The Discrete Ordinates Method

The directional domain is broken down into the specified number of equal solid angles or directions. The total number of directions is defined as:

where RL is the Discretization level specified by the user. Within each direction the radiation intensity is considered constant.

In the absence of scattering the radiative transfer equation (RTE) can be written as:

where I is the radiation intensity per solid angle, is the blackbody radiation intensity, α is the medium absorption coefficient, n is the refraction index.

At the surfaces of opaque solids the incident heat radiation is absorbed depending on the specified emissivity coefficient, the rest of the incident radiation is reflected. The opaque surfaces can also emit heat radiation diffusively in accordance with the surface temperature and the specified emissivity coefficient.

Since all fluids are considered as transparent to heat radiation, the heat radiation propagates through them, as well as through transparent solids, without any interaction with them. However, as the heat radiation is traced through the computational domain by the discrete ordinates method, the “false scattering” effect caused by the discretization inaccuracies can appear - it is similar to the “numerical diffusion” effect in fluid flow calculations. Creating a finer computational mesh allows to reduce this effect.

When the radiation propagates from a small source to a significant distance, the “ray effect” can be encountered as a result of breaking down the directional domain into several directions. As radiation in these directions is traced from the source, it begin to demonstrate a ray-like behavior because more and more cells fall within the same direction with the distance and the radiation intensity distribution within the direction becomes non-uniform. This effect must be considered when decreasing the cell size to avoid the “false scattering” effect, so the discretization level must be increased if the finer mesh is used.