A combined P₁ and monte carlo model for multidimensional radiative transfer problems in scattering media

A combined two-step computational method incorporating (1) transport approximation of the scattering phase function, (2) P₁ approximation and the finite element method for computing the radiation source function at the first step, and (3) the Monte Carlo method for computing radiative intensity at the second step is developed. The accuracy of the combined method is examined for model problems involving two multidimensional configurations of an anisotropically scattering medium. A detailed analysis is performed for a medium with scattering phase function described by a family of the Henyey-Greenstein functions. The accuracy of the two-step method is assessed by comparing the angular distribution of the radiative flux leaving the medium to that obtained by a reference-complete Monte Carlo method. This study confirms the main results of previous articles on the errors of the two-step solution method. The combined method leads to a significant reduction in computational time as compared to the reference method by at least 1 order of magnitude. Finally, possible applications of the combined method are briefly discussed.