Computing enhancement of the nonlinear SPN approximations of radiative heat transfer in participating material

Abstract

Anisotropic mesh adaptation is an efficient procedure for controlling the output error of finite element simulations, particularly when used for three-dimensional problems. In this paper, we present an enhanced computational algorithm based on an anisotropic mesh adaptation for nonlinear SPN approximations of radiative heat transfer in both two- and three-dimensional enclosures. Using an asymptotic analysis for the optical scale in the radiative transfer, the integro-differential equation is replaced by a series of partial differential equations of elliptic type. The nonlinear coupling between the heat transfer and radiation in the SPN equations does not depend on the direction ordinates. In an anisotropic participating media, internal boundary layers with different magnitudes occur for each direction and developing an efficient numerical algorithm to accurately resolve them is a challenging task. In the present study, we propose an adaptive finite element method using an efficient hierarchical error estimator. A second-order scheme is used for the time integration and a Newton-type solver is implemented for the fully coupled nonlinear system. The proposed method has the potential to use large timesteps in the simulations for radiative heat transfer in anisotropic media at high temperatures. To demonstrate the viability of the method, several examples are presented for two- and three-dimensional problems. The numerical results confirm the capability of the proposed method to efficiently solve the nonlinear SPN approximations of radiative transfer in anisotropic media.