The Monte Carlo method and the solution of the radiative transfer equation - Berrocal Tito, Mariella (2010)
The radiation pathway through a medium where occur the absorption, scattering and emission phenoma is described by the radiative transfer equation (ETR). For purely absorbing media, the dispersion phenomenon is neglected by reducing the ETR to a linear differential equation with analytical solution. For dispersive media, the ETR is a nonlinear differential equation, with non analytical solution and the solution must be approximated by deterministic numerical methods. Monte Carlo is a stochastic method based in probabilities and use random numbers to simulate the occurrence of an event, in this case, the pathways radiation in a participating media. In this study, we have used finite difference and discrete ordinates methods to solve the ETR in one dimension, the results were compared with the Monte Carlo results, Test case results are presented, also the source code used for the solution of both methods in the Scilab.