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DOE OSTI2013

Forward and adjoint sensitivity computation of chaotic dynamical systems

This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged “statistical” quantities to infinitesimal perturbations of the system parameters. The algorithms are demonstrated on the Lorenz attractor. We show that sensitivity derivatives of statistical quantities can be accurately estimated using a single, short trajectory (over a time interval of 20) on the Lorenz attractor.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

Development and application of a hybrid transport methodology for active interrogation systems

A hybrid Monte Carlo and deterministic methodology has been developed for application to active interrogation systems. The methodology consists of four steps: i) neutron flux distribution due to neutron source transport and subcritical multiplication; ii) generation of gamma source distribution from (n, 7) interactions; iii) determination of gamma current at a detector window; iv) detection of gammas by the detector. This paper discusses the theory and results of the first three steps for the case of a cargo container with a sphere of HEU in third-density water cargo. To complete the first step, a response-function formulation has been developed to calculate the subcritical multiplication and neutron flux distribution. Response coefficients are pre-calculated using the MCNP5 Monte Carlo code. The second step uses the calculated neutron flux distribution and Bugle-96 (n, 7) cross sections to find the resulting gamma source distribution. In the third step the gamma source distribution is coupled with a pre-calculated adjoint function to determine the gamma current at a detector window. The AIMS (Active Interrogation for Monitoring Special-Nuclear-Materials) software has been written to output the gamma current for a source-detector assembly scanning across a cargo container using the pre-calculated values and taking significantly less time than a reference MCNP5 calculation. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

The Aharonov–Bohm effect in scattering theory

The Aharonov–Bohm effect is considered as a scattering event with nonrelativistic charged particles of the wavelength which is less than the transverse size of an impenetrable magnetic vortex. The quasiclassical WKB method is shown to be efficient in solving this scattering problem. We find that the scattering cross section consists of two terms, one describing the classical phenomenon of elastic reflection and another one describing the quantum phenomenon of diffraction; the Aharonov–Bohm effect is manifested as a fringe shift in the diffraction pattern. Both the classical and the quantum phenomena are independent of the choice of a boundary condition at the vortex edge, providing that probability is conserved. We show that a propagation of charged particles can be controlled by altering the flux of a magnetic vortex placed on their way. -- Highlights: •Aharonov–Bohm effect as a scattering event. •Impenetrable magnetic vortex of nonzero transverse size. •Scattering cross section is independent of a self-adjoint extension employed. •Classical phenomenon of elastic reflection and quantum phenomenon of diffraction. •Aharonov–Bohm effect as a fringe shift in the diffraction pattern.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2011

A magnetospheric energy principle extended to include neutral atmosphere

The problem of ideal magnetohydrodynamic stability of plasmas in a magnetosphere-atmosphere system, in which the unperturbed magnetic field is assumed to be perpendicular to the plasma-atmosphere interface (ionospheric surface), is investigated by means of an extended magnetospheric energy principle. The derivation of the principle and conditions under which it applies to a real terrestrial magnetosphere is given. In the principle, the atmosphere is considered to be a very heavy and compressible gas with finite pressure. A thin ionospheric layer is taken into account as boundary conditions, but energetics within it are neglected. The solid-earth surface is assumed to be a perfectly conducting wall for perturbations. For a perturbation that satisfies either rigid or horizontally free boundary conditions at the plasma-atmosphere interface, the self-adjointness of the force operator is satisfied and an extended magnetospheric energy principle can be developed on the basis of the extended energy principle for fusion plasmas. These two boundary conditions are shown to be realized in the magnetosphere when the ionospheric conductivity is either very large or very small. Whereas in fusion plasmas the perturbed magnetic energy in the vacuum makes a stabilizing contribution to the potential energy, in the magnetosphere the perturbed magnetic energy in the atmosphere makes no such stabilizing contribution. This is due to the difference of the assumed field configurations of the magnetospheric and fusion plasmas. The ionospheric surface makes a destabilizing negative contribution to the potential energy owing to a horizontal plasma displacement on the spherical ionospheric surface. The method is applied to magnetospheric ballooning and interchange instabilities. The existence of a new type of magnetospheric interchange instability is shown and its structure in the magnetosphere-atmosphere system is clarified. Possible consequences of the instabilities and their relevance to magnetospheric physics are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

High-resolution source imaging and moment tensor estimation of acoustic emissions during brittle creep of basalt undergoing carbonation

