Benoit Forget

Generalized Energy Condensation Theory

Abstract A generalization of multigroup energy condensation theory has been developed. The new method generates a solution within the few-group framework that exhibits the energy spectrum characteristic of a many-group transport solution, without the computational time usually associated with such solutions. This is accomplished by expanding the energy dependence of the angular flux in a set of general orthogonal functions. The expansion leads to a set of equations for the angular flux moments in the few-group framework. The zeroth moment generates the standard few-group equation while the higher-moment equations generate the detailed spectral resolution within the few-group structure. It is shown that by carefully choosing the orthogonal function set (e.g., Legendre polynomials), the higher-moment equations are only coupled to the zeroth-order equation and not to each other. The decoupling makes the new method highly competitive with the standard few-group method since the computation time associated with determining the higher moments becomes negligible as a result of the decoupling. The method is verified in several one-dimensional benchmark problems typical of boiling water reactor configurations with mild to high heterogeneity.

Data decomposition of Monte Carlo particle transport simulations via tally servers

United States. Dept. of Energy. Naval Reactors Division. Rickover Fellowship Program in Nuclear Engineering

Parallel Fission Bank Algorithms in Monte Carlo Criticality Calculations

Abstract In this work we describe a new method for parallelizing the source iterations in a Monte Carlo criticality calculation. Instead of having one global fission bank that needs to be synchronized, as is traditionally done, our method has each processor keep track of a local fission bank while still preserving reproducibility. In doing so, it is required to send only a limited set of fission bank sites between processors, thereby drastically reducing the total amount of data sent through the network. The algorithm was implemented in a simple Monte Carlo code and shown to scale up to hundreds of processors and furthermore outperforms traditional algorithms by at least two orders of magnitude in wall-clock time.

A Discrete Generalized Multigroup Energy Expansion Theory

Abstract This study describes the generalized multigroup energy treatment for the neutron transport equation. Discrete Legendre orthogonal polynomials (DLOPs) are used to expand the energy dependence of the angular flux into a set of flux moments. The leading (zeroth)-order equation is identical to a standard multigroup solution, while the higher-order equations are decoupled from each other and only depend on the leading-order solution because of the orthogonality property of the DLOPs. This decoupling leads to computational times comparable to the coarse-group calculation but provides an accurate fine-group energy spectrum. One-dimensional single-assembly and core calculations were performed to demonstrate the potential of the discrete generalized multigroup method. Computational results show that the discrete generalized multigroup method can produce an accurate fine-group whole-core solution for less computational time. A source update process is also introduced that provides improvement of integral quantities such as eigenvalue and reaction rates over the coarse-group solution.

Performance Analysis of a Reduced Data Movement Algorithm for Neutron Cross Section Data in Monte Carlo Simulations

Current Monte Carlo neutron transport applications use continuous energy cross section data to provide the statistical foundation for particle trajectories. This “classical” algorithm requires storage and random access of very large data structures. Recently, Forget et al. [1] reported on a fundamentally new approach, based on multipole expansions, that distills cross section data down to a more abstract mathematical format. Their formulation greatly reduces memory storage and improves data locality at the cost of also increasing floating point computation. In the present study, we abstract the multipole representation into a “proxy application”, which we then use to determine the hardware performance parameters of the algorithm relative to the classical continuous energy algorithm. This study is done to determine the viability of both algorithms on current and next-generation high performance computing platforms.

Preliminary Coupling of the Monte Carlo Code OpenMC and the Multiphysics Object-Oriented Simulation Environment for Analyzing Doppler Feedback in Monte Carlo Simulations

In recent years, the use of Monte Carlo methods for modeling reactors has become feasible due to the increasing availability of massively parallel computer systems. One of the primary challenges yet to be fully resolved, however, is the efficient and accurate inclusion of multiphysics feedback in Monte Carlo simulations. The research in this paper presents a preliminary coupling of the open-source Monte Carlo code OpenMC with the open-source Multiphysics Object-Oriented Simulation Environment (MOOSE). The coupling of OpenMC and MOOSE will be used to investigate efficient and accurate numerical methods needed to include multiphysics feedback in Monte Carlo codes. An investigation into the sensitivity of Doppler feedback to fuel temperature approximations using a two-dimensional 17 × 17 pressurized water reactor (PWR) fuel assembly is presented in this paper. The results show a functioning multiphysics coupling between OpenMC and MOOSE. The coupling utilizes functional expansion tallies to transfer accurately and efficiently pin power distributions tallied in OpenMC to unstructured finite element meshes used in MOOSE. The two-dimensional PWR fuel assembly case also demonstrates that for a simplified model, the pin-by-pin Doppler feedback can be adequately replicated by scaling a representative pin based on pin relative powers.

