Method of Manufactured Solutions for the Neutron Kinetics Equations

Although it is commonplace to solve the space-time kinetics form of the neutron diffusion equation and the delayed neutron precursor equations, accurate benchmark solutions for such problems are lacking. In this work, an analytic solution to the neutron kinetics equations is provided via the Method of Manufactured Solutions. The form of the solution is a manufactured neutron flux and a prescribed absorption cross section . For the first time, an exact solution for the neutron flux as a function of space and time is provided in a form that can be used to verify existing neutron kinetics methods. Then, this solution is used to verify the neutron kinetics methods in the LMFR Utility for Physics Informed Nuclear Engineering (LUPINE) to demonstrate how this solution can be used for practical verification and quantifying the order of convergence of existing neutron kinetics methods.