Kord Smith

Application of the Jacobian-Free Newton-Krylov Method to Nonlinear Acceleration of Transport Source Iteration in Slab Geometry

Abstract The use of the Jacobian-free Newton-Krylov (JFNK) method within the context of nonlinear diffusion acceleration (NDA) of source iteration is explored. The JFNK method is a synergistic combination of Newton’s method as the nonlinear solver and Krylov methods as the linear solver. JFNK methods do not form or store the Jacobian matrix, and Newton’s method is executed via probing the nonlinear discrete function to approximate the required matrix-vector products. Current application of NDA relies upon a fixed-point, or Picard, iteration to resolve the nonlinearity. We show that the JFNK method can be used to replace this Picard iteration with a Newton iteration. The Picard linearization is retained as a preconditioner. We show that the resulting JFNK-NDA capability provides benefit in some regimes. Furthermore, we study the effects of a two-grid approach, and the required intergrid transfers when the higher-order transport method is solved on a fine mesh compared to the low-order acceleration problem.

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

Analysis of communication costs for domain decomposed Monte Carlo methods in nuclear reactor analysis

A domain decomposed Monte Carlo communication kernel is used to carry out performance tests to establish the feasibility of using Monte Carlo techniques for practical Light Water Reactor (LWR) core analyses. The results of the prototype code are interpreted in the context of simplified performance models which elucidate key scaling regimes of the parallel algorithm.

Impact of inflow transport approximation on light water reactor analysis

The impact of the inflow transport approximation on light water reactor analysis is investigated, and it is verified that the inflow transport approximation significantly improves the accuracy of the transport and transport/diffusion solutions. A methodology for an inflow transport approximation is implemented in order to generate an accurate transport cross section. The inflow transport approximation is compared to the conventional methods, which are the consistent- P N and the outflow transport approximations. The three transport approximations are implemented in the lattice physics code STREAM, and verification is performed for various verification problems in order to investigate their effects and accuracy. From the verification, it is noted that the consistent- P N and the outflow transport approximations cause significant error in calculating the eigenvalue and the power distribution. The inflow transport approximation shows very accurate and precise results for the verification problems. The inflow transport approximation shows significant improvements not only for the high leakage problem but also for practical large core problem analyses.

Quadratic Depletion Method for Gadolinium Isotopes in CASMO-5

Abstract The huge absorption cross sections of 155Gd and 157Gd cause strong spatial shielding effects in Gd-bearing pins. A high-order depletion method has been developed for CASMO-5 to address the issue of the small depletion steps typically required for Gd-bearing fuel assemblies. In this method, the microscopic absorption reaction rates of gadolinium isotopes are assumed to be quadratic functions of the number density of 155Gd rather than the constant reaction rate assumption in the conventional predictor-corrector (PC) method. This quadratic function assumption models the variations of the spatial shielding effects over the depletion step and therefore improves the accuracy of depletion calculations with a negligible amount of calculation time increase. With this new method, a depletion step size four times larger than the step size used in a conventional PC method can be used for Gd-bearing assemblies without compromising accuracy.

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.

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.

A task-based parallelism and vectorized approach to 3D Method of Characteristics (MOC) reactor simulation for high performance computing architectures

Abstract In this study we present and analyze a formulation of the 3D Method of Characteristics (MOC) technique applied to the simulation of full core nuclear reactors. Key features of the algorithm include a task-based parallelism model that allows independent MOC tracks to be assigned to threads dynamically, ensuring load balancing, and a wide vectorizable inner loop that takes advantage of modern SIMD computer architectures. The algorithm is implemented in a set of highly optimized proxy applications in order to investigate its performance characteristics on CPU, GPU, and Intel Xeon Phi architectures. Speed, power, and hardware cost efficiencies are compared. Additionally, performance bottlenecks are identified for each architecture in order to determine the prospects for continued scalability of the algorithm on next generation HPC architectures.

On the diffusion coefficient calculation in two-step light water reactor core analysis

ABSTRACT This paper presents consistent and rigorous accuracy assessments of various methods for calculating the diffusion coefficients in a two-step reactor core analysis of light water reactors (LWRs). The diffusion coefficients are significantly affected by the transport correction and critical spectrum calculations. There are various methods for the transport corrections (inflow/outflow/hybrid corrections) and critical spectrum calculations (B1/P1/CASMO-4E methods) so that it is necessary to decide the best combination to achieve a high accuracy in the transport/diffusion two-step analysis. Numerical tests are performed step-by-step to search for the best combination of the methods by comparing each other the transport one-step results, transport/diffusion two-step results, and Monte Carlo results. Numerical test results with a large and a small LWR core show that the combination of inflow transport correction and CASMO-4E critical spectrum calculation is most accurate than the other combinations in terms of eigenvalues and assembly power distributions.