Participating media exposed to collimated short-pulse irradiation – A Laguerre–Galerkin solution

A new method is developed for the solution of radiative transfer in a one-dimensional absorbing and isotropically scattering medium with short-pulse irradiation on one of its boundaries. The time-dependent radiative intensity is expanded in a series of Laguerre polynomials with time as the argument. Moments of the radiative transfer equation, as well as of the boundary conditions, then yield a set of coupled time-independent radiative transfer problems. This set, in turn, is reduced to a set of algebraic equations by the application of the Galerkin method. The transient transmittance and reflectance of the medium are evaluated for various values of the optical thickness, scattering albedo and pulse duration. It is demonstrated that the Laguerre–Galerkin method is not only easier to implement and more efficient but also yields more accurate results compared to the direct application of the Galerkin method. The results are in very good agreement with those available in the literature.