L.M. Ruan

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

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.

Numerical approach for reflections and transmittance of finite plane-parallel absorbing and scattering medium subjected to normal and diffuse incidence

The discrete ordinate method (DOM) is used to analyze the radiative energy transfer in one-dimensional absorbing, scattering and non-emitting planar slab subjected to normal and diffuse incidence. To improve the ability of DOM to treat complex scattering phase function, a revision of DOM is presented. The reflectance and transmittance of a semitransparent planar slab is calculated by the DOM. The results are compared with the exact values and the solution arrived at other approximate method. It is shown that the DOM has a good accuracy in solving the reflectance and transmittance of a semitransparent planar slab, and can easily treat the complex scattering phase function.

The Combined Radiative Integral Equations and Finite-Element Method for Radiation in Anisotropic Scattering Media

A combined procedure of the radiative integral equation and finite-element method (IEFEM) is proposed for handling radiative heat transfer in linearly anisotropic scattering media. The IEFEM can eliminate the angular discretization and easily handle irregular geometries. The present work provides a solution of radiative transfer in rectangular and irregular quadrilateral enclosures containing participating media. The influences of emissivities, albedos, and anisotropy on the boundary fluxes or incident intensity have been analyzed. Compared with the results in published references, the present IEFEM has no limitation to geometry and can predict the radiative heat transfer in linearly anisotropic scattering media accurately.