Improved Iterative Convergence of the Finite-Element Method in the Solution of the Second-Order Radiative Transfer Equation by Modified Diffusion Synthetic Acceleration

Abstract

A modified diffusion synthetic acceleration model is developed to improve the convergence of the second-order radiative transfer equation (SORTE). The model considers the influence of a diffusely reflecting boundary and adopts the P₁ diffusion approximation to rectify the scattering source term of the SORTE and the reflecting term of the boundary condition. It can remarkably reduce the computational time in the solution of the SORTE, especially when the participating medium with intensive diffusely reflecting walls is simulated. The accuracy of the model is verified by comparing the results with those of the Monte Carlo method and the finite-element method without any accelerative technique. The effects of the emissivity of walls, the optical thickness, and the scattering albedo on the convergence are also investigated. The results indicate that the accuracy of the proposed model is reliable and its accelerative effect is significant for optically thick and scattering-dominated media with intensive diffusely reflecting walls.

Acknowledgments

Support of this work by the National Natural Science Foundation of China (No. 51006074/E060302), Postdoctoral Foundation of China (No. 20100470725), and Postdoctoral Foundation of Shanghai (No. 11R21415900), are gratefully acknowledged.