===== Namelist "Radiative_Heat_Transfer_DOM" =====

__** Not for the release SUNFLUIDH_EDU**__ .\\
This data set is used to define the radiative problem. Otherwise, it can be omitted.\\
This module considers the Radiative Transfer Equation (RTE) for an emitting-absorbing non-scattering medium enclosed by diffuse boundaries.
To take into account the gas behavior, it considers both gray-gas assumption as well as real gas behavior through the Spectral-Line-Weighted-Sum-of-Gray-Gases (SLW) model. \\
The final RTE-SLW problem is then discretize with the Discrete Ordinates Method (DOM).

**The DOM** discretize the $4\pi$ steradians integration in a set of $M$ discrete directions represented by their direct cosines and corresponding weights $\vec{q_m} = (\vec{s_m},\omega_m) = (\mu_m,\eta_m,\xi_m,\omega_m)$ for all $m \in [1,M]$.\\
**The SLW model** will change the spectral integration in a weighted sum of $N_g$ gray-gases represented by their absorption coefficient and corresponding weights $(\kappa_j,a_j)$ for all $j \in [1,N_g]$.

Thus, the resulting **RTE-SLW-DOM** problem for emitting-absorbing non-scattering medium stands as below :

\begin{equation}
\vec{s}_m \cdot \nabla I_j^m (x_i,\vec{s}_m) = \kappa_j \left[ a_j I_b({T}(x_i)) - I_j^m(x_i,\vec{s}_m) \right]; \quad \forall (m,j) \in [M,N_g]
\end{equation}

where $I_j^m$ is the radiative intensity for the virtual gray-gas $j$ in direction $m$ and $I_b$ is the blackbody radiative intensity.




The **dimensional** radiative source term $S_r$ and boundary net radiative heat flux $q_r^{net}$ are defined as :


\begin{eqnarray}
S_r(x_i,{T}) & = & - \sum_{j=0}^{N_g} \kappa_j \left[ \sum_{m=1}^{M} \omega_m I_j^m (x_i,\vec{s}_m)  - 4 a_j \sigma_B ({T}(x_i))^4 \right] \\
{q}_r^{net}(x_i^{wall}) & = & \varepsilon_{wall} \left[ \sigma_B ({T}(x_i^{wall}))^4 - \sum_{j=0}^{N_g} \sum_{m:\vec{s}_m \cdot \vec{n} > 0} \omega_m |\vec{s}_m\cdot \vec{n}| I_j^m (x_i^{wall},\vec{s}_m) \right]
\end{eqnarray}

where $\sigma_b$ is the Stefan-Boltzmann constant, $\varepsilon$ is the boundary emissivity and $\vec{n}$ is the normal to the wall pointing out of the domain.


<note warning>This radiative solver implementation considers only **cartesian** problems and **does not support immersed bodies**.</note>
===== Full data set of the namelist =====

    &Radiative_Heat_Transfer_DOM  activateRadiation = .false., RadiativePeriod = 1, FirstIterations = 20, 
				RadiativeLocalIterations = 1, RadiativeConvergenceTolerance = 1.E-15,
				WallRadcoeff = 1.0 , VolRadCoeff = 1.0, RadiativeScheme = "STEP",
				ActivateGas = .false., NbGas = 1, ka_max = 0.0, ka_min = 0.0,
				Pref = 101325.0, Tref = 300., Href = 1, speca = "H2O", xaref = 0.07, xaUniform = 0.07,
				SQuad = 8, WallEmissivity = 0.0 0.0 0.0 0.0 0.0 0.0 /

