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Optimization-based property preserving finite element methods for transport equations.
Abstract not provided.
Determination of critical experiment correlations using the sampler sequence within scale 6.2 - 14602
The validation of neutron transport methods used in nuclear criticality safety analyses is required by consensus American National Standards Institute/American Nuclear Society (ANSI/ANS) standards. In the last decade, there has been an increased interest in correlations among critical experiments used in validation that have shared physical attributes and which impact the independence of each measurement. The statistical methods included in many of the frequently cited guidance documents on performing validation calculations incorporate the assumption that all individual measurements are independent, so little guidance is available to practitioners on the topic. Typical guidance includes recommendations to select experiments from multiple facilities and experiment series in an attempt to minimize the impact of correlations or common-cause errors in experiments. Recent efforts have been made both to determine the magnitude of such correlations between experiments and to develop and apply methods for adjusting the bias and bias uncertainty to account for the correlations. This paper describes recent work performed at Oak Ridge National Laboratory using the Sampler sequence from the SCALE code system to develop experimental correlations using a Monte Carlo sampling technique. Sampler will be available for the first time with the release of SCALE 6.2, and a brief introduction to the methods used to calculate experiment correlations within this new sequence is presented in this paper. Techniques to utilize these correlations in the establishment of upper subcritical limits are the subject of a companion paper and will not be discussed here. Example experimental uncertainties and correlation coefficients are presented for a variety of low-enriched uranium water-moderated lattice experiments selected for use in a benchmark exercise by the Working Party on Nuclear Criticality Safety Subgroup on Uncertainty Analysis in Criticality Safety Analyses. The results include studies on the effect of fuel rod pitch on the correlations, and some observations are also made regarding difficulties in determining experimental correlations using the Monte Carlo sampling technique. (authors)
Historical review and proof-of-concept future method demonstration of adaptive mesh refinement in nuclear engineering for increased fidelity and computational efficiency
As the nuclear industry's use of computational tool increases, the need for increased fidelity and computational efficiency is well known. While most approaches to increased fidelity rely on applying a fine mesh over the problem domain, a more efficient method is to apply an adaptive mesh refinement (AMR) algorithm to the mesh definition. In the field of nuclear engineering, AMR has previously been used in conjunction with deterministic methods, including: S{sub N} transport methods, Lattice Boltzmann Methods, and COMSOL. The future of AMR in nuclear engineering is to couple it to a Monte Carlo code with the goal of reducing calculation time. A proof-of-concept example yielded positive results for using the gradient of the flux as a refinement criteria. The refinement criteria was varied from 0.01 to 0.10, which yielded a recommended range of 0.01 to 0.04, and the number of refinement iterations was varied from 0 to 7, with diminishing returns seen after 5 iterations. After the success of the proof-of-concept exercise, work began on creating a full program coupling MCNP6.2 and the AMR algorithm in the deal.II library. (authors)
An approach to improving transporting velocity in the long-range ultrasonic transportation of micro-particles
In existing ultrasonic transportation methods, the long-range transportation of micro-particles is always realized in step-by-step way. Due to the substantial decrease of the driving force in each step, the transportation is lower-speed and stair-stepping. To improve the transporting velocity, a non-stepping ultrasonic transportation approach is proposed. By quantitatively analyzing the acoustic potential well, an optimal region is defined as the position, where the largest driving force is provided under the condition that the driving force is simultaneously the major component of an acoustic radiation force. To keep the micro-particle trapped in the optimal region during the whole transportation process, an approach of optimizing the phase-shifting velocity and phase-shifting step is adopted. Due to the stable and large driving force, the displacement of the micro-particle is an approximately linear function of time, instead of a stair-stepping function of time as in the existing step-by-step methods. An experimental setup is also developed to validate this approach. Long-range ultrasonic transportations of zirconium beads with high transporting velocity were realized. The experimental results demonstrated that this approach is an effective way to improve transporting velocity in the long-range ultrasonic transportation of micro-particles.
