Robert E. Grove

The Multi-Step CADIS method for shutdown dose rate calculations and uncertainty propagation

Abstract Shutdown dose rate (SDDR) analysis requires (a) a neutron transport calculation to estimate neutron flux fields, (b) an activation calculation to compute radionuclide inventories and associated photon sources, and (c) a photon transport calculation to estimate final SDDR. In some applications, accurate full-scale Monte Carlo (MC) SDDR simulations are needed for very large systems with massive amounts of shielding materials. However, these simulations are impractical because calculation of space- and energy-dependent neutron fluxes throughout the structural materials is needed to estimate distribution of radioisotopes causing the SDDR. Biasing the neutron MC calculation using an importance function is not simple because it is difficult to explicitly express the response function, which depends on subsequent computational steps. Typical SDDR calculations do not consider how uncertainties in MC neutron calculation impact SDDR uncertainty, even though MC neutron calculation uncertainties usually dominate SDDR uncertainty. The Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS) hybrid MC/deterministic method was developed to speed SDDR MC neutron transport calculation using a deterministically calculated importance function representing the neutron importance to the final SDDR. Undersampling is usually inevitable in large-problem SDDR simulations because it is very difficult for the MC method to simulate particles in all space and energy elements of the neutron calculation. MS-CADIS can assess the degree of undersampling in SDDR calculations by determining the fraction of the SDDR response in the space and energy elements that did not have any scores in the MC neutron calculation. It can also provide estimates for upper and lower limits of SDDR statistical uncertainties resulting from uncertainties in MC neutron calculation. MS-CADIS was applied to the ITER SDDR benchmark problem that resembles the configuration and geometrical arrangement of an upper port plug in ITER. Without using the hybrid MC/deterministic methods to speed MC neutron calculations, SDDR calculations were significantly undersampled for all tallies, even when MC neutron calculation computational time was 32 CPU-days. However, all SDDR tally results with MC neutron calculations of only 2 CPU-days converged with the standard Forward-Weighted CADIS (FW-CADIS) method and the MS-CADIS method. Compared to the standard FW-CADIS approach, MS-CADIS decreased the undersampling in the calculated SDDR by factors between 0.9% and 0.3% for computational times between 4 and 32 CPU-days, and it increased the computational efficiency of the SDDR neutron MC calculation by factors between 43% and 69%.

Shutdown Dose Rate Analysis Using the Multi-Step CADIS Method

Abstract The Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS) hybrid Monte Carlo (MC)/deterministic radiation transport method was proposed to speed up the shutdown dose rate (SDDR) neutron MC calculation using an importance function that represents the neutron importance to the final SDDR. In this work, the MS-CADIS method was applied to the ITER SDDR benchmark problem. The MS-CADIS method was also used to calculate the SDDR uncertainty resulting from uncertainties in the MC neutron calculation and to determine the degree of undersampling in SDDR calculations because of the limited ability of the MC method to tally detailed spatial and energy distributions. The analysis that used the ITER benchmark problem compared the efficiency of the MS-CADIS method to the traditional approach of using global MC variance reduction techniques for speeding up SDDR neutron MC calculation. Compared to the standard Forward-Weighted-CADIS (FW-CADIS) method, the MS-CADIS method increased the efficiency of the SDDR neutron MC calculation by 69%. The MS-CADIS method also increased the fraction of nonzero scoring mesh tally elements in the space-energy regions of high importance to the final SDDR.

Automatic Mesh Adaptivity for Hybrid Monte Carlo/Deterministic Neutronics Modeling of Difficult Shielding Problems

Abstract The well-established Consistent Adjoint Driven Importance Sampling (CADIS) and the Forward Weighted Consistent Adjoint Driven Importance Sampling (FW-CADIS) hybrid Monte Carlo/deterministic techniques have dramatically increased the efficiency of neutronics simulations, yielding accurate solutions for increasingly complex problems through full-scale, high-fidelity simulations. However, for full-scale simulations of very large and geometrically complex nuclear energy systems, even the CADIS and FW-CADIS techniques can reach the CPU and memory limits of all but the very powerful supercomputers. In this work, three mesh adaptivity algorithms were developed to reduce the computational resource requirements of CADIS and FW-CADIS without sacrificing their efficiency improvements. First, a macromaterial approach was developed to enhance the fidelity of the deterministic models without changing the mesh. Second, a deterministic mesh refinement algorithm was developed to generate meshes that capture as much geometric detail as possible without exceeding a specified maximum number of mesh elements. Finally, a weight window (WW) coarsening (WWC) algorithm was developed to decouple the WW mesh and energy bins from the mesh and energy group structure of the deterministic calculations. By removing the memory constraint of the WW map from the resolution of the mesh and the energy group structure of the deterministic calculations, the WWC algorithm allows higher-fidelity deterministic calculations that, consequently, increase the efficiency and reliability of the CADIS and the FW-CADIS simulations. The three algorithms were used to enhance an FW-CADIS calculation of the prompt dose rate throughout the ITER experimental facility. Using these algorithms increased both the number of mesh tally elements in which nonzero results were obtained (+23.3%) and the overall efficiency of the calculation (a factor of >3.4). The three algorithms enabled this difficult calculation to be accurately solved using an FW-CADIS simulation on a 94-CPU computer cluster, eliminating the need for a world-class supercomputer.