Transient radiative tranfer in the grey case: well-balanced and asymptotic-preserving schemes built on Case's elementary solutions

Laurent Gosse (1)

1 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"

An original well-balanced (WB) Godunov scheme relying on an exact Riemann solver involving a nonconservative (NC) product is developed in order to solve accurately the time-dependent one-dimensional radiative transfer equation in the discrete-ordinates approximation with an arbitrary even number of velocities. The collision term is thus concentrated onto a discrete lattice by means of Dirac masses; this induces steady jump relations across with the stationary problem is solved by taking advantage of the method of elementary solutions mainly developed by Case, Zweifel and Cercignani. This approach produces a rather simple scheme that compares advantageously to standard existing upwind schemes, especially for the decay in time toward a Maxwellian distribution. It is possible to reformulate this scheme in order to handle properly the parabolic scaling in order to generate a so--called asymptotic-preserving (AP) discretization for which the consistency with the diffusive approximation holds independently of the computational grid. Several numerical results are displayed to show the realizability and the efficiency of the method.

Mots clés: Radiative transfer; Diffusive approximation; Discrete ordinate method; Slab geometry; Case's elementary solutions; Well-balanced schemes; Asymptotic-preserving schemes; Non-conservative products

Domaines: Analyse numérique [math.NA]; Physique Nucléaire Théorique [nucl-th]

Laurent Gosse. Transient radiative tranfer in the grey case: well-balanced and asymptotic-preserving schemes built on Case's elementary solutions. Journal of Quantitative Spectroscopy and Radiative Transfer, 2011, 112, pp.1995-2012. ⟨10.1016/j.jqsrt.2011.04.003⟩. ⟨hal-00540294⟩