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

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35 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)43-53
Number of pages11
JournalAnnals of Nuclear Energy
StatePublished - 2013


  • Benchmarking
  • Non-linear neutron kinetics
  • Reactor equations

ASJC Scopus subject areas

  • Nuclear Energy and Engineering


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