In this paper, we formulated, applied, and tested the FTn Finite Volume Method (FTn FVM) for transient radiative transfer in three-dimensional absorbing, emitting, and anisotropically scattering medium. Both the STEP and the Curved-Line Advection Method (CLAM) are introduced for spatial discretization of the transient radiative transfer equation. The results show that FTn FVM reduces largely the ray effects and it is more accurate than the standard FVM. Also, using both STEP and CLAM schemes, FTn FVM has smaller convergence time than the standard FVM for all cases. On the contrary, the STEP scheme is faster than the CLAM scheme but it has less accuracy. Then, the effects of optical thickness, scattering albedo, and anisotropy factor on incident radiation and radiative flux are presented and discussed.
In this paper, 3-D heterogeneous medium, containing small inhomogeneous zones, subjected to a short-pulse laser has been examined by solving the transient radiative transfer equation. Both curved-line advection method and STEP schemes of the FTn finite volume method have been applied. The curved-line advection method predictions proved that a decrease of the false scattering and ray effects are obtained. In fact, there was a good agreement between the curved-line advection method and the Monte Carlo method. However, the STEP results are slightly mismatching the predictions of the aforementioned reference method. Then, the effects of the absorption coefficient, the size, the number and the position of inhomogeneous zone on the transmittance and reflectance signals have been analyzed. The predictions showed that the increase of the size of the inhomogeneity reduces the intensity of radiation. For both homogenous and heterogonous medium, the change of the detector position varies both the broadening of the signal pulse-width and the time with peak reflectance and/or transmittance. That is can be explained by the effects of the distance and the medium property between the laser-incident source and the detector position. Thus, these both parameters are the main factors for determining the peak position and the pulse broadening. Finally, the effects of the absorption coefficient in the inhomogeneity zone on the absolute values of logarithmic slope has been discussed. The results proved that the absolute values of logarithmic slope may be a perfect indicator for detecting any abnormal absorbing zones in the medium.
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