Solution of the Space-Dependent Reactor Kinetics Equations in Three Dimensions

Abstract

A general class of two-step alternating-direction semi-implicit methods is proposed for the approximate solution of the semidiscrete form of the space-dependent reactor kinetics equations. An exponential transformation of the semi-discrete equations is described which has been found to significantly reduce the truncation error when several alternating-direction semi-implicit methods are applied to the transformed equations. A subset of this class is shown to be a consistent approximation to the differential equations and to be numerically stable. Specific members of this subset are compared in one-and two-dimensional numerical experiments. An "optimum" method, termed the NSADE (Non-Symmetric Alternating-Direction Explicit) method is extended to three-dimensional geometries. Subsequent three-dimensional numerical experiments confirm the truncation error, accuracy, and stability properties of this method.

Finite difference solution of the time dependent neutron group diffusion equations

“…In order to describe these /4 methods it is first necessary to examine the spatial and temporal discretization of finite difference methods. 21 The spatial discretization of the neutron diffusion …”

Stability analysis of the Backward Euler time discretization for the pin-resolved transport transient reactor calculation

“…The dynamic parameters at the end of the time step are calculated using Eq. (14) to Eq. (17) and are based on the flux at the beginning of the time step but material composition at the end of time step which are estimated using first order perturbation theory [22].…”

Solving the multigroup integro-differential equation of the neutron diffusion kinetics in 3D-Cartesian geometry

“…The 1st application was an instantaneous change of the thermal removal (absorption) cross section in the homogeneous reactor by an amount of DR R2 = À0.369 Â 10 À4 (reference in Nahla et al, 2012b). Table 4 shows the BP 2 results of the central thermal and fast neutron flux calculation (Ds = 20 cm and integration time step Dt = 10 À3 s), along with the results of 3DKIN (Ferguson andHansen, 1973 referenced in Nahla et al, 2012b) for Dt = 10 À3 s, AMF (Dt = 10 À4 s) and NT-FMM/AM (Nahla et al, 2012b). From that Table it can be seen a good agreement of BP 2 with the other codes.…”