# 4.4.1.2. SPn Radiation

Beta Capability

is not well tested and should not be considered a production capability.

Below is an example input deck with relevant command blocks for the SPn equations coupled monolithically to the energy equation through a radiative heating source and radiative heat flux. Note several command lines and blocks have been left out to focus on the incremental change needed to add the equations (with relevant boundary conditions and initial conditions) to a model.

    # Use aprepro to define the SPn order as it will need to be referenced
    # in multiple locations in a consistent fashion.
    #{SPN_ORDER=3}

    Begin Sierra myJob
      ...

      Begin Global Constants
        Stefan Boltzmann Constant = 5.67e-8
      End

      # define absorbtion, scatter, emissivity models for the block
      Begin Aria Material my_pmr_material
        ...
        absorption cross section = constant abs = 0.5
        scattering cross section = constant scat = 0.1
        emissivity = constant e = 1.0
      End
      ...

      Begin Procedure My_Aria_Procedure
        ...
        Begin Aria Region My_Region
          ...

          # Define steady heat conduction
          EQ energy for temperature on block_1 using Q1 with diff src
          BC dirichlet for temperature on my_dirichlet_surfaces = constant value = 1000

          # Couple to SPn eqns via radiative heat source
          source for energy on block_1 = rte_sp order = {SPN_ORDER}

          # Couple to SPn eqns via radiative flux
          BC flux for energy on my_rad_flux_surfaces = RTE_SP order = {SPN_ORDER}

          # Define SPn radiation equation set of order N resulting in (N + 1) / 2 angular intensity DOFs
          EQ sp {SPN_ORDER} for angular_intensity on block_1 using Q1

          # Apply Mark BCs for the SPn equation(s)
          BC Flux for sp on all_surfaces = mixed

          IC for temperature on block_1 = constant value = 1000.0

          # Define SPn ICs (initial guess to steady problem)
          IC for angular_intensity_0 on block_1 = constant value = 10420.116122115
          IC for angular_intensity_1 on block_1 = constant value = 10420.116122115

          # Define SPn nodal variables for output
          Begin Results Output Label Spn
            ...
            nodal variables = rte_scalar_flux as G
            nodal variables = rte_radiative_flux as q
            nodal variables = SPn_flux_0 as S0
            nodal variables = SPn_flux_1 as S1
            nodal variables = solution->angular_Intensity_0 as I0
            nodal variables = solution->angular_Intensity_1 as I1
          End
        End
      End
    End Sierra myJob