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In this work, the STEP scheme and several schemes based on the normalized variable diagram (NVD), such as MINMOD, GAMMA, CLAM, NOTABLE, MUSCL, CUBISTA, SMART, WACEB, and VANOS schemes, are evaluated for solving the radiative transfer equation. Two‐dimensional and three‐dimensional rectangular enclosures containing transparent, emitting–absorbing, emitting–absorbing–scattering, or nonhomogeneous participating media are investigated using the modified FTn finite volume method. Although the NVD schemes are much more accurate than the STEP scheme, but they have more time‐consuming and require more iterations. Moreover, most of them often necessitate underrelaxation to ensure convergence. Results show that the MINMOD and GAMMA schemes are still much less accurate than other NVD schemes, but they converge the fastest of the NVD schemes, and do not require underrelaxation. Although the VANOS, WACEB, and SMART schemes give more accurate solutions, they are not competitive with other NVD schemes. However, the CLAM, NOTABLE, and CUBISTA schemes are relatively fast and accurate.

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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.

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