Projection-operator methods for classical transport in magnetized plasmas. Part 2. Nonlinear response and the Burnett equations [Projection-operator methods for classical transport in magnetized plasmas. Part 1. Nonlinear response and the Burnett equations]
The time-independent projection-operator formalism for the derivation of Burnett equations is extended and considered in the context of multispecies and magnetized plasmas. The procedure provides specific formulas for transport coefficients in terms of two-time correlation functions involving both two and three phase-space points. It is shown how to calculate those correlation functions in the limit of weak coupling. The results are used to demonstrate, with the aid of a particular non-trivial example, that the Chapman–Enskog methodology employed by Catto & Simakov (CS) (Phys. Plasmas, vol. 11, 2004, pp. 90–102) to calculate the contributions to the parallel viscosity driven by temperature gradients is consistent with formulas previously derived from the two-time formalism by Brey (J. Chem. Phys., vol. 79, 1983, pp. 4585–4598). Here, the work serves to unify previous work on plasma kinetic theory with formalism usually applied to turbulence. Additional contributions include discussions of (i) Braginskii-order interspecies momentum exchange from the point of view of two-time correlations; and (ii) a simple stochastic model, unrelated to many-body theory, that exhibits Burnett effects. Insights from that model emphasize the role of non-Gaussian statistics in the evaluation of Burnett transport coefficients, including the effects calculated by CS that stem from the nonlinear collision operator. Together, Parts 1 and 2 of this series provide an introduction to projection-operator methods that should be broadly useful in theoretical plasma physics.
Methods of galactic heavy ion transport
Two methods of calculating the transition of galactic heavy ions in the earth's atmosphere are compared with respect to accuracy, generality, and computer efficiency. The most general method is shown to have the highest accuracy and is a simple numerical procedure.
Conditional Point Sampling: A Monte Carlo Method for Radiation Transport in Stochastic Media.
Current methods for stochastic media transport are either computationally expensive or, by nature, approximate. Moreover, none of the well-developed, benchmarked approximate methods can compute the variance caused by the stochastic mixing, a quantity especially important to safety calculations. Therefore, we derive and apply a new conditional probability function (CPF) for use in the recently developed stochastic media transport algorithm Conditional Point Sampling (CoPS), which 1) leverages the full intra-particle memory of CoPS to yield errorless computation of stochastic media outputs in 1D, binary, Markovian-mixed media, and 2) leverages the full inter-particle memory of CoPS and the recently developed Embedded Variance Deconvolution method to yield computation of the variance in transport outputs caused by stochastic material mixing. Numerical results demonstrate errorless stochastic media transport as compared to reference benchmark solutions with the new CPF for this class of stochastic mixing as well as the ability to compute the variance caused by the stochastic mixing via CoPS. Using previously derived, non-errorless CPFs, CoPS is further found to be more accurate than the atomic mix approximation, Chord Length Sampling (CLS), and most of memory-enhanced versions of CLS surveyed. In addition, we study the compounding behavior of CPF error as a function of cohort size (where a cohort is a group of histories that share intra-particle memory) and recommend that small cohorts be used when computing the variance in transport outputs caused by stochastic mixing.
Oak Ridge National Laboratory Shutdown Dose Rate Code Suite
The Oak Ridge National Laboratory (ORNL) shutdown dose rate (SDDR) code suite calculates gamma dose rates at a location of interest due to activation of materials. The code suite is based on the rigorous two-step (R2S) method that involves two radiation transport calculations: (1) neutron radiation transport to determine neutron fluxes in the material for which activation calculations will be performed and (2) gamma radiation transport to determine dose rates at a location of interest, due to material activation. The ORNL SDDR code suite is used to determine an importance function that characterizes the neutron’s importance to the final SDDR when the Monte Carlo radiation transport method is used. This report demonstrates how the ORNL SDDR code suite is implemented through the following codes: Monte Carlo N-Particle (MCNP) code Version 5-1.60, Oak Ridge Isotope Generator (ORIGEN), MSX suite of utilities, Neutron Activation Gamma Source Sampler (NAGSS), and Automated Variance Reduction Generator (ADVANTG). For this demonstration, the International Thermonuclear Experimental Reactor (ITER) SDDR benchmark problem is used and the dose rate result is compared to previously published work.
