A consistent 2D/1D approximation to the 3D neutron transport equation

A new “2D/1D” equation is proposed to approximate the 3D linear Boltzmann equation. The approximate 2D/1D equation preserves the exact transport physics in the radial directions x and y but employs diffusion physics in the axial direction z. The 2D/1D equation can be systematically discretized, yielding accurate simulation methods for 3D reactor core problems. The resulting 2D/1D solutions are more accurate than 3D diffusion solutions, and are less expensive to calculate than standard 3D transport solutions. In this paper, we (i) show that the simplest 2D/1D equation has certain desirable properties, (ii) systematically discretize this equation, (iii) derive stable iteration schemes for solving the discrete system of equations, and (iv) give numerical results for simple problems that confirm the theoretical predictions of accuracy and iterative stability.