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. 23
) and yield S
N
approximations with
N
(
N
+
2
)
directions in 3D or
N
(
N
+
2
)/
2
in 2D (see
Ref. 22
). The quasi-uniform quadrature set yields T
N
approximations with
8
N
2
directions in 3D or
4
N
2
in 2D (
Ref. 44
,
Ref. 45
). These approximations are not designed using moment-matching conditions but allow for higher-order discretization compared with S
N
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
I
1
,
I
2
, …,
I
n
.
Radiation in Participating Media
Each dependent variable satisfies the equation
subject to appropriate boundary conditions, where
S
i
is the
i
th discrete direction.
Opaque surface
The node
Opaque Surface (Radiation in Participating Medium and Radiation in Absorbing-Scattering Medium Interfaces)
defines the default boundary condition for radiative intensities
I
1
,
I
2
, …,
I
n
:
,
with
.
Incident Intensity
The
Incident Intensity (Radiation in Participating Medium and Radiation in Absorbing-Scattering Medium Interfaces)
node defines a boundary that receives incident radiative intensity
I
ext
and that is transparent for outgoing intensity:
.
Radiative source
The node
Radiative Source
accounts for a directional power density
I
i
in the radiative transfer equation:
.
,
.
.
.