Finite-Volume Solution of the Second-Order Radiative Transfer Equation: Accuracy and Solution Cost

Abstract

The finite-volume method is applied to the second-order radiative transfer equation, proposed by Zhao and Liu, to study its accuracy and solution cost for two simple two-dimensional problems. The second-order equation leads to results that are accurate and bounded, but the iterative solution of the equations is expensive, especially for weakly participating media. The high cost is due mainly to the elliptic character of the second-order equation and the lack of diagonal dominance of the algebraic equations.

This work was financially supported by the Climate Change Technology and Innovation Initiative (CCTII) through CANMET Energy Technology Centre, Natural Resources Canada, of the Canadian Federal Government, and through an Operating Grant to G. D. Raithby from the Natural Sciences and Engineering Council of Canada. The authors also gratefully acknowledge the contributions of Dr. E. H. Chui and Prof. G. D. Stubley.

Notes

¹Note that the order of the RTE refers to the order of the highest derivative in the integrodifferential equation, while the order of the discretization refers to the rate at which the numerical solution of the RTE approaches its exact solution with grid refinement.