This research proposal focuses on the study, through modeling and numerical simulation, of heat transfer within a heterogeneous medium composed of opaque solids and a transparent or semi-transparent fluid. The considered modes of transfer are radiation and conduction.

Depending on the scale of interest, the radiance is the solution of the Radiative Transfer Equation (RTE). In its classical form, the RTE describes heat transfer phenomena at the so-called local scale, where solids are explicitly represented in the domain. At the mesoscopic scale of an equivalent homogeneous medium, however, the radiance is governed by a generalized RTE (GRTE) when the medium no longer follows the Beer–Lambert law. In this work, we focus on the numerical resolution of the RTE in both configurations, ultimately coupled with the energy conservation equation for temperature.

In deterministic resolution of the RTE, a standard approach for handling the angular variable is the Discrete Ordinates Method (Sn), which relies on quadrature over the unit sphere. For non-Beerian media, solving the GRTE is a very active research topic, with Monte Carlo methods often receiving more attention. Nevertheless, the GRTE can be linked to the generalized transport equation, as formulated in the context of particle transport, and a spectral method can be applied for its deterministic Sn resolution. This is the direction pursued in this PhD project.

The direct application of this work is the numerical simulation of accidents in Light Water Reactors (LWR) with thermal neutrons. Modeling radiative heat transfer is crucial because, in the case of core uncovering and fuel rod drying, radiation becomes a major heat removal mechanism as temperatures rise, alongside gas convection (steam). This topic is also relevant in the context of the nuclear renaissance, with startups developing advanced High Temperature Reactors (HTR) cooled by gas.

The goal of this thesis is the analysis and development of an innovative and efficient numerical method for solving the GRTE (within a high-performance computing environment), coupled with thermal conduction. From an application standpoint, such a method would enable high-fidelity simulations, useful for validating and quantifying the bias of simplified models used in engineering calculations.

Successful completion of this thesis would prepare the student for a research career in high-performance numerical simulation of complex physical problems, beyond nuclear reactor physics alone.