Nodal neutron kinetics model based on nonlinear iteration procedure for LWR analysis

Abstract

A 3-dimensional neuron kinetics model based on the analytical nodal method and nonlinear iteration procedure is developed for Light Water Reactor (LWR) transient calculations. The solution procedure is decoupled on a local solution of the nodal equations for two-node problems and global iterations of the coarse-mesh finite-difference method. An orthogonality of the basic functions used for the neutron flux expansion results in an efficient algorith of the solution of the nodal equations for the two-node problem. The initial system of 8 G nodal equations is reduced to a set of G and 2 G equations, where G is a number of neutron energy groups. A fully implicit scheme with an analytical treatment of the delayed neutron precursors equations is used for time integration. An adaptive time-step size control procedure based on the time-step doubling technique is applied. The described numerical methods are implemented into the computer code SKETCH-N. The 3D LWR Langenbuch-Maures Werner (LMW) operational transient and 2D and 3D Boiling Water Reactor (BWR) LRA super-prompt-critical benchmark problems are calculated in order to verify the code. A comparison of the computed results with the solutions obtained by the other nodal computer codes demostrate fidelity and efficiency of the SKETCH-N code.