The P1 approximation is available as a radiation discretization method in
The Radiation in Participating Media Interface.
From a computational point of view this approximation has a limited impact because it introduces only one additional degree of freedom for the incident radiation G (SI unit: W/m
2), which is a scalar quantity and adds a heat source or sink to the temperature equation to account for radiative heat transfer contributions. This method, however, fails to accurately represent cases where the radiative intensity propagation dominates over its diffusivity or where the scattering effects cannot be described by a linear isotropic phase function.
When scattering is modeled as isotropic, a1=0 and the P1 diffusion coefficient reduces to
where qr, net is the net radiative heat flux at the boundary.
In addition Qr, defined by
Equation 4-126, is added as an heat source in the heat transfer equation:
The Opaque Surface (Radiation in Participating Media and Radiation in Absorbing-Scattering Media Interfaces) boundary condition defines a boundary opaque to radiation and defines the incident intensity on a boundary:
The Semitransparent Surface (Radiation in Participating Media and Radiation in Absorbing-Scattering Media Interfaces) boundary condition defines a boundary that emits radiation, and reflects one part of the incident intensity while the remaining is transmitted diffusively.
The net radiative heat flux, qr, net, accounted for in the heat balance, is defined as
where ρd is the surface diffuse reflectivity, and
τd is the surface diffuse transmissivity.
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. On these boundaries, the relation between
G (incident radiation),
qr, net (net radiative heat flux) and
Iext (incident radiative intensity) is
The node Radiative Source accounts for a power density
Q in the P1 approximation: