H. Qi

Least-Squares Finite Element Analysis for Transient Radiative Transfer in Absorbing and Scattering Media

should be considered. In present research, a finite element model, which is based on the discrete ordinates method and least-squares variational principle, is developed to simulate the transient radiative transfer in absorbing and scattering media. The numerical formulations and detailed steps are given. Moreover, two transient radiative transfer problems are investigated and the results are compared with those by integral method and finite volume method. It indicates that the present model can simulate the transient radiative transfer effectively and accurately. DOI: 10.1115/1.2190694

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.

Finite Element Simulation for Short Pulse Light Radiative Transfer in Homogeneous and Nonhomogeneous Media

With the rapid progress on ultrashort pulse laser, the transient radiative transfer in absorbing and scattering media has attracted increasing attention. The temporal radiative signals from a medium irradiated by ultrashort pulses offer more useful information which reflects the internal structure and properties of media than that by the continuous light sources. In the present research, a finite element model, which is based on the discrete ordinates method and least-squares variational principle, is developed to simulate short-pulse light radiative transfer in homogeneous and nonhomogeneous media. The numerical formulations and detailed steps are given. The present models are verified by two benchmark cases, and several transient radiative transfer cases in two-layer and three-layer nonhomogeneous media are investigated and analyzed. The results indicate that the reflected signals can imply the break of optical properties profile and their location. Moreover, the investigation for uniqueness of temporal reflected and transmitted signals indicate that neither of these two kinds of signals can be solely taken as experimental measurements to predict the optical properties of medium. They should be measured simultaneously in the optical imaging application. The ability of the present model to deal with multi-dimensional problems is proved by the two cases in the twodimensional enclosure. DOI: 10.1115/1.2430720

Study on the Imaginary Temperature of Open Boundary Wall in Cylindrical Medium by Partition Allocation Method

By the partition allocation method, the radiative heat transfer in a cylindrical medium is approximated, in which every subdomain is overlapped with each other and isolated by an imaginary black wall at certain temperatures. The flux equivalent temperature (FET) from the incident radiative flux on the imaginary interface is proposed as the imaginary temperature of open boundary. Compared with the conventional method of the local medium temperature (LMT) as the imaginary temperature, the FET method is more suitable. The effects of the overlap optical thickness and the aspect ratio on the accuracy of partition allocation method were also investigated.

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.