- TinfinityFunctor for the far-field temperature of the body in radiative heat transfer. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:Functor for the far-field temperature of the body in radiative heat transfer. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
- boundaryThe list of boundary IDs from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundary IDs from the mesh where this object applies
- diffusion_coeffFunctor for the thermal conductivity. Must match the diffusion_coeff used in LinearFVDiffusion, as it serves as the alpha coefficient in the Robin formulation. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:Functor for the thermal conductivity. Must match the diffusion_coeff used in LinearFVDiffusion, as it serves as the alpha coefficient in the Robin formulation. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
- emissivityFunctor describing the surface emissivity for the radiative boundary condition. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:Functor describing the surface emissivity for the radiative boundary condition. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
- variableThe name of the variable that this boundary condition applies to
C++ Type:LinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this boundary condition applies to
LinearFVFunctorRadiativeBC
Description
LinearFVFunctorRadiativeBC applies a radiative heat flux boundary condition to a linear finite volume (LinearFV) variable. It is the LinearFV counterpart of FVFunctorRadiativeBC.
The radiative outward heat flux at a boundary is:
q_\text{out} = \sigma \varepsilon \left( T4 - T_\infty4 \right)
where is the Stefan-Boltzmann constant, is the surface emissivity (supplied as a functor), and is the far-field radiation temperature.
Linearization
The LinearFV framework solves a linear system at each time step. The diffusion and time-derivative terms are treated implicitly, but the nonlinear radiative term cannot appear directly in the linear system. It must be linearized by lagging the nonlinear coefficients to the previous iteration's solution. The linear system can be solved repeatedly within a fixed point iteration loop if the nonlinear term is to be treated implicitly (in time) or is treated explicitly if the linear system is only solved once.
First-order Taylor expansion
The term is expanded around the extrapolated boundary face temperature** from the previous iteration:
T_{b,\text{old}} = T_{P,\text{old}} + \nabla T_\text{old} \cdot \mathbf{d}_{cf}
where is the vector from the cell center to the face centroid. A first-order Taylor expansion gives:
T_b4 \approx T_{b,\text{old}}4 + 4\,T_{b,\text{old}}^3 \left(T_b - T_{b,\text{old}}\right) = 4\,T_{b,\text{old}}^3\,T_b - 3\,T_{b,\text{old}}^4
Substituting into the radiative flux and rearranging as a Robin boundary condition yields:
k \frac{\partial T}{\partial n} + \underbrace{4 \sigma \varepsilon\, T_{b,\text{old}}^3}_{\beta}\, T_b = \underbrace{\sigma \varepsilon \left( 3\, T_{b,\text{old}}^4 + T_\infty^4 \right)}_{\gamma}
This is implemented by inheriting from LinearFVAdvectionDiffusionFunctorRobinBCBase with:
(
diffusion_coeff)
The Robin base class handles all matrix and RHS contributions, including non-orthogonal mesh corrections. Using (face) instead of (cell center) eliminates the truncation error in the flux, restoring second-order spatial accuracy**.
The diffusion_coeff parameter must match the diffusion coefficient used in the LinearFVDiffusion kernel, as it is the coefficient in the Robin formulation.
Iterative Convergence
Because and depend on from the previous iteration, the linear system must be reassembled with updated coefficients until the solution converges to the nonlinear radiative balance. The diffusion and time-derivative terms are fully implicit; only the radiative coefficients are lagged. If the linear system is only solved once within the time step, the nonlinear coefficients are explicit in time. This implicit-explicit split does not affect the steady-state solution, only the convergence path.
Two strategies can be chosen to drive the solution of this nonlinear problem:
Pseudo-transient stepping**: use
LinearFVTimeDerivative+Transientexecutioner with large time steps. The matrix is rebuilt at each step with the updated solution, and the time derivative vanishes at steady state.Iterative multi-system solve**: if the temperature variable is part of a multi-system problem, the outer multi-system iteration updates the lagged coefficients between solves. If converged for each time step, this enables an implicit time integration scheme.
Input Parameters
- stefan_boltzmann_constant5.67037e-08The Stefan-Boltzmann constant
Default:5.67037e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The Stefan-Boltzmann constant
Optional Parameters
- absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
- extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
- extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
- matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)
- matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Controllable:No
Description:The tag for the matrices this Kernel should fill
- vector_tagsrhsThe tag for the vectors this Kernel should fill
Default:rhs
C++ Type:MultiMooseEnum
Controllable:No
Description:The tag for the vectors this Kernel should fill
Contribution To Tagged Field Data Parameters
- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
- enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
- implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
- search_methodnearest_node_connected_sidesChoice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
Default:nearest_node_connected_sides
C++ Type:MooseEnum
Controllable:No
Description:Choice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).