A dynamic multi-scale model for transient radiative transfer calculations

Maxime Roger (1) , Nicolas Crouseilles (2, 3)

1 mechanical engineering department LAETA IDMEC Institut Superior Técnico, Universidade de Lisboa, Portugal
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 IPSO - Invariant Preserving SOlvers

A dynamic multi-scale model which couples the transient radiative transfer equation (RTE) and the diffusion equation (DE) is proposed and validated. It is based on a domain decomposition method where the system is divided into a mesoscopic subdomain, where the RTE is solved, and a macroscopic subdomain where the DE is solved. A buffer zone is introduced between the mesoscopic and the macroscopic subdomains, as proposed by Degond and Jin in \cite{Degond05}, where a coupled system of two equations, one at the mesoscopic and the other at the macroscopic scale, is solved. The DE and the RTE are coupled through the equations inside the buffer zone, instead of being coupled through a geometric interface like in standard domain decomposition methods. One main advantage is that no boundary or interface conditions are needed for the DE. The model is compared to Monte Carlo, finite volume and P1 solutions in one dimensional stationary and transient test cases, and presents promising results in terms of trade-off between accuracy and computational requirements.

Mots clés: transient radiative transfer; multi-scale model; finite volume method; diffusion equation; domain decomposition

Domaines: Physique Numérique [physics.comp-ph]

Maxime Roger, Nicolas Crouseilles. A dynamic multi-scale model for transient radiative transfer calculations. Journal of Quantitative Spectroscopy and Radiative Transfer, 2013, 116, pp.110-121. ⟨10.1016/j.jqsrt.2012.10.009⟩. ⟨hal-00728874⟩