Calculation of k-Eigenvalues and Multi-Group Eigenfunctions Using the Hybrid 'Functional Monte Carlo' Method

摘要

The Functional Monte Carlo (FMC) method is a recent hybrid technique for neutron transport simulations in which Monte Carlo (MC) methods do not directly estimate the neutron flux. Instead, MC is used to estimate nonlinear functionals, which occur in low-order equations that are derived without approximation from the high-order Boltzmann transport equation. (The deterministic solution of the low-order equations yields the FMC estimates of the eigenvalue and eigenfunction.) Because the low-order equations are derived without approximation from the Boltzmann transport equation, the FMC solution contains only statistical errors. Also, because the MC-estimated nonlinear functionals have much smaller statistical errors than the MC-estimated fluxes, the resulting FMC solution has much smaller statistical errors than the standard MC solution. In this paper, we generalize the FMC method to account for a high-order continuous-energy transport problem and a low-order spatially-discrete multigroup diffusion problem. (In our previous work, the low-order problem was energy-integrated.) We present numerical results showing that the resulting multigroup FMC fluxes and eigenvalue are much more accurate than the standard MC fluxes and eigenvalue.