R. N. Slaybaugh

Denovo: A New Three-Dimensional Parallel Discrete Ordinates Code in SCALE

Abstract Denovo is a new, three-dimensional, discrete ordinates (SN) transport code that uses state-of-the-art solution methods to obtain accurate solutions to the Boltzmann transport equation. Denovo uses the Koch-Baker-Alcouffe parallel sweep algorithm to obtain high parallel efficiency on O(100) processors on XYZ orthogonal meshes. As opposed to traditional SN codes that use source iteration, Denovo uses nonstationary Krylov methods to solve the within-group equations. Krylov methods are far more efficient than stationary schemes. Additionally, classic acceleration schemes (diffusion synthetic acceleration) do not suffer stability problems when used as a preconditioner to a Krylov solver. Denovo’s generic programming framework allows multiple spatial discretization schemes and solution methodologies. Denovo currently provides diamond-difference, theta-weighted diamond-difference, linear-discontinuous finite element, trilinear-discontinuous finite element, and step characteristics spatial differencing schemes. Also, users have the option of running traditional source iteration instead of Krylov iteration. Multigroup upscatter problems can be solved using Gauss-Seidel iteration with transport, two-grid acceleration. A parallel first-collision source is also available. Denovo solutions to the Kobayashi benchmarks are in excellent agreement with published results. Parallel performance shows excellent weak scaling up to 20000 cores and good scaling up to 40000 cores.

THE ARIES-CS COMPACT STELLARATOR FUSION POWER PLANT

Abstract An integrated study of compact stellarator power plants, ARIES-CS, has been conducted to explore attractive compact stellarator configurations and to define key research and development (R&D) areas. The large size and mass predicted by earlier stellarator power plant studies had led to cost projections much higher than those of the advanced tokamak power plant. As such, the first major goal of the ARIES-CS research was to investigate if stellarator power plants can be made to be comparable in size to advanced tokamak variants while maintaining desirable stellarator properties. As stellarator fusion core components would have complex shapes and geometry, the second major goal of the ARIES-CS study was to understand and quantify, as much as possible, the impact of the complex shape and geometry of fusion core components. This paper focuses on the directions we pursued to optimize the compact stellarator as a fusion power plant, summarizes the major findings from the study, highlights the key design aspects and constraints associated with a compact stellarator, and identifies the major issues to help guide future R&D.

DESIGNING ARIES-CS COMPACT RADIAL BUILD AND NUCLEAR SYSTEM : NEUTRONICS, SHIELDING, AND ACTIVATION

Abstract Within the ARIES-CS project, design activities have focused on developing the first compact device that enhances the attractiveness of the stellarator as a power plant. The objectives of this paper are to review the nuclear elements that received considerable attention during the design process and provide a perspective on their successful integration into the final design. Among these elements are the radial build definition, the well-optimized in-vessel components that satisfy the ARIES top-level requirements, the carefully selected nuclear and engineering parameters to produce an economic optimum, the modeling - for the first time ever - of the highly complex stellarator geometry for the three-dimensional nuclear assessment, and the overarching safety and environmental constraints to deliver an attractive, reliable, and truly compact stellarator power plant.

Massively Parallel, Three-Dimensional Transport Solutions for the k-Eigenvalue Problem

Abstract We have implemented a new multilevel parallel decomposition in the Denovo discrete ordinates radiation transport code. In concert with Krylov subspace iterative solvers, the multilevel decomposition allows concurrency over energy in addition to space-angle, enabling scalability beyond the limits imposed by the traditional Koch-Baker-Alcouffe (KBA) space-angle partitioning. Furthermore, a new Arnoldi-based k-eigenvalue solver has been implemented. The added phase-space concurrency combined with the high-performance Krylov and Arnoldi solvers has enabled weak scaling to O(105) cores on the Titan XK7 supercomputer. The multilevel decomposition provides a mechanism for scaling to exascale computing and beyond.

Multigrid in energy preconditioner for Krylov solvers

We have added a new multigrid in energy (MGE) preconditioner to the Denovo discrete-ordinates radiation transport code. This preconditioner takes advantage of a new multilevel parallel decomposition. A multigroup Krylov subspace iterative solver that is decomposed in energy as well as space-angle forms the backbone of the transport solves in Denovo. The space-angle-energy decomposition facilitates scaling to hundreds of thousands of cores. The multigrid in energy preconditioner scales well in the energy dimension and significantly reduces the number of Krylov iterations required for convergence. This preconditioner is well-suited for use with advanced eigenvalue solvers such as Rayleigh Quotient Iteration and Arnoldi.

Application of CAD-neutronics coupling to geometrically complex fusion systems

An innovative computational tool (DAG-MCNP) has been developed for efficient and accurate 3-D nuclear analysis of geometrically complex fusion systems. Direct coupling with CAD models allows preserving the geometrical details, eliminating possible human error, and faster design iterations. DAG-MCNP has been applied to perform 3-D nuclear analysis for several fusion designs and demonstrated the ability to generate high-fidelity high-resolution results that significantly improve the design process. This tool will be the core for a full CAD-based simulation predictive capability that couples engineering analyses directly to the CAD solid model.

