- #1
taitae25
- 10
- 0
Hi,
I'm new to the entire neutronics field. I've learned about adjoints as a physics student in undergrad and I'm doing nuclear engineering for my graduate studies. I understand how to derive the adjoint operator for the diffusion equation, but I'm a bit confused as to how to calculate the adjoint flux for a critical system.
I'm tryring to calculate the adjoint flux numerically. The regular flux is simple to calculate using power iteration, but what does criticality mean for adjoint flux? Can I use power iteration for adjoint flux calculation? If adjoint flux gives a sense of importance of the flux, then I can use this to perform sensitivity analysis on the criticality (keff). But I also learned that the adjoint operator for the transport equation is non-conservative. In that case, how can I calculate adjoint flux numerically?
Can I still solve for it using power iteration? or do I simply solve for the regular flux, determine what the criticality (keff) is and then solve for the linear system for the adjoint flux? i.e. For my two group diffusion equation, with only down scatter, would my adjoint diffusion equation read as follows? (assuming prompt fission neutron only appears in the lowest energy group (group 0,fast neutrons)).
-D [tex] _0[/tex][tex]\frac{\partial^2 \phi_0}{\partial x^2} + (\Sigma_{a,0} + \Sigma_{s,0->1})\phi_0 - \Sigma_{s,0->1}\phi_1 = (\nu_{0} \chi_{0}\Sigma_{f,0}\phi_0 + \nu_{1} \chi_{0}\Sigma_{f,1}\phi_1)/k [/tex]
-D [tex] _1[/tex][tex]\frac{\partial^2 \phi_1}{\partial x^2} + (\Sigma_{a,1})\phi_1 = 0[/tex]
And just solve for the coupled linear system?
Thank you very much.
I'm new to the entire neutronics field. I've learned about adjoints as a physics student in undergrad and I'm doing nuclear engineering for my graduate studies. I understand how to derive the adjoint operator for the diffusion equation, but I'm a bit confused as to how to calculate the adjoint flux for a critical system.
I'm tryring to calculate the adjoint flux numerically. The regular flux is simple to calculate using power iteration, but what does criticality mean for adjoint flux? Can I use power iteration for adjoint flux calculation? If adjoint flux gives a sense of importance of the flux, then I can use this to perform sensitivity analysis on the criticality (keff). But I also learned that the adjoint operator for the transport equation is non-conservative. In that case, how can I calculate adjoint flux numerically?
Can I still solve for it using power iteration? or do I simply solve for the regular flux, determine what the criticality (keff) is and then solve for the linear system for the adjoint flux? i.e. For my two group diffusion equation, with only down scatter, would my adjoint diffusion equation read as follows? (assuming prompt fission neutron only appears in the lowest energy group (group 0,fast neutrons)).
-D [tex] _0[/tex][tex]\frac{\partial^2 \phi_0}{\partial x^2} + (\Sigma_{a,0} + \Sigma_{s,0->1})\phi_0 - \Sigma_{s,0->1}\phi_1 = (\nu_{0} \chi_{0}\Sigma_{f,0}\phi_0 + \nu_{1} \chi_{0}\Sigma_{f,1}\phi_1)/k [/tex]
-D [tex] _1[/tex][tex]\frac{\partial^2 \phi_1}{\partial x^2} + (\Sigma_{a,1})\phi_1 = 0[/tex]
And just solve for the coupled linear system?
Thank you very much.
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