An angular reduced order model for radiative transfer in non grey media

Abstract

This paper investigates a reduced order model for the angular discretisation of the radiative transfer equation (RTE) when considering non grey participating gases. The key idea is to use a global model for the gas radiative properties and to derive an angular reduced order model, based on

Deterministic radiative transfer equation solver on unstructured tetrahedral meshes: Efficient assembly and preconditioning

“…To deal with larger problems, at least two modern ways to solve the RTE have emerged. First, the use of reduced order models [55] or sparse grids may be used to deal efficiently with the "curse of dimensionality" [56,57] (up to 3 • 10 6 unknowns solved sequentially). Second, Jacobian-free Newton-Krylov methods [58] have been extended to the RTE [59] (up to 512 MPI processes and 8 threads per MPI process on a Cartesian grid of 65 thousand elements with up to 120 directions).…”

Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor

“…In recent years, many data-driven ROMs have been developed using these techniques for linear problems involving the BTE. Dimensionality reduction in the angular variable has been formulated using both the POD and reduced-basis methods [43,44,45,46,47]. POD-Petrov-Galerkin projections have been formulated for the steady-state BTE in 1D geometry [48,49].…”

“…A new approach based on data-driven reduced-order models (ROMs) has been gaining popularity in recent years which make use of data-based methodologies to dimensionality reduction. Data-driven models have been developed for (i) linear particle transport problems [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48] (ii) nonlinear RT problems [49,50,51,52,53,54,55,56,57,58,59,60], and (iii) various problems in nuclear reactor-physics [61,62,63,64,65,66,67,68,69,70,71]. The fundamental idea behind these ROMs is to leverage databases of solutions to their problems of interest (known a-priori) to develop some reduction in the dimensionality for their involved equations.…”

An adaptive reduced order model for the angular discretization of the Boltzmann transport equation using independent basis sets over a partitioning of the space‐angle domain

“…Early examples of ROMs in the field include Reference 28, which used several ROM techniques to analyze the transient dynamics of reactor‐driven systems; Reference 29, which applied them to one dimensional transient radiation problems; and Reference 30, which applied POD to the spatial dimensions of eigenvalue problems in the context of reactor physics. Further developments include the application of POD to the angular dimension of the BTE, 31‐33 space‐angle ROMs for radiative heat transfer, 34 and the use of range‐finding algorithms for the linear transformation of parameters in multiphysics problems 35 . More recently, POD has been used to model fuel burnup 36 and reactor power distributions 37 .…”