A coupled model for radiative transfer: Doppler effects, equilibrium, and nonequilibrium diffusion asymptotics

Multiscale Modeling and Simulation

Volumn 4, Issue 4, 2005, Pages 1245-1279

  Godillon Lafitte, Pauline ^a   Goudon, Thierry ^a  

^a UNIVERSITÉ LILLE 1   (France)

Author keywords

Diffusion approximation; Doppler correction; Hydrodynamic limits; Radiative transfer

Indexed keywords

COMPUTER SIMULATION; DIFFUSION; DOPPLER EFFECT; HEAT TRANSFER; NONLINEAR EQUATIONS; TEMPERATURE;

DIFFUSION APPROXIMATION; DOPPLER CORRECTION; HYDRODYNAMIC LIMITS; RADIATIVE TRANSFER;

HEAT RADIATION;

EID: 33845587012     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/040621041     Document Type: Article

References (33)

1. D. Aregba-Driollet and R. Natalini, Convergence of relaxation schemes for conservation laws, Appl. Anal., 61 (1996), pp. 163-193.
2. C. Buet and S. Cordier, Asymptotic preserving scheme and numerical methods for radiative hydrodynamic models, C. R. Math. Acad. Sci. Paris, 338 (2004), pp. 951-956.
3. C. Bardos, F. Golse, and B. Perthame, The Rosseland approximation for the radiative transfer equations, Comm. Pure Appl. Math., 40 (1987), pp. 691-721.
4. C. Bardos, F. Golse, and B. Perthame, Erratum to "The Rosseland approximation for the radiative transfer equations," Comm. Pure Appl. Math., 42 (1989), pp. 891-894.
5. C. Bardos, F. Golse, B. Perthame, and R. Sentis, The nonaccretive radiative transfer equations: Existence of solutions and Rosseland approximations, J. Funct. Anal., 77 (1988), pp. 434-460.
6. E. Battaner, Astrophysical Fluid Dynamics, Cambridge University Press, Cambridge, UK, 1996.
7. F. Bouchut, F. R. Guarguaglini, and R. Natalini, Diffusive BGK approximations for nonlinear multidimensional parabolic equations, Indiana Univ. Math. J., 49 (2000), pp. 723-749.
8. Ch. Buet and B. Després, Asymptotic analysis of fluid models for the coupling of radiation and hydrodynamics, J.Q.S.R.T., 85 (2004), pp. 385-418.
9. F. Chalub, P. Markowich, B. Pethame, and C. Schmeiser, Kinetic models for chemotaxis and their drift-diffusion limits, Monatsh. Math., 142 (2004), pp. 123-141.
10. P. Degond, T. Goudon, and F. Poupaud, Diffusion limit for nonhomogeneous and nonmicro-reversible processes, Indiana Univ. Math. J., 49 (2000), pp. 1175-1198.
11. S. Descombes and M. Massot, Operator splitting for nonlinear reaction-diffusion systems with an entropic structure: Singular perturbation and order reduction, Numer. Math., 97 (2004), pp. 667-698.
12. p regularity of velocity averages, Ann. Inst. H. Poincaré Anal. Non Linéaire, 8 (1991), pp. 271-287.
13. C. Dogbe, The radiative transfer equations: Diffusion approximation under accretiveness and compactness assumptions, Comput. Math. Appl., 42 (2001), pp. 783-791.
14. F. Golse, From kinetic to macroscopic models, in Kinetic Equations and Asymptotic Theory, Ser. Appl. Math. (Paris) 4, B. Perthame and L. Desvillettes, eds., Gauthier-Villars, Paris, 2000, pp. 41-121.
15. F. Golse, P.-L. Lions, B. Perthame, and R. Sentis, Regularity of the moments of the solution of a transport equation, J. Funct. Anal., 76 (1988), pp. 110-125.
16. F. Golse and F. Poupaud, Limite fluide des équations de Boltzmann des semi-conducteurs pour une statistique de Fermi-Dirac, Asymptot. Anal., 6 (1992), pp. 135-160.
17. T. Goudon and F. Poupaud, Approximation by homogenization and diffusion of kinetic equations, Comm. Partial Differential Equations, 26 (2001), pp. 537-569.
18. S. Jin and Z.-P. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Comm. Pure Appl. Math., 48 (1995), pp. 235-276.
19. A. Klar and C. Schmeiser, Numerical passage from radiative heat transfer to nonlinear diffusion models, Math. Models Methods Appl. Sci., 11 (2001), pp. 749-767.
20. P.-L. Lions and G. Toscani, Diffuse limit for finite velocity Boltzmann kinetic models, Rev. Mat. Iberoamericana, 13 (1997), pp. 473-513.
21. R. B. Lowrie, J. E. Morel, and J. A. Hittinger, The coupling of radiation and hydrodynamics, Astrophys. J., 521 (1999), pp. 432-450.
22. P. Marcati and A. Milani, The one-dimensional Darcy's law as the limit of a compressible Euler flow, J. Differential Equations, 84 (1990), pp. 129-147.
23. G. I. Marchuk, Splitting and alternating direction methods, in Handbook of Numerical Analysis, Vol. I, North-Holland, Amsterdam, 1990, pp. 197-462.
24. D. Mihalas and B. W. Mihalas, Foundations of Radiation Hydrodynamics, Oxford University Press, New York, 1984.
25. P. J. Mohr and B. N. Taylor, The 2002 CODATA recommended values of the fundamental physical constants, Rev. Modern Phys., 77 (2005), pp. 1-107; also available online from http://physics.nist.gov/constants (31 October 2005).
26. R. Natalini, Metodi Numerici per Problemi di Evoluzione, Lecture Notes Istituto per le Applicazioni del Calcolo M. Picone, Roma.
27. R. Natalini, Recent results on hyperbolic relaxation problems in Analysis of Systems of Conservation Laws (Aachen, 1997), Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math. 99, Chapman & Hall/CRC, Boca Raton, FL, 1999, pp. 128-198.
28. F. Poupaud, Diffusion approximation of the linear semiconductor Boltzmann equation: Analysis of boundary layers, Asymptot. Anal., 4 (1991), pp. 293-317.
29. R. Richtmyer and K. Morton, Difference Methods for Initial-Value Problems, 2nd ed., Interscience, John Wiley, New York, 1967.
30. R. J. Rutten, Radiative Transfer in Stellar Atmospheres, 8th ed., Utrecht University Lecture Notes, Utrecht, The Netherlands, 2003.
31. G. Strang, Approximating semigroups and the consistency of difference schemes, Proc. Amer. Math. Soc., 20 (1969), pp. 1-7.
32. p (0, T; B), Ann. Mat. Pura Appl. (4), 146 (198T), pp. 65-96.
33. L. Tartar, Remarks on homogenization, in Homogenization and Effective Moduli of Materials and Media, IMA Vol. Math. Appl. 1, Springer-Verlag, New York, 1986, pp. 228-246.