic theory of the Boltzmann equation, Physics of Fluids, 6 (1963), 147-181.
doi: 10.1063/1.1706716. |
[23] |
H. Grad, Asymptotic theory of the Boltzmann equation. II, in "1963 Rarefied Gas Dyn." (Proc. 3rd Internat. Sympos., Palais de l'UNESCO, Paris, 1962), Vol. I, Academic Press, New York, (1962), 26-59. |
[24] |
H. Grad, Asymptotic equivalence of the Navier-Stokes and nonlinear Boltzmann equations, in "1965 Proc. Symp. Appl. Math.," Vol. XVII, Amer. Math. Soc., Providence, RI, (1965), 154-183. |
[25] |
Y. Sone, "Kinetic Theory and Fluid Dynamics," Modeling and Simulations in Science, Engineering and Technology, Birkhäuser Boston, Inc., Boston, MA, 2002.
doi: 10.1007/978-1-4612-0061-1. |
[26] |
Y. Sone, K. Aoki, S. Takata, H. Sugimoto and A. Bobylev, Inappropriateness of the heat-conduction equation for description of a temperature field of a stationary gas in the continuum limit: Examination by asymptotic analysis and numerical computation of the Boltzmann equation, Physics of Fluids, 8 (1996), 628-638. Erratum: Physics of Fluids, 8 (1996), 841.
doi: 10.1063/1.869133. |
[27] |
Y. Sone and T. Doi, Ghost effect of infinitesimal curvature in the plane Couette flow of a gas in the continuum limit, Phys. Fluids, 16 (2004), 952-971.
doi: 10.1063/1.1649738. |
[28] |
S. Taguchi, K. Aoki and S. Takata, Vapor flows at incidence onto a plane condensed phase in the presence of a non condensable gas. II. Supersonic condensation, Physics of Fluids, 16 (2004), 79.
doi: 10.1063/1.1630324. |
[29] |
S. Takata, Kinetic theory analysis of the two-surface problem of vapor-vapor mixture in the continuum limit, Physics of Fluids, 16 (2004), 7.
doi: 10.1063/1.1723464. |
[30] |
S. Takata and K. Aoki, Two-surface-problems of a multicomponent mixture of vapors and noncondensable gases in the continuum limit in the light of kinetic theory, Physics of Fluids, 11 (1999), 2743-2756.
doi: 10.1063/1.870133. |
[31] |
S. Takata and K. Aoki, The ghost effect in the continuum limit for a vapor-gas mixture around condensed phases: Asymptotic analysis of the Boltzmann equation, in "The Sixteenth International Conference on Transport Theory, Part I" (Atlanta, GA, 1999), Transport Theory Statist. Phys., 30 (2001), 205-237. Erratum: Transport Theory an Statistical Physic, 31 (2001), 289. |
[32] |
R. V. Thompson and S. K. Loyalka, Chapman-Enskog solution for diffusion: Pidduck's equation for arbitrary mass ratio, Physics of Fluids, 30 (1987), 2073.
doi: 10.1063/1.866142. |
show all references
References:
[1] |
K. Aoki, The behaviour of a vapor-gas mixture in the continuum limit: Asymptotic analysis based on the Boltzman equation, in "Rarefied Gas Dynamic" (eds. T. J. Bartel and M. A. Gallis), AIP, Melville, (2001), 565-574. |
[2] |
K. Aoki, C. Bardos and S. Takata, Knudsen layer for a gas mixture, Journ. Stat. Phys., 112 (2003), 629-655.
doi: 10.1023/A:1023876025363. |
[3] |
K. Aoki, S. Takata and S. Kosuge, Vapor flows caused by evaporation and condensation on two parallel plane surfaces: Effect of the presence of a noncondensable gas, Physics of Fluids, 10 (1998), 1519-1532.
doi: 10.1063/1.869671. |
[4] |
K. Aoki, S. Takata and S. Taguchi, Vapor flows with evaporation and condensation in the continuum limit: Effect of a trace of non condensable gas, European Journal of Mechanics B Fluids, 22 (2003), 51-71.
doi: 10.1016/S0997-7546(02)00008-0. |
[5] |
L. Arkeryd, R. Esposito, R. Marra and A. Nouri, Stability of the laminar solution of the Boltzmann equation for the Benard problem, Bull. Inst. Math. Academia Sinica (N.S.), 3 (2008), 51-97. |
[6] |
L. Arkeryd, R. Esposito, R. Marra and A. Nouri, Stability for Rayleigh-Benard convective solutions of the Boltzmann equation, Arch. Ration. Mech. Anal., 198 (2010), 125-187.
doi: 10.1007/s00205-010-0292-z. |
[7] |
L. Arkeryd, R. Esposito, R. Marra and A. Nouri, Ghost effect by curvature in planar Couette flow, to appear in Kinetic and Related Models. |
[8] |
L. Arkeryd and A. Nouri, The stationary nonlinear Boltzmann equation in a Couette setting with multiple, isolated $L^q$-solutions and hydrodynamic limits, Journ. Stat. Phys., 118 (2005), 849-881.
doi: 10.1007/s10955-004-2708-3. |
[9] |
L. Arkeryd and A. Nouri, On a Taylor-Couette type bifurcation for the stationary nonlinear Boltzmann equation, Journ. Stat. Phys., 124 (2006), 401-443.
