Evaluation of Radiances Generated by Solving the Radiative-Transfer Equation with Different Approaches

Radiative transfer is the main phenomenon in the basis of several relevant problems of scientific and technological interest. Examples of application of the mathematical and computational modeling of such phenomenon can be found in astronomy, environmental sciences, engineering and medicine among many different areas. The integro-differential equation known as Boltzmann equation describes mathematically the interaction of the radiation with the participating medium, i.e. a medium which may absorb, scatter and emit radiation. Several methods have been developed for the solution of the Bolztmann equation. In the present work we present a comparison of the solutions obtained for the one-dimensional problem with four different methods: (i) Monte Carlo (MC) method; (ii) Discrete Ordinates method (S-N) combined with a finite difference approximation; (iii) Analytical Discrete Ordinates method (AS(N)); and (iv) Laplace Transform Discrete Ordinates method (LTSN). Our final objective is to solve the inverse radiative transfer problem and for that purpose, we want to investigate methods that may provide accurate and fast solutions for the direct problem.