COMSOL 6.2 - Discrete Ordinates Method (DOM)

	The discrete ordinates method is implemented for 3D, 2D and 2D axisymmetric 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. 24) and yield SN approximations with N(N + 2) directions in 3D or N(N + 2)/2 in 2D and 2D axisymmetric (see Ref. 23). The quasi-uniform quadrature set yields TN approximations with 8N2 directions in 3D or 4N2 in 2D and 2D axisymmetric (Ref. 46, Ref. 47). 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 I1, I2, …, In.

Each dependent variable satisfies, in a cartesian coordinates system, the equation

subject to appropriate boundary conditions, where Si is the ith discrete direction.

The node Opaque Surface (Radiation in Participating Media and Radiation in Absorbing-Scattering Media Interfaces) defines the default boundary condition for radiative intensities I1, I2, …, In:

In Equation 4-125, the first term in the right hand side is the emitted radiative intensity, while the second term represents the reflected radiative intensity.

The node Semitransparent Surface (Radiation in Participating Media and Radiation in Absorbing-Scattering Media Interfaces) defines the following boundary condition for radiative intensities I1, I2, …, In:

for all Si such that n · Si < 0, with

In Equation 4-126, the right hand side is composed of the emitted radiative intensity, the reflected radiative intensity, and the radiative intensity transmitted in a diffuse and specular way.

The Incident Intensity (Radiation in Participating Media and Radiation in Absorbing-Scattering Media Interfaces) node defines a boundary that receives incident radiative intensity Iext and that is transparent for outgoing intensity: