Time-dependent boundary source term for advanced nodal diffusion theory

Abstract

An extension to nodal diffusion theory was developed to deal with time-dependent boundary source terms. It is shown that this extension is easily introduced in advanced, full-functional diffusion theory by means of Dirac's delta spatially-dependent functions at the nodal boundaries, and allows the evaluation of reactor transients showing the propagation of neutron waves or the effects of pulsed neutron sources. A model problem with exact solutions for both the diffusion and the P 1 (telegrapher's) equations was developed to test the capabilities of the theoretical extension. The larger discrepancies occur at the earliest times computed showing, at t=50 μs, mean-square deviations between the exact diffusion solution and the numerical approximations of 2.95, 1.72, 0.32, and 0.16% for the fourth, sixth, eighth, and tenth polynomial expansion order, respectively. The availability of the exact telegrapher's solution, however, demonstrates that improved accuracy is meaningless since the mean-square deviation between the exact diffusion and exact telegrapher's solution is very similar to the mean-square deviation between the exact diffusion and the poorer (fourth-order) diffusion approximation.