A modal multidimensional kinetics method using pseudo-harmonics

This work proposes to use the pseudo-harmonics technique as a modal method in spatial kinetics. The pseudo-harmonics are the eigenfunctions associated with the leakage + removal operators in the multigroup steady-state diffusion equation. In this work, the pseudo-harmonics are obtained from the diffusion equation discretized with the Coarse Mesh Finite Difference Method (CMFD) coupled to the Nodal Expansion Method (NEM). Modal methods approximate the time-dependent flux by expanding it in predetermined functions which represent the space dependence, so that the unknowns are the expansion coefficients, which carry all time dependence of the problem. To obtain the system of equations whose solutions are the modal expansion coefficients, use is made of a weighting function procedure. This process leads to a linear system of ordinary differential equations whose dimension equals the number of pseudo-harmonics employed. The solution of these equations is obtained through analytical integration of the delayed neutrons precursor equations, while the time dependence of the neutrons flux is treated by the Rosenbrock Generalized Runge-Kutta method with automatic time step size control. A direct method was developed from the spatial kinetics equations discretized by CMFD coupled to NEM in order to compare the methods. The proposed modal method was tested for the case of an operational transient and for the case of a transient with scram, and presented good results, when compared with this direct method