A second-order maximum-entropy inspired interpolative closure for radiative heat transfer in gray participating media

A new interpolative-based approximation to the second-order maximum-entropy, M-2, moment closure for predicting radiative heat transfer in gray participating media is proposed and described. In addition to preserving many of the desirable mathematical properties of the original M-2 closure, the proposed interpolative approximation provides significant reductions in computational costs compared to the costs of the original M-2 closure by avoiding repeated numerical solution of the corresponding optimization problem for entropy maximization. Theoretical details of the proposed interpolative-based closure, along with a description of an efficient Godunov-type finite-volume scheme that has been developed for the numerical solution of the resulting system of hyperbolic moment equations, are presented. The finite-volume method makes use of limited linear solution reconstruction, multi-block body-fitted quadrilateral meshes with anisotropic adaptive mesh refinement (AMR), and an efficient Newton-Krylov-Schwarz (NKS) iterative method for solution of the resulting non-linear algebraic equations arising from the spatial discretization procedure. The predictive capabilities of the proposed interpolative M-2 closure are assessed by considering a number of model problems involving radiative heat transfer within one- and two-dimensional enclosures, the results for which are compared to solutions of the first-order maximum entropy, M-1, moment closure, as well as those of the more commonly adopted spherical harmonic moment closure techniques (first-order P-1 and third-order P-3) and the popular discrete ordinates method (DOM). The latter is used as a benchmark for comparisons, whenever exact solutions are not available. The numerical results illustrate the promise of the proposed M-2 closure, with the closure outperforming the M-1, P-1 and P-3 closures for virtually all cases considered. (C) 2020 Elsevier Ltd. All rights reserved.