A 3-D multiband closure for radiation and neutron transfer moment models

Radiative Heat Transfer and Effective Transport Coefficients

“…The associated methods are sometimes named multi-group, multi-band, or multi-bin methods. For details, we refer the reader to Turpault (2005), Ripoll & Wray (2008), Nordborg & Iordanidis (2008), and the literature cited therein. In the following we will consider the equations for the spectrally averaged quantities, which are obtained by integration of Eqs.…”

“…Ripoll & Wray (2008)) and partial moments(Frank et al (2006), Frank (2007), as well as for an arbitrarily large number of (generalized) moments(Struchtrup (1998)). It is clear that this closure can equally be applied to particles obeying Fermi statistics (seeCernohorsky & Bludman 3 In part of the more mathematically oriented literature, the entropy is defined with different sign and the principle is called "minimum entropy closure".…”

Minimum entropy production closure of the photo-hydrodynamic equations for radiative heat transfer

“…Equations (6) and (7) define the photo-hydrodynamic equations for the variables e and p of the photon gas. In order to solve a complete radiation problem, Eqs.…”

“…Although equivalent, it might be more convenient to work with P e or with representations as in, e.g., Ref. [7] than with κ e , if general simulations of a fully coupled hydrodynamic radiation problem are performed. Figure 8 shows the effective absorption coefficient κ p (e, p)/κ 1 as a function of pc/e for different e/e (eq) -values.…”

“…A frequently used approximate radiation model is photo-hydrodynamics, which is based on a two-moment expansion of the radiative transfer equation and a variable Eddington factor (VEF) closure [6]. This concept can even be realized in a multiband framework, where the relevant quantities are decomposed according to their spectral properties [7].…”