A second-order maximum-entropy inspired interpolative closure for radiative heat transfer in gray participating media. (November 2020) - Sarr, Joachim A.R.; Groth, Clinton P.T.
Highlights: New second-order interpolative-based M2 maximum-entropy closure for constructing approximate solutions of the radiative transport equation in gray-participating media governed Bose-Einstein statistics. Review of and new insight into the necessary and sufficient conditions for realizability of predicted moments up to second order in multiple space dimensions. Demonstration of hyperbolicity of proposed interpolative-based M2 closure via numerical experiments. Development of boundary conditions for M2 moment closure based on partial moment approach. Illustration of predictive capabilities of interpolative-based M2 closure for several one and twodimensional canonical test problems. Abstract: A new interpolative-based approximation to the second-order maximum-entropy, M2, 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 M2 closure, the proposed interpolative approximation provides significant reductions in computational costs compared to the costs of the original M2 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 M2 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, M1, moment closure, as well as those of the more commonly adopted spherical harmonic moment closure techniques (first-order P1 and third-order P3 ) 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 M2 closure, with the closure outperforming the M1, P1 and P3 closures for virtually all cases considered.