A highly accurate technique for the solution of the non-linear point kinetics equations

A novel methodology for the solution of non-linear point kinetic (PK) equations is proposed. The technique, based on a piecewise constant approximation (Kinard and Allen, 2004), is enhanced by explicitly accounting for the feedback and the reactivity variation within a time step through an iterative cycle. High accuracy is achieved by introducing a sub-mesh for the numerical evaluation of integrals involved and by correcting the source term to include the non-linear effect on a finer time scale. The resulting Enhanced Piecewise Constant Approximation (EPCA) is tested on a set of classical linear problems with several types of reactivity insertions (step, linear, sinusoidal, zig-zag) and shows extreme accuracy (to 9 digits) even when large time steps are considered (i.e., 100 times the neutron mean life). Non-linear reactor kinetics is then considered and compared to highly accurate results obtained via convergence acceleration. Its accuracy and the fast convergence make the EPCA algorithm particularly attractive for applications.