Discrete Ordinates Method (DOM)
The discrete ordinates method is implemented for 3D and 2D geometries.
Radiative intensity is defined for any direction Ω, because the angular space is continuous. In order to handle the radiative intensity equation numerically, the angular space is discretized.
The discrete ordinates method provides a discretization of angular space. The quadrature sets Level Symmetric Even, Level Symmetric Hybrid and Equal Weight Odd are designed using moment-matching conditions (see Ref. 21) and yield SN approximations with N(N + 2) directions in 3D or N(N + 2)/2 in 2D (see Ref. 20). The quasi-uniform quadrature set yields TN approximations with 8N2 directions in 3D or 4N2 in 2D (Ref. 42, Ref. 43). These approximations are not designed using moment-matching conditions but allow for higher-order discretization compared with SN approximations.
Thanks to angular space discretization, integrals over directions are replaced by numerical quadratures of discrete directions:
Depending on the value of N, a set of n dependent variables has to be defined and solved for I1I2, …, In.
Each dependent variable satisfies the equation
where Si is the i-th discrete ordinate, with the following boundary condition
with