A comparative study of computational methods in cosmic gas dynamics
Many theoretical investigations of fluid flows in astrophysics require extensive numerical calculations. The selection of an appropriate computational method is, therefore, important for the astronomer who has to solve an astrophysical flow problem. The present investigation has the objective to provide an informational basis for such a selection by comparing a variety of numerical methods with the aid of a test problem. The test problem involves a simple, one-dimensional model of the gas flow in a spiral galaxy. The numerical methods considered include the beam scheme, Godunov's method (G), the second-order flux-splitting method (FS2), MacCormack's method, and the flux corrected transport methods of Boris and Book (1973). It is found that the best second-order method (FS2) outperforms the best first-order method (G) by a huge margin.
Neutron Transport Models and Methods for HZETRN and Coupling to Low Energy Light Ion Transport
Exposure estimates inside space vehicles, surface habitats, and high altitude aircraft exposed to space radiation are highly influenced by secondary neutron production. The deterministic transport code HZETRN has been identified as a reliable and efficient tool for such studies, but improvements to the underlying transport models and numerical methods are still necessary. In this paper, the forward-backward (FB) and directionally coupled forward-backward (DC) neutron transport models are derived, numerical methods for the FB model are reviewed, and a computationally efficient numerical solution is presented for the DC model. Both models are compared to the Monte Carlo codes HETCHEDS and FLUKA, and the DC model is shown to agree closely with the Monte Carlo results. Finally, it is found in the development of either model that the decoupling of low energy neutrons from the light ion (A<4) transport procedure adversely affects low energy light ion fluence spectra and exposure quantities. A first order correction is presented to resolve the problem, and it is shown to be both accurate and efficient.
Validation of MCNP6 Version 1.0 with the ENDF/B-VII.1 Cross Section Library for Uranium Metal, Oxide, and Solution Systems on the High Performance Computing Platform Moonlight
In this document, the code MCNP is validated with ENDF/B-VII.1 cross section data under the purview of ANSI/ANS-8.24-2007, for use with uranium systems. MCNP is a computer code based on Monte Carlo transport methods. While MCNP has wide reading capability in nuclear transport simulation, this validation is limited to the functionality related to neutron transport and calculation of criticality parameters such as k eff .
Automated Hybrid Variance Reduction on Advanced Architectures in the Shift Monte Carlo Code
Monte Carlo transport methods are the most accurate schemes for solving problems with complex energy and spatial features, but they come with a high computational cost. Although hybrid methods have enabled the use of Monte Carlo transport for a large class of problems, they still require significant computing resources. Modern multicore CPUs with large numbers of compute cores and graphical processing units (GPUs) provide opportunities to optimize the memory and run-time costs of hybrid Monte Carlo methods. This paper documents the development and analysis of three Monte Carlo transport algorithms that support hybrid transport using the consistent adjoint-driven importance sampling (CADIS) and forward-weighted CADIS methods in the Shift Monte Carlo code: history-based transport using static and dynamic threading on multicore CPUs and event-based transport enabling weight window tracking on GPUs. The results are shown for two challenging hybrid problems on the Frontier supercomputer at the Oak Ridge Leadership Computing Facility. The results show that all three methods yield good performance and enable solutions of difficult fixed-source transport problems in less than 2 min on 20 nodes of Frontier. Dynamic threading was observed to give up to 20% better scaling behavior than static threading. Moreover, the AMD Instinct 250X GPU was found to give 9 to 11 times greater throughput per graphics compute die than the best CPU performance. In conclusion, additional opportunities for optimization of hybrid transport on GPUs are discussed.