SUMMARY As the high-frequency analogue to field-scale earthquakes, acoustic emissions (AEs) provide a valuable complement to study rock deformation mechanisms. During the load-stepping creep experiments with CO2-saturated water injection into a basaltic sample from Carbfix site in Iceland, 8791 AE events are detected by at least one of the seven piezoelectric sensors. Here, we apply a cross-correlation-based source imaging method, called geometric-mean reverse-time migration (GmRTM) to locate those AE events. Besides the attractive picking-free feature shared with other waveform-based methods (e.g. time-reversal imaging), GmRTM is advantageous in generating high-resolution source images with reduced imaging artefacts, especially for experiments with relatively sparse receivers. In general, the imaged AE locations are found to be scattered across the sample, suggesting a complicated fracture network rather than a well-defined major shear fracture plane, in agreement with X-ray computed tomography imaging results after retrieval of samples from the deformation apparatus. Clustering the events in space and time using the nearest-neighbour approach revealed a group of ‘repeaters’, which are spatially co-located over an elongated period of time and likely indicate crack, or shear band growth. Furthermore, we select 2196 AE events with high signal-to-noise-ratio (SNR) and conduct moment tensor estimation using the adjoint (backpropagated) strain tensor fields at the locations of AE sources. The resulting AE locations and focal mechanisms support our previously assertion that creep of basalt at the experimental conditions is accommodated dominantly by distributed microcracking.

58 GEOSCIENCES↗

DOE OSTI2014

ITS version 6.4: The Integrated TIGER Series of Monte Carlo Electron/Photon Radiation Transport Codes - Paper 40

ITS (Integrated TIGER Series) is a suite of fully coupled electron/photon Monte Carlo radiation transport codes. The package contains programs to perform 1D, 2D and 3D simulations. The 3D geometry representations include the traditional combinatorial geometry (CG), facet-based models, CAD models for those users who have a license for the ACIS{sup R} CAD libraries, and hybrid models of any combination. There is a multigroup version which permits adjoint analysis. The availability of source code permits the more sophisticated user to tailor the code to specific applications and to extend the capabilities of the codes to more complex applications. ITS is presently available only through a U.S.-government-use license. It is available once again through the Radiation Safety Information Computational Center (RSICC). (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2013

Commuting projections on graphs

For a given (connected) graph, we consider vector spaces of (discrete) functions defined on its vertices and its edges. These two spaces are related by a discrete gradient operator, Grad and its adjoint, ₋Div, referred to as (negative) discrete divergence. We also consider a coarse graph obtained by aggregation of vertices of the original one. Then a coarse vertex space is identified with the subspace of piecewise constant functions over the aggregates. We consider the ℓ 2 -projection Q H onto the space of these piecewise constants. In the present paper, our main result is the construction of a projection π H from the original edge-space onto a properly constructed coarse edge-space associated with the edges of the coarse graph. The projections π H and Q H commute with the discrete divergence operator, i.e., we have div π H = Q H div. The respective pair of coarse edge-space and coarse vertexspace offer the potential to construct two-level, and by recursion, multilevel methods for the mixed formulation of the graph Laplacian which utilizes the discrete divergence operator. The performance of one two-level method with overlapping Schwarz smoothing and correction based on the constructed coarse spaces for solving such mixed graph Laplacian systems is illustrated on a number of graph examples.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2007

Anisotropic Solution Adaptive Unstructured Grid Generation Using AFLR

An existing volume grid generation procedure, AFLR3, was successfully modified to generate anisotropic tetrahedral elements using a directional metric transformation defined at source nodes. The procedure can be coupled with a solver and an error estimator as part of an overall anisotropic solution adaptation methodology. It is suitable for use with an error estimator based on an adjoint, optimization, sensitivity derivative, or related approach. This offers many advantages, including more efficient point placement along with robust and efficient error estimation. It also serves as a framework for true grid optimization wherein error estimation and computational resources can be used as cost functions to determine the optimal point distribution. Within AFLR3 the metric transformation is implemented using a set of transformation vectors and associated aspect ratios. The modified overall procedure is presented along with details of the anisotropic transformation implementation. Multiple two-and three-dimensional examples are also presented that demonstrate the capability of the modified AFLR procedure to generate anisotropic elements using a set of source nodes with anisotropic transformation metrics. The example cases presented use moderate levels of anisotropy and result in usable element quality. Future testing with various flow solvers and methods for obtaining transformation metric information is needed to determine practical limits and evaluate the efficacy of the overall approach.

Marcum, David L.↗

DOE OSTI2025

Computational Optimization of 133m Xe Production via Neutron Irradiation in a TRIGA Reactor

Here, the Comprehensive Nuclear-Test-Ban Treaty bans all nuclear tests worldwide. As part of treaty compliance, the concentration of radioactive nuclides in the atmosphere is monitored to detect nuclear weapons tests. Radioactive noble gas fission products, specifically radioxenon, can vent into the atmosphere after a nuclear weapons test, even if the test is well contained underground or underwater. Radioxenon thus serves as a signal for nuclear weapons tests. All atmospheric monitoring systems require samples of radioxenon isotopes for detector calibration, quality control, and certification. Here, we present a novel, improved method for creating samples of 133m Xe via neutron irradiation of 132 Xe in the Washington State University TRIGA reactor. 132 Xe neutron absorption results in either 133 Xe or 133m Xe—thermal neutron absorption results in 133m Xe 12% of the