-----
===== Definition of the data set for the DOM-RTE problem =====
-----
==== activateRadiation ====
   * Type : Boolean value
   * This option activates the radiative module.
     * .false. : no radiation considered 
     * .true.  : radiation problem is considered
   * Default value = .false.
==== RadiativePeriod ====
   * Type : Integer value
   * This option set the periodicity of resolution of the Radiative problem in time iteration.
   * Default value = 1
==== FirstIterations ====
   * Type : Integer value
   * In the case that no restart fields are available (start radiation from scratch), the solver will iterates "FirstIterations" times before entering the time loop.
   * Default value = 20
==== RadiativeLocalIterations ====
   * Type : Integer value
   * Number of sub-iteration for the RTE solving at each radiative iteration.
   * Default value = 1
==== RadiativeConvergenceTolerance ====
   * Type : Real value
   * Convergence criteria on the wall Fluxes and radiative source term for the sub-iteration.
   * Default value = 1.E-15
==== WallRadcoeff ====
   * Type : Real value
   * Prescaler on the net radiative heat flux $q_r^{net}$ at walls.
   * **For debugging only**.
   * Default value = 1.0
==== VolRadcoeff ====
   * Type : Real value
   * Prescaler on the radiative source term $S_r$.
   * **For debugging only**.
   * Default value = 1.0
==== RadiativeScheme ====
   * Type : Character string with a maximum size of 20
   * Name of the interpolation scheme used in the Discrete Ordinates Method.
   * Available values :
     * "STEP"    : first order interpolation scheme (robust)
     * "DIAMOND" : second order centered interpolation scheme (could lead to negative intensity)
     * "LATHROP" : second order interpolation scheme with limiter (time-consuming)
   * Default value = "STEP"
==== SQuad ====
   * Type : Integer value.
   * Order N of the level symmetric angular quadrature ($S_N$)
   * This quadrature leads to $M = (N+2)\times N$ directions in volume and half at boundaries
   * Available values are 2, 4, 6, 8, 10, 12, 14
   * Default value = 8
==== Tref ====
   * Type : Real value.
   * Reference temperature $T_{ref}$ in [$K$].
   * Default value = Fluid_Properties%Reference_Temperature
==== Href ====
   * Type : Real value.
   * Reference Length $H_{ref}$ in [$m$].
   * Default value = Nondimensionalization%Reference_Length
==== WallEmissivity ====
   * Type : Real array of size 6.
   * Boundaries emissivities $\varepsilon$ sorted as (x-,x+,y-,y+,z-,z+).
   * Default values = 0.0 0.0 0.0 0.0 0.0 0.0

===== Definition of the data set for the SLW model =====
-----
==== activateGas ====
   * Type : Boolean value
   * This option activates the SLW module.
     * .false. : **transparent medium** under gray-gas assumption is considered (i.e. $\kappa = 0$)
     * .true.  : Gas absorption and emission is considered 
   * Default value = .false.

<note important>**if activateGas == .false.**, the settings below are unnecessary.</note>

==== NbGas ====
   * Type : Integer value
   * This option sets the number of weighted gray-gases $N_g$ used in the SLW model.
     * NbGas $=$ 1   : gray-gas assumption with $\kappa$ = //ka_min//
     * NbGas $\ge$ 2  : SLW model is employed
   * Default value = 1

<note> Setting **NbGas $=$ 1 and ka_min = 0** is equivalent to **wall-to-wall radiation** du to the presence of transparent medium </note>
==== ka_min , ka_max ====
   * Type : Real values
   * These options set the lower and upper bounds of dimensional absorbing coefficient [$m^{-1}$] for the SLW model.
     * if NbGas $=$ 1 : $\kappa$ = //ka_min//, **//ka_max// is useless**
     * if NbGas $\ge$ 2 : //ka_min// < $\kappa_j$ < //ka_max//  for all $j \in [1,N_g]$
   * Default value = [ ka_min , ka_max ] = [ 0.0 , 0.0 ]
==== SPECA ====
   * Type : Character string with a maximum size of 3
   * Name of the absorbing species when NbGas $\ge$ 2 (SLW model).
     * **if "NbGas" $=$ 1 : useless**
   * Available values :
     * "H2O" : $air-H_2O$ mixture
     * "CO2" : $air-CO_2$ mixture
   * Default value = "H2O"
==== xaref ====
   * Type : Real value
   * This option set the reference molar fraction $x_{ref}$ of the absorbing species for the SLW model.
     * **if "NbGas" $=$ 1 : useless**
   * Default value = 0.07
==== xaUniform ====
   * Type : Real value
   * As long as the SLW model is not coupled with species equations, this option set a uniform molar fraction $x_{a}$ of the absorbing species in the overall domain.
     * **if NbGas $=$ 1 : useless**
   * Default value = 0.07
==== Pref ====
   * Type : Real value.
   * Reference pressure $P_{ref}$ in [$Pa$].
     * **if "NbGas" $=$ 1 : useless**
   * Default value = obtained from Fluid_Properties quantities