A nodal modal method for the neutron diffusion equation. Application to BWR instabilities analysis

Fast codes, capable of dealing with three-dimensional geometries, are needed to be able to simulate spatially complicated transients in a nuclear power reactor. In this paper, we propose a modal method to integrate the neutron diffusion equation in which the spatial part has been previously dicretized using a nodal collocation method. For the time integration of the resulting system of differential equations it is supposed that the solution can be expanded as a linear combination of the dominant Lambda modes associated with a static configuration of the reactor core and, using the eigenfunctions of the adjoint problem, a system of differential equations of lower dimension is obtained. This system is integrated using a variable time step implicit method. Furthermore, for realistic transients, it would be necessary to calculate a large amount of modes. To avoid this, the modal method has been implemented making use of an updating process for the modes at each certain time step. Five transients have been studied: a homogeneous reactor, a non-homogeneous reactor, the 3D Langenbuch reactor and two transients related with in-phase and out-of-phase oscillations of Leibstadt NPP. The obtained results have been compared with the ones provided by a method based on a one-step backward discretization formula.