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

2005 ◽  
Vol 15 (04) ◽  
pp. 643-665 ◽  
Author(s):  
MATTHIAS SCHÄFER ◽  
MARTIN FRANK ◽  
RENÉ PINNAU
Keyword(s):  
Heat Transfer ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Numerical Results ◽  
Well Posedness ◽  
Direct Solution ◽  
Modelling Analysis ◽  
Transfer Equations ◽  
Moment Models

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.

NUMERICAL PASSAGE FROM RADIATIVE HEAT TRANSFER TO NONLINEAR DIFFUSION MODELS

2001 ◽  
Vol 11 (05) ◽  
pp. 749-767 ◽  
Author(s):  
A. KLAR ◽  
C. SCHMEISER
Keyword(s):  
Heat Transfer ◽  
Radiative Heat Transfer ◽  
Nonlinear Diffusion ◽  
Radiative Heat ◽  
Mean Free Path ◽  
Rigorous Results ◽  
Asymptotic Preserving ◽  
Milne Problem ◽  
Transfer Equations ◽  
Radiative Transfer Equations

Radiative heat transfer equations including heat conduction are considered in the small mean free path limit. Rigorous results on the asymptotic procedure leading to the equilibrium diffusion equation for the temperature are given. Moreover, the nonlinear Milne problem describing the boundary layer is investigated and an existence result is proven. An asymptotic preserving scheme for the radiative transfer equations with the diffusion scaling is developed. The scheme is based on the asymptotic analysis. It works uniformly for all ranges of mean free paths. Numerical results for different physical situations are presented.

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