Assuming that a model is invariant in the z direction, the radiative transfer equation in two directions,
Si+ and
Si-, for the discrete ordinates method (DOM) reads:
In addition if can be rewritten as a function of Si ⋅ Sj, as it is in the COMSOL Multiphysics implementation, then
Using results from Equation 4-123 and
Equation 4-124 the DOM is formulated in 2D using only radiative intensities,
, on half of the 3D DOM directions,
, except for the scattering term. In other expressions than the scattering term, the
z component of the radiative intensities
Ii and of the discrete directions
Ωi can be ignored (or set to zero) and the weight
wi, multiplied by 2.