A study on the solution of the spatial kinetics equations in the neutron diffusion theory. (March 2022) - Zanette, R.; Barichello, L.B.; Petersen, C.Z.
Abstract: In this work, recent studies on the solution of the spatial kinetics equations in the neutron diffusion theory are presented. A nodal technique for the treatment of spatial variables is applied, resulting in the definition of average quantities with respect to neutron fluxes, delayed neutron precursor concentrations, and current densities. The current densities are expressed in terms of the average neutron fluxes to adjust the number of additional unknowns that originate in the nodal scheme. Thus, two systems of coupled differential equations, dependent on the temporal variable and involving the neutron fluxes and delayed neutron precursor concentrations must be solved. A proposal for an iterative scheme with independent solutions of these two systems is developed. Analytical solutions are derived for the delayed neutron precursor concentrations equations. For neutron fluxes equations, numerical and analytical solutions are discussed. The latter use Padé approximations and the Schur–Parlett algorithm to evaluate matrix exponentials. Numerical results obtained through the proposed techniques are compared with results available in the literature, showing satisfactory agreement and contributing to establishing benchmark results. The proposed approach of solving the two systems independently lead to a reduction of the stiffness of the system, a relevant issue for the global approach, and required lower computational costs. Highlights: A study is presented on the solution of time-dependent neutron diffusion equations. A nodal integration technique is applied for the treatment of spatial variables. An iterative scheme is proposed for the time-dependent differential systems. Analytical solutions are derived for the precursor concentrations equations. Numerical and analytical solutions are discussed for the neutron fluxes equations.