Perturbation-based coupling of monte carlo with depletion for multiple Burnable Regions

Using the new collision history implementation in Serpent, a perturbation-based burn-up coupling scheme for multiple burnable regions has been developed. This scheme approximates the change in flux and cross-section across a burn-up step by calculating their partial derivatives with respect to chosen nuclide densities which are generated during the Monte Carlo simulation. This scheme is compared against the Predictor-Corrector method and LE/QI Substep method in terms of accuracy and runtime. Preliminary consideration is also given to the stability of the GPT scheme relative to the Substep and Stochastic Implicit Euler schemes.