A DISCONTINUOUS FINITE-ELEMENT FORMULATION FOR MULTIDIMENSIONAL RADIATIVE TRANSFER IN ABSORBING, EMITTING, AND SCATTERING MEDIA

Abstract

This article presents a discontinuous finite-element formulation for the numerical solution of internal thermal radiation problems in multidimensional domains. In contrast with the conventional finite-element formulation, the discontinuous finite element is based on the idea of allowing the discontinuity of field variables across the internal interelement boundaries and thus is particularly useful for the integral-differential equations governing the thermal radiative transfer phenomena in emitting, absorbing, and scattering media. Mathematical formulation and numerical details using the discontinuous finite element method for internal radiation heat transfer calculations are given. Computational procedures are presented. A parallel computing algorithm exploiting the advantages of the localized discontinuous finite-element formulation and space/solid-angle discretization characteristics is presented. The computed results are given and compared with analytical solutions whenever available as reported in references. Examples include both nonscattering and scattering cases. Parallel computing performance is also evaluated for both 2-D and 3-D cases and results show that the parallel algorithm can be easily implemented within the framework of the discontinuous finite-element method. For the cases tested, the parallel scheme based on the solid-angle discretization gives a reduction in CPU time approaching to almost an idealized parallel CPU scenario.

The authors gratefully acknowledge the support of this work by the U.S. Air Force Office of Research, subcontracted through VLOC, Inc. (Grant VAN00138704451) and by NASA (Grant NAG8-1693). The assistance of Mr. Xin Ai with the unstructured mesh generation is also acknowledged.