A thermodynamical approach to Eddington factors

Anile, A. M.; Pennisi, Sebastiano; Sammartino, M.

doi:10.1063/1.529391

Cited by 84 publications

(97 citation statements)

References 7 publications

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“…The reader is refered to [32][33][34] for pionner derivations of the radiative pressure law P (E, F ). Finally, c is the speed of the light, a > 0 is a given constant, ρ = ρ(T ) is the density which is supposed to be a given function, and σ e , σ a , and σ f denote the opacities mean values.…”

Section: The M1 Model For Radiative Transfermentioning

confidence: 99%

Asymptotic preserving HLL schemes

Berthon

Turpault

2010

Numer. Methods Partial Differential Eq.

110

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This work concerns the derivation of HLL schemes to approximate the solutions of systems of conservation laws supplemented by source terms. Such a system contains many models such as the Euler equations with high friction or the M1 model for radiative transfer. The main difficulty arising from these models comes from a particular asymptotic behavior. Indeed, in the limit of some suitable parameter, the system tends to a diffusion equation. This article is devoted to derive HLL methods able to approximate the associated transport regime but also to restore the suitable asymptotic diffusive regime. To access such an issue, a free parameter is introduced into the source term. This free parameter will be a useful correction to satisfy the expected diffusion equation at the discrete level. The derivation of the HLL scheme for hyperbolic systems with source terms comes from a modification of the HLL scheme for the associated homogeneous hyperbolic system. The resulting numerical procedure is robust as the source term discretization preserves the physical admissible states. The scheme is applied to several models of physical interest. The numerical asymptotic behavior is analyzed and an asymptotic preserving property is systematically exhibited. The scheme is illustrated with numerical experiments.

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Section: The M1 Model For Radiative Transfermentioning

confidence: 99%

Asymptotic preserving HLL schemes

Berthon

Turpault

2010

Numer. Methods Partial Differential Eq.

110

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“…Similar theories for non-LRE, e.g. [2,10,11,12], however, do not provide a proper description of radiative processes because the variety of deviations from the equilibrium state cannot be described by the two quantities energy and momentum alone.…”

Section: Introductionmentioning

confidence: 94%

An Extended Moment Method in Radiative Transfer: The Matrices of Mean Absorption and Scattering Coefficients

Struchtrup

1997

Annals of Physics

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“…Approximate equations can be derived from the full transport equations by asymptotic analysis or simply by taking suitable moments and closure relations. Examples are diffusion or Rosseland equations, the P N equations, and moment equations closed by the entropy minimization principle [2,6,[8][9][10]12]. The latter have turned out to describe certain physical situations, i.e., solutions of the full transport equation, much better than diffusion-type equations (see [6,12]).…”

Section: Introductionmentioning

confidence: 99%