| Abstract: | The time-dependent P 1 equation for two-dimensional neutron transport is numerically solved by a finite difference approximation of the explicit form along the bicharacteristics of the P 1 equation. Applying von Neumann's stability condition to this numerical procedure in an infinite space, we can derive the condition necessary for the solution to be stable. This condition is that the mesh widths satisfy the inequality o<λ≦√3/2 with λ=time mesh δt/space mesh δ or δz, where the time t is measured in units of inverse neutron speed l/v. The sufficient stability condition on the ratio λ is to be determined by numerical experiments. It has been found that the upper bound of λ becomes larger for smaller values of space mesh width. In respect of the stability of numerical solution, the P1 approximation is more advantageous than the diffusion approximation. Transient behavior of neutron flux distribution due to a stationary neutron source is numerically determined assuming zero initial values. After the transient state terminates, the steady state distribution is obtained. |
