Saphir¶

Problem description¶

This is a standard nuclear engineering benchmark (IAEA number EIR-2) describing an external-force-driven configuration without fissile materials present, using one-group neutron diffusion approximation

(1) $-\nabla \cdot (D(x,y) \nabla \Phi) + \Sigma_a(x,y) \Phi - Q_{ext}(x,y) = 0.$

The domain of interest is a 96 x 86 cm rectangle consisting of five regions:

Schematic picture for the saphir example.

The unknown is the neutron flux $\Phi(x, y)$ . The values of the diffusion coefficient $D(x, y)$ , absorption cross-section $\Sigma_a(x, y)$ and the source term $Q_{ext}(x,y)$ are constant in the subdomains. The source $Q_{ext} = 1$ in areas 1 and 3 and zero elsewhere. Boundary conditions for the flux $\Phi$ are zero everywhere.