Adaptive Time Stepping for the Neutron Transport Solution with the Alpha Eigenvalue

Abstract

Reactivity insertion accidents are one of the design-basis accidents that drive nuclear reactor limits. In order to operate nuclear reactors both safely and efficiently, reactor response to such an accident scenario must be well understood through simulation. While state-of-the-art reactor codes, such as MPACT, are capable of modeling transport physics for heterogeneous geometry, the computational cost is significant. This cost is only amplified for reactor transients, where the solution in the time domain is obtained through a series of calculations at discrete time points. One way to improve the computational efficiency is to adaptively select the time points at which to perform a calculation based on the evolution of the reactor through the transient.

The objective of this work is to develop an adaptive time stepping algorithm specifically for neutron transport that is able to properly characterize the evolution of the reactor throughout a transient and provide an appropriate time step size based on that characterization. In order to accomplish this, the leading order error term of the time discretization is limited. For implicit Euler, the standard time discretization method for neutron transport codes, this error term is inversely proportional to the second derivative of the angular flux in time.

Two methods are investigated for estimating the second derivative—a traditional finite difference approach and a novel alpha (time) eigenvalue approach. The methods were implemented in MPACT and characterized on a variety of transient test cases. The finite difference method is shown to suffer from two major drawbacks: untenable storage demands and oscillatory time step selection. The former issue is shown to be resolved satisfactorily by substituting the scalar flux for the angular flux without loss of accuracy. The latter issue is partially resolved by employing an alternative formulation of the finite difference approximation, but this only serves to reduce, not eliminate, the oscillations. The alpha eigenvalue method is shown to resolve both of these issues, though at a higher computational cost than the finite difference method. Both methods present a range of choices that are explored and characterized for their performance.

The result of this work is a robust adaptive time stepping scheme for MPACT that is able to increase computational efficiency of reactor transient simulations without an adversarial effect on accuracy. The capability is demonstrated for one of the C5G7 computational benchmarks and a miniature version of the SPERT reactor experiments.