Nonclassical particle transport in one-dimensional random periodic media

We investigate the accuracy of the recently proposed nonclassical transport equation. This equation contains an extra independent variable compared to the classical transport equation (the path length s), and models particle transport in homogenized random media in which the distance to collision of a particle is not exponentially distributed. To solve the nonclassical equation, one needs to know the s-dependent ensemble-averaged total cross section Σt(μ, s) or its corresponding path-length distribution function p(μ, s). We consider a one-dimensional (1-D) spatially periodic system consisting of alternating solid and void layers, randomly placed along the x-axis. We obtain an analytical expression for p(μ, s) and use this result to compute the corresponding Σt(μ, s). Then, we proceed to solve numerically the nonclassical equation for different test problems in rod geometry; that is, particles can move only in the directions μ = ±1. To assess the accuracy of these solutions, we produce benchmark results obtained by (i) generating a large number of physical realizations of the system, (ii) numerically solving the transport equation in each realization, and (iii) ensemble-averaging the solutions over all physical realizations. We show that the numerical results validate the nonclassical model; the solutions obtained with the nonclassical equation accurately estimate the ensemble-averaged scalar flux in this 1-D random periodic system, greatly outperforming the widely used atomic mix model in most problems.

Nonclassical Particle Transport in 1-D Random Periodic Media

We investigate the accuracy of the recently proposed nonclassical transport equation. This equation contains an extra independent variable compared to the classical transport equation (the path length s), and models particle transport in homogenized random media in which the distance to collision of a particle is not exponentially distributed. To solve the nonclassical equation, one needs to know the s-dependent ensemble-averaged total cross section Σt(μ, s) or its corresponding path-length distribution function p(μ, s). We consider a one-dimensional (1-D) spatially periodic system consisting of alternating solid and void layers, randomly placed along the x-axis. We obtain an analytical expression for p(μ, s) and use this result to compute the corresponding Σt(μ, s). Then, we proceed to solve numerically the nonclassical equation for different test problems in rod geometry; that is, particles can move only in the directions μ = ±1. To assess the accuracy of these solutions, we produce benchmark results obtained by (i) generating a large number of physical realizations of the system, (ii) numerically solving the transport equation in each realization, and (iii) ensemble-averaging the solutions over all physical realizations. We show that the numerical results validate the nonclassical model; the solutions obtained with the nonclassical equation accurately estimate the ensemble-averaged scalar flux in this 1-D random periodic system, greatly outperforming the widely used atomic mix model in most problems.

Improved Monte Carlo Variance Reduction for Space and Energy Self-Shielding

Abstract Continued demand for accurate and computationally efficient transport methods to solve optically thick, fixed-source transport problems has inspired research on variance-reduction (VR) techniques for Monte Carlo (MC). Methods that use deterministic results to create VR maps for MC constitute a dominant branch of this research, with Forward Weighted–Consistent Adjoint Driven Importance Sampling (FW-CADIS) being a particularly successful example. However, locations in which energy and spatial self-shielding are combined, such as thin plates embedded in concrete, challenge FW-CADIS. In these cases the deterministic flux cannot appropriately capture transport behavior, and the associated VR parameters result in high variance in and following the plate. This work presents a new method that improves performance in transport calculations that contain regions of combined space and energy self-shielding without significant impact on the solution quality in other parts of the problem. This method is based on FW-CADIS and applies a Resonance Factor correction to the adjoint source. The impact of the Resonance Factor method is investigated in this work through an example problem. It is clear that this new method dramatically improves performance in terms of lowering the maximum 95% confidence interval relative error and reducing the compute time. Based on this work, we recommend that the Resonance Factor method be used when the accuracy of the solution in the presence of combined space and energy self-shielding is important.

Gnowee: A Hybrid Metaheuristic Optimization Algorithm for Constrained, Black Box, Combinatorial Mixed-Integer Design

Abstract This paper introduces Gnowee, a modular, Python-based, open-source hybrid metaheuristic optimization algorithm (available from https://github.com/SlaybaughLab/Gnowee). Gnowee is designed for rapid convergence to nearly globally optimum solutions for complex, constrained nuclear engineering problems with mixed-integer (MI) and combinatorial design vectors and high-cost, noisy, discontinuous, black box objective function evaluations. Gnowee’s hybrid metaheuristic framework is a new combination of a set of diverse, robust heuristics that appropriately balance diversification and intensification strategies across a wide range of optimization problems. There are many potential applications for this novel algorithm both within the nuclear community and beyond. Given that a set of well-known and studied nuclear benchmarks does not exist for the purpose of testing optimization algorithms, comparisons between Gnowee and several well-established metaheuristic algorithms are made for a set of 18 established continuous, MI, and combinatorial benchmarks representing a wide range of types of engineering problems and solution space behaviors. These results demonstrate Gnoweee to have superior flexibility and convergence characteristics over this diverse set of design spaces. We anticipate this wide range of applicability will make this algorithm desirable for many complex engineering applications.