Properties and frequential hybridisation of the multigroup M1M1 model for radiative transfer

Radiative transfer is a phenomenon that has importance in a wide range of applications from climatology to astrophysics. Depending on the physical regimes involved, a hierarchy of models may be used, each of which having drawbacks and qualities. However, there are still applications for which no model is fully satisfying. An example is ICF (Inertial Confinement Fusion) where dozens of lasers converge on a fuel pellet of the size of a pinehead. This kind of simulation requires a coupling between radiation and other processes and hence one would require a model that is cheap enough in terms of computation cost to carry it out. The M1M1 model (Dubroca and Klar (2002) [14]) may then seem to be an interesting choice. But the directional complexity of the problem and the fact that the energy is mainly located inside a narrow frequency interval is hardly compatible with this model and one would rather use an (expensive) model such as a kinetic model.In this paper, we prove several important properties of the multigroup M1M1 model that extends the results of the grey M1M1 model. Then we introduce a hybrid model that mixes it with a kinetic model. This hybrid model intends to be an extension of both of them and therefore adds degrees of freedom that allows us to properly take into account a wide variety of problems. We also show that it possesses important properties including the correct asymptotic limit in the diffusion regime and the local decreasing of the total entropy.