A HIERARCHY OF APPROXIMATIONS TO THE RADIATIVE HEAT TRANSFER EQUATIONS: MODELLING, ANALYSIS AND SIMULATION

We thoroughly investigate a hierarchy of approximations to the radiative heat transfer equations which is intermediate between moment models and the direct solution. We discuss the modelling of this hierarchy, prove well-posedness and physically expected bounds, and show numerical results validating our approach.

[1]  B. Dubroca,et al.  Etude théorique et numérique d'une hiérarchie de modèles aux moments pour le transfert radiatif , 1999 .

[2]  J. Keller,et al.  Asymptotic solution of neutron transport problems for small mean free paths , 1974 .

[3]  Henning Struchtrup.  On the Number of Moments in Radiative Transfer Problems , 1998 .

[4]  Rainer Koch,et al.  DISCRETE ORDINATES QUADRATURE SCHEMES FOR MULTIDIMENSIONAL RADIATIVE TRANSFER , 1995 .

[5]  J. Sykes,et al.  Approximate integration of the equation of transger , 1951 .

[6]  Axel Klar,et al.  A half space moment approximation to the radiative heat transfer equations , 2003 .

[7]  Axel Klar,et al.  New Frequency-Averaged Approximations to the Equations of Radiative Heat Transfer , 2004, SIAM J. Appl. Math..

[8]  Axel Klar,et al.  Simplified P N approximations to the equations of radiative heat transfer and applications , 2002 .

[9]  I. Max Krook,et al.  On the Solution of Equations of Transfer. , 1955 .

[10]  Marco Sammartino,et al.  A thermodynamical approach to Eddington factors , 1991 .

[11]  C. D. Levermore,et al.  Relating Eddington factors to flux limiters , 1984 .

[12]  M. P. Mengüç,et al.  Modeling of radiative transfer using multiple spherical harmonics approximations , 1988 .

[13]  Mareschal,et al.  Heat transfer in a gas between parallel plates: Moment method and molecular dynamics. , 1988, Physical review. A, General physics.

[14]  James Paul Holloway,et al.  One-dimensional Riemann solvers and the maximum entropy closure , 2001 .

[15]  A. Schuster.  Radiation through a foggy atmosphere , 1903 .

[16]  M. N. Özişik,et al.  Half-range moment method for solution of the transport equation in a spherically symmetric geometry , 1975 .

[17]  Axel Klar,et al.  Efficient numerical methods for radiation in gas turbines , 2004 .

[18]  M. P. Sherman,et al.  Moment methods in radiative transfer problems , 1967 .