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Divergence operator for multi-dimensional neutron diffusion
This is exactly the rule I needed, Thank you so much! So to start: -∇⋅D(x,y)∇Φ(x,y) [3] expands to - (∇⋅D(x,y))⋅(∇Φ(x,y)) - D(x,y)ΔΦ(x,y) [4] then - (∂D/∂x+∂D/∂y)⋅(∂Φ/∂x+∂Φ/∂y) - D(x,y)(∂2Φ/∂x2+∂2Φ/∂y2)] [5] distributing the lefthand term, removing null terms, and reducing to simpler...- englisham
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- Forum: Calculus and Beyond Homework Help
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Divergence operator for multi-dimensional neutron diffusion
Homework Statement [1] is the one-speed steady-state neutron diffusion equation, where D is the diffusion coefficient, Φ is the neutron flux, Σa is the neutron absorption cross-section, and S is an external neutron source. Solving this equation using a 'homogeneous' material allows D to be...- englisham
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- Del Diffusion Divergence Laplacian Multivariate Neutron Operator
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- Forum: Calculus and Beyond Homework Help