Time-dependent boundary source term for advanced nodal diffusion theory

An extension to nodal di€usion theory was developed to deal with time-dependent bound- ary source terms. It is shown that this extension is easily introduced in advanced, full-func- tional di€usion theory by means of Diracʹs delta spatially-dependent functions at the nodal boundaries, and allows the evaluation of reactor transients showing the propagation of neu- tron waves or the e€ects of pulsed neutron sources. A model problem with exact solutions for both the di€usion and the P1 (telegrapherʹs) equations was developed to test the capabilities of the theoretical extension. The larger discrepancies occur at the earliest times computed showing, at t =ˆ 50 ms, mean-square deviations between the exact di€usion 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 telegrapherʹs solution, however, demonstrates that improved accuracy is meaningless since the mean-square deviation between the exact di€usion and exact telegrapherʹs solution is very similar to the mean-square deviation between the exact di€usion and the poorer (fourth-order) di€usion approximation.