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| | VacuumConcBC (const InputParameters ¶meters) |
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| | ScalarTransportBase (const InputParameters ¶meters) |
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| virtual Real | computeConcentration (const VariableValue &u, unsigned int qp) |
| | Computes \(c\).
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| virtual RealVectorValue | computeConcentrationGradient (const VariableValue &u, const VariableGradient &grad_u, unsigned int qp) |
| | Computes \(\nabla c\).
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| virtual Real | computeConcentrationDerivative (const VariableValue &u, const VariablePhiValue &phi, unsigned int j, unsigned int qp) |
| | Computes \(\frac{\partial c}{\partial u_j}\).
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| virtual RealVectorValue | computeConcentrationGradientDerivative (const VariableValue &u, const VariableGradient &grad_u, const VariablePhiValue &phi, const VariablePhiGradient &grad_phi, unsigned int j, unsigned int qp) |
| | Computes \(\nabla \frac{\partial c}{\partial u_j}\).
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| virtual Real | computeConcentrationDot (const VariableValue &u, const VariableValue &u_dot, unsigned int qp) |
| | Computes \(\frac{\partial c}{\partial t}\).
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| virtual Real | computeConcentrationDotDerivative (const VariableValue &u, const VariableValue &u_dot, const VariableValue &du_dot_du, const VariablePhiValue &phi, unsigned int j, unsigned int qp) |
| | Computes \(\frac{\partial}{\partial t} \frac{\partial c}{\partial u_j}\).
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Implements a simple VacuumConc BC for neutron diffusion on vacuum boundaries. VacuumConc BC is defined as \( D\frac{du}{dn}+\frac{u}{\alpha} = 0\), where u is neutron flux. Hence, \( D\frac{du}{dn}=-\frac{u}{\alpha} \) and \( -\frac{u}{\alpha} \) is substituted into the Neumann BC term produced from integrating the diffusion operator by parts.
The three types of vacuum BCs available are Marshak ($\alpha=2$), Mark ($\alpha=\sqrt{3}$), and Milne ($\alpha=3\times 0.710446$). VacuumConcBC defaults to Marshak if bc_type is not set.