Uncertainty quantification in neutron transport with generalized polynomial chaos using the method of characteristics

The polynomial chaos expansion has been used to solve the mono-energetic stochastic neutron transport equation with the spatial and angular components discretised using the step characteristics method. Uncertainties were assumed to arise purely from the material cross sections and a novel method for treating uncertainties in discrete, uncorrelated, material regions has been proposed. The method is illustrated by numerical and Monte Carlo simulation of the mean, variance and probability density of the scalar flux for the fixed source Reed cell problem and a critical benchmark in one dimension. For the case of the critical benchmark we compare the results from the Newton–Krylov root finding method to that of the stochastic collocation method. We find that there is no benefit in the extra computation of using the Newton–Krylov method.

► The general theory for the stochastic method of characteristics is given.
► Stochastic space is discretised using the polynomial chaos technique.
► Stochastic Galerkin and collocation methods are used to solve the working equations.
► Fixed source and multiplying problems are used to illustrate the theory.
► For increased compute time, Galerkin methods show little benefit over collocation.