Least-Squares Finite-Element Method of Multidimensional Radiative Heat Transfer in Absorbing and Scattering Media

Abstract

A least-squares finite-element method (LSFEM) is developed to simulate the radiative transfer in absorbing and scattering media. This model is based on the discrete ordinates method (DOM) and the least-squares finite-element method. It can be presented as an alternative to the traditional Galerkin finite-element method (GFEM). This method is used to overcome the spurious oscillation which be found in the GFEM for radiative transfer. In addition, the resulting coefficients matrix produced by the LSFEM is symmetric and positive-definite. Only half of a sparse matrix needs to be stored. Some efficient iterative algorithms for symmetrical systems of equations can be used successfully. In order to validate this method, two 2-D problems and a 3-D problem of radiative transfer are examined. The computational results indicate that the present model can simulate the radiative transfer in the multidimensional complex geometric enclosure efficiently and accurately. More important, the present model is proved to be wiggle-free.