Preventing xenon oscillations in Monte Carlo burnup calculations by enforcing equilibrium xenon distribution

A gPC-intrusive Monte-Carlo scheme for the resolution of the uncertain linear Boltzmann equation

“…The next steps consist in considering uncertain nonlinear couplings involving the linear Boltzmann equation: Bateman equations for neutronics [22,33,34,23,5], Stefan's law for photonics [41] or even hydrodynamics with the resolution of the BGK [6] model, solved with the new gPC-i-MC scheme. The efficiency of the new method is closely related to the unconditional stability of the MC scheme for the linear Boltzmann equation (less frequent parallel reductions).…”

“…Expression (34) echoes (23). The same apply to the sampling of the outer 24 velocity V Xp and to the weight modification of the uncertain MC particles: the cross-sections at play in (26)-(32) must be used at both the physical (x p (t), v p (t)) and uncertain (X p ) fields of the uncertain MC particle.…”

“…The gain in computational time, for this test-case, is approximatively of N GL ≈ 4. In the above example, it remains relatively low: if one has access to 4(N GL ) × 32(N replications ) = 128 processors, which is common nowadays, the computational times are equivalent and the gain is only in term of computational ressources 34 . We here recall that MC simulation codes are known to be computationally intensive and even such low factor (gain of only 4) may be welcome.…”

“…It takes advantage of the independence between MC particles, hence populations of MC particles: N replication processors each have a batch of particles and the processors only communicate at the end of the time step to average over the N replication populations. 34 Note that rigorously speaking, the cost of ni-gPC remains given by the more costly run amongst the N GL but we will keep considering the average CPU time over the N GL calculations as a reference in the following.…”

“…The relevance of the latter integrodifferential PDE is not to demonstrate. Amongst the applications (non exhaustive list), one can quote biology [58] with population dynamics, plasma physics (transport of ions and electrons) [21], photonics [64,50,17,41,31,52] or neutronics [68,40,22,33,34,23]. (ii) Second, gPC can be applied intrusively (see for examples [43,76,20]) or non-intrusively (the most common way) and whether one strategy performs better than the other is far from being obvious.…”