High order backward discretization of the neutron diffusion equation

Application of Backward Differentiation Formula to Spatial Reactor Kinetics Calculation With Adaptive Time Step Control

“…There was an earlier study by Ginestar et al 7 about the application of the BDF method to the solution of the time-dependent neutron diffusion equation. In that study, the BDF formulation was applied to the ordinary differential equation for flux, which is obtained after spatial discretization of the time-dependent neutron diffusion equation.…”

“…Using the CMFD relation for the interface current 7 , the current terms J in the loss term of Eq. (22) Note that the BDF coefficients, ai, has the dimension of inverse time because the time step sizes appear in the denominator as indicated in Eq.…”

“…With this rationale, the transient fixed term is now added to the transverse leakage source term and is represented as a simple quadratic polynomial as in the standard nodal methods. The higher solution for the one-dimensional equation is obtained by the source expansion nodal method (SENM) 7 , which represents the source term, including the fission source term, as a quartic order polynomial that leads to the exponential functions in the homogeneous part of the solution.…”

“…The CMFD-and BDF-based transient calculation method was implemented in the RENUS multigroup nodal code 7 , which has a simplified closed channel thermalhydraulics calculation module that determines the intrapellet fuel temperature distribution for assembly averaged fuel pins. This code performs iterative estimation of the fuel temperature distribution at the current time point to incorporate prompt reactivity feedback due to fuel temperature change.…”

“…In this comparison, which will be shown in the following subsection, the same set of predefined time step sizes are used for both methods. The two important transients of control rod ejection and uncontrolled withdrawal are examined with the NEACRP benchmark problem specification 7,8 . Note that these benchmark problems are used to demonstrate the transient capability of industry standard codes such as ANCK 14 .…”