A Truly Two-Dimensional, Asymptotic-Preserving Scheme for a Discrete Model of Radiative Transfer

Laurent Gosse (1) , Nicolas Vauchelet (2)

1 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"
2 LAGA - Laboratoire Analyse, Géométrie et Applications

For a four-stream approximation of the kinetic model of radiative transfer wih isotropic scattering, a numerical scheme endowed with both truly-2D well-balanced and diffusive asymptotic-preserving properties is derived, in the same spirit as what was done in [14] in the 1D case. Building on former results of Birkhoff and Abu-Shumays, [4], it is possible to express 2D kinetic steady-states by means of harmonic polynomials, and this allows to build a scattering Smatrix yielding a time-marching scheme. Such a S-matrix can be decomposed, as in [15], so as to deduce another scheme, well-suited for a diffusive approximation of the kinetic model, for which rigorous convergence can be proved. Challenging benchmarks are also displayed on coarse grids.

Mots clés: Diffusive scaling; Four-stream approximation; Grey radiative transfer; S-matrix

Domaines: Equations aux dérivées partielles [math.AP]

Laurent Gosse, Nicolas Vauchelet. A Truly Two-Dimensional, Asymptotic-Preserving Scheme for a Discrete Model of Radiative Transfer. SIAM Journal on Numerical Analysis, 2020, 58 (2), pp.1092-1116. ⟨10.1137/19M1239829⟩. ⟨hal-03841186⟩