The quasi-static method revisited

The quasi-static method is a standard tool for the space–time solution of neutron transport problems in multiplying media. Its basic principle lies in a factorization of the angular flux into the product of two functions, ‘amplitude’ and ‘shape’, where the amplitude depends only on time (and contains the major part of the time-dependence) while the shape function depends on all variables, time included. The shape equation is solved on a long time-scale, while the amplitude is determined on a short time-scale. The factorization is made unique by proper normalization conditions for the shape function. Most implementations replace the basic equation (transport or diffusion) by the set of coupled amplitude and shape equations derived from the factorization, the so-called ‘Improved Quasi-static Method’ (IQM). In this paper we describe an alternate approach already known for some time we have called ‘Predictor–Corrector Quasi-static Method’ (PCQM). We discuss its efficiency for both solid- and liquid-fuel systems dynamics.