Multigroup diffusion preconditioners for multiplying fixed-source transport problems

Several preconditioners based on multigroup diffusion are developed for application to multiplying fixed-source transport problems using the discrete ordinates method. By starting from standard, one-group, diffusion synthetic acceleration (DSA), a multigroup diffusion preconditioner is constructed that shares the same fine mesh as the transport problem. As a cheaper but effective alternative, a two-grid, coarse-mesh, multigroup diffusion preconditioner is examined, for which a variety of homogenization schemes are studied to generate the coarse mesh operator. Finally, a transport-corrected diffusion preconditioner based on application of the Newton-Shulz algorithm is developed. The results of several numerical studies indicate the coarse-mesh, diffusion preconditioners work very well. In particular, a coarse-mesh, transport-corrected, diffusion preconditioner reduced the computational time of multigroup GMRES by up to a factor of 17 and outperformed best-case Gauss-Seidel results by over an order of magnitude for all problems studied.

Improved cache performance in Monte Carlo transport calculations using energy banding

Abstract We present an energy banding algorithm for Monte Carlo (MC) neutral particle transport simulations which depend on large cross section lookup tables. In MC codes, read-only cross section data tables are accessed frequently, exhibit poor locality, and are typically too much large to fit in fast memory. Thus, performance is often limited by long latencies to RAM, or by off-node communication latencies when the data footprint is very large and must be decomposed on a distributed memory machine. The proposed energy banding algorithm allows maximal temporal reuse of data in band sizes that can flexibly accommodate different architectural features. The energy banding algorithm is general and has a number of benefits compared to the traditional approach. In the present analysis we explore its potential to achieve improvements in time-to-solution on modern cache-based architectures.

Monte Carlo domain decomposition for robust nuclear reactor analysis

Spatial domain decomposition implemented in production-scale neutron transport code.An efficient inter-domain particle communication algorithm is presented.An updated performance model accurately predicts load imbalance penalties.Load-balancing can effectively mitigate load imbalances for reactor problems.Terabyte-scale tallies do not significantly degrade particle tracking rates. Monte Carlo (MC) neutral particle transport codes are considered the gold-standard for nuclear simulations, but they cannot be robustly applied to high-fidelity nuclear reactor analysis without accommodating several terabytes of materials and tally data. While this is not a large amount of aggregate data for a typical high performance computer, MC methods are only embarrassingly parallel when the key data structures are replicated for each processing element, an approach which is likely infeasible on future machines. The present work explores the use of spatial domain decomposition to make full-scale nuclear reactor simulations tractable with Monte Carlo methods, presenting a simple implementation in a production-scale code. Good performance is achieved for mesh-tallies of up to 2.39TB distributed across 512 compute nodes while running a full-core reactor benchmark on the Mira Blue Gene/Q supercomputer at the Argonne National Laboratory. In addition, the effects of load imbalances are explored with an updated performance model that is empirically validated against observed timing results. Several load balancing techniques are also implemented to demonstrate that imbalances can be largely mitigated, including a new and efficient way to distribute extra compute resources across finer domain meshes.

Using the Neutron Excess Concept to Determine Starting Fuel Requirements for Minimum Burnup Breed-and-Burn Reactors

Abstract In a breed-and-burn (B&B) reactor, the reactor is first started with enriched uranium or other fissile material but thereafter can be refueled with natural or depleted uranium. B&B reactors have the potential to achieve >10% uranium utilization in a once-through fuel cycle versus <1% for light water reactors. A newly developed method for analyzing B&B reactors—the “neutron excess” concept—is used to determine the minimum amount of startup fuel needed to establish a desired equilibrium cycle in a minimum burnup B&B reactor. Here, a minimum burnup B&B reactor is defined as one in which neutron leakage is minimized and feed fuel can be discharged at uniform burnup. The neutron excess concept reformulates the k-effective of a system in terms of material depletion quantities: the total number of neutrons absorbed and produced by a given volume of fuel, which are termed “neutron excess quantities.” This concept is useful because neutron excess quantities are straightforward to estimate using simple one-dimensional (1-D) and zero-dimensional (0-D) models. A set of equations is developed that allows the quantity of starter fuel needed to establish a given B&B equilibrium cycle to be expressed in terms of neutron excess quantities. A simple 1-D example of a sodium-cooled, metal fuel reactor with a startup enrichment of 15% is used to illustrate how the method is applied. An estimate for the required amount of starter fuel based on a 0-D depletion model is found to differ by only 3% from the actual amount computed using the 1-D example model.