Comparison of Spatial Discretization Methods for Solving the S N Equations Using a Three-Dimensional Method of Manufactured Solutions Benchmark Suite with Escalating Order of Nonsmoothness
For this study, a comparison of the accuracy and computational efficiency of spatial discretization methods of the three-dimensional S N equations is conducted, including discontinuous Galerkin finite element methods, the arbitrarily high-order transport method of nodal type (AHOTN), the linear-linear method, the linear-nodal (LN) method, and the higher-order diamond difference method. For this purpose, we have developed a suite of method of manufactured solutions benchmarks that provides an exact solution of the S N equations even in the presence of scattering. Most importantly, our benchmark suite permits the user to set an arbitrary level of smoothness of the exact solution across the singular characteristics. Our study focuses on the computational efficiency of the considered spatial discretization methods. Numerical results indicate that the best-performing method depends on the norm used to measure the discretization error. We employ discrete Lp norms and integral error norms in this work. For configurations with continuous exact angular flux, high-order AHOTNs perform best under L p error norms, while the LN method performs best when measured by integral error norms. Lastly, when the angular flux is discontinuous, a new singular-characteristic tracking method for three-dimensional geometries performs best among the considered methods.
Neutron (and other Particle) Transport at LANL: An Overview [Presentation]
For decades, Los Alamos National Laboratory has been at the forefront of neutron transport methods research and code development. One such code is PARTISN, the LANL parallel time-dependent discrete ordinate neutron transport code. In this presentation, we describe the various research efforts currently underway by the PARTISN and other code teams. Some examples of current research are a block automated mesh refinement scheme, the application of tensor trains to the discretized neutron transport equation, and GPU code porting. The block automated mesh refinement scheme uses cross section information to refine and coarsen the solution mesh to improve time to solution and reduce memory. The tensor train approach expresses discretized transport operators as tensor products of vectors and matrices to compress the size of linear systems being solved by transport codes. Rather than relying on matrix-free methods such as the transport sweep, we have access to an operator that can be inverted, reshaped, or manipulated algebraically. Finally, we describe how PARTISN is used, what problems we are looking to solve, and what the future holds for neutron transport at LANL. In addition to this, we briefly describe the various research efforts in other particle transport teams using both deterministic and Monte Carlo methods. In the presentation, we list possible opportunities for collaboration between the laboratory and faculty and students.
Electron transport in graphene/graphene side-contact junction by plane-wave multiple-scattering method
Electron transport in graphene is along the sheet but junction devices are often made by stacking different sheets together in a “side-contact” geometry which causes the current to flow perpendicular to the sheets within the device. Such geometry presents a challenge to first-principles transport methods. We solve this problem by implementing a plane-wave-based multiple-scattering theory for electron transport. In this study, this implementation improves the computational efficiency over the existing plane-wave transport code, scales better for parallelization over large number of nodes, and does not require the current direction to be along a lattice axis. As a first application, we calculate the tunneling current through a side-contact graphene junction formed by two separate graphene sheets with the edges overlapping each other. We find that transport properties of this junction depend strongly on the AA or AB stacking within the overlapping region as well as the vacuum gap between two graphene sheets. Finally, such transport behaviors are explained in terms of carbon orbital orientation, hybridization, and delocalization as the geometry is varied.
Methods for producing thin film charge selective transport layers
Methods for producing thin film charge selective transport layers are provided. In one embodiment, a method for forming a thin film charge selective transport layer comprises: providing a precursor solution comprising a metal containing reactive precursor material dissolved into a complexing solvent; depositing the precursor solution onto a surface of a substrate to form a film; and forming a charge selective transport layer on the substrate by annealing the film.
Conservation of migration area by transport cross sections using Cumulative Migration Method in deterministic heterogeneous reactor transport analysis
Not provided.