doi: 10.1007/s10955-005-8008-8. |
[10] |
C. Bardos, R. E. Caflisch and B. Nicolaenko, The Milne and Kramer problems for the Boltzmann Equation of a hard sphere gas, Commun. Pure and Applied Math., 39 (1986), 323-352. |
[11] |
S. Brull, "Etude Cinétique d'un Gaz à Plusieurs Composantes," Ph.D thesis, Université de Provence, 2006. |
[12] |
S. Brull, The stationary Boltzmann equation for a two-component gas in the slab, Math. Meth. Appl. Sci., 31 (2008), 153-178.
doi: 10.1002/mma.897. |
[13] |
S. Brull, The stationary Boltzmann equation for a two-component gas for soft forces in the slab, Math. Meth. Appl. Sci., 31 (2008), 1653-1666.
doi: 10.1002/mma.991. |
[14] |
S. Brull, Problem of evaporation-condensation for a two component gas in the slab, Kinetic and Related Models, 1 (2008), 185-221.
doi: 10.3934/krm.2008.1.185. |
[15] |
S. Brull, The stationary Boltzmann equation for a two-component gas in the slab for different molecular masses, Adv. in Diff. Eq., 15 (2010), 1103-1124. |
[16] |
R. E. Caflisch, The fluid dynamic limit of the nonlinear Boltzmann equation, Commun. Pure and Applied Math., 33 (1980), 651-666.
doi: 10.1002/cpa.3160330506. |
[17] |
C. Cercignani, "The Boltzman Equation and its Applications," Applied Mathematical Sciences, 67, Springer-Verlag, New York, 1988. |
[18] |
C. Cercignani, R. Illner and M. Pulvirenti, "The Mathematical Theory of Dilute Gases," Applied Mathematical Sciences, 106, Springer-Verlag, New York, 1994. |
[19] |
L. Desvillettes, Sur quelques hypothèses nécessaires à l'obtention du développement de Chapman-Enskog, preprint, 1994. |
[20] |
R. Esposito, J. L. Lebowitz and R. Marra, Hydrodynamic limit of the stationary Boltzmann Equation in a slab, Comm. Math. Phys., 160 (1994), 49-80.
doi: 10.1007/BF02099789. |
[21] |
R. Esposito, J. L. Lebowitz and R. Marra, The Navier-Stokes limit of stationary solutions of the nonlinear Boltzmann equation, Journ. Stat. Phys., 78 (1995), 389-412.
doi: 10.1007/BF02183355. |
[22] |
H. Grad, Asymptotic theory of the Boltzmann equation, Physics of Fluids, 6 (1963), 147-181.
doi: 10.1063/1.1706716. |
[23] |
H. Grad, Asymptotic theory of the Boltzmann equation. II, in "1963 Rarefied Gas Dyn." (Proc. 3rd Internat. Sympos., Palais de l'UNESCO, Paris, 1962), Vol. I, Academic Press, New York, (1962), 26-59. |
[24] |
H. Grad, Asymptotic equivalence of the Navier-Stokes and nonlinear Boltzmann equations, in "1965 Proc. Symp. Appl. Math.," Vol. XVII, Amer. Math. Soc., Providence, RI, (1965), 154-183. |
[25] |
Y. Sone, "Kinetic Theory and Fluid Dynamics," Modeling and Simulations in Science, Engineering and Technology, Birkhäuser Boston, Inc., Boston, MA, 2002.
doi: 10.1007/978-1-4612-0061-1. |
[26] |
Y. Sone, K. Aoki, S. Takata, H. Sugimoto and A. Bobylev, Inappropriateness of the heat-conduction equation for description of a temperature field of a stationary gas in the continuum limit: Examination by asymptotic analysis and numerical computation of the Boltzmann equation, Physics of Fluids, 8 (1996), 628-638. Erratum: Physics of Fluids, 8 (1996), 841.
doi: 10.1063/1.869133. |
[27] |
Y. Sone and T. Doi, Ghost effect of infinitesimal curvature in the plane Couette flow of a gas in the continuum limit, Phys. Fluids, 16 (2004), 952-971.
doi: 10.1063/1.1649738. |
[28] |
S. Taguchi, K. Aoki and S. Takata, Vapor flows at incidence onto a plane condensed phase in the presence of a non condensable gas. II. Supersonic condensation, Physics of Fluids, 16 (2004), 79.
doi: 10.1063/1.1630324. |
[29] |
S. Takata, Kinetic theory analysis of the two-surface problem of vapor-vapor mixture in the continuum limit, Physics of Fluids, 16 (2004), 7.
doi: 10.1063/1.1723464. |
[30] |
S. Takata and K. Aoki, Two-surface-problems of a multicomponent mixture of vapors and noncondensable gases in the continuum limit in the light of kinetic theory, Physics of Fluids, 11 (1999), 2743-2756.
doi: 10.1063/1.870133. |
[31] |
S. Takata and K. Aoki, The ghost effect in the continuum limit for a vapor-gas mixture around condensed phases: Asymptotic analysis of the Boltzmann equation, in "The Sixteenth International Conference on Transport Theory, Part I" (Atlanta, GA, 1999), Transport Theory Statist. Phys., 30 (2001), 205-237. Erratum: Transport Theory an Statistical Physic, 31 (2001), 289. |
[32] |
R. V. Thompson and S. K. Loyalka, Chapman-Enskog solution for diffusion: Pidduck's equation for arbitrary mass ratio, Physics of Fluids, 30 (1987), 2073.
doi: 10.1063/1.866142. |
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