Numerical Solutions of Transient Radiative Transfer Using Time and Frequency-Domain Approaches

The one-dimensional transient radiative transfer problem in the Cartesian coordinate system — an absorbing and scattering medium illuminated by a short laser pulse — is solved by the use of time and frequency-domain approaches. In both cases, a Discrete Ordinates–Finite Volume method is adopted. Results for transmittance show that even if high order spatial schemes coupled with flux limiters can minimize the non-physical results associated with the temporal approach (transmitted flux emerging earlier than the minimal time required by the radiation to leave the medium), early transmitted radiation are always present. Transmittances obtained from the space-frequency method are more accurate, without unrealistic behaviors at early time periods. However, the frequency-dependent approach is computationally expensive with respect to its temporal counterpart, and the implementation of a Fast Fourier Transform algorithm is therefore considered. Finally, promising applications regarding optical diagnosis of absorbing and scattering media, using the radiation transport equation in the space-frequency domain, are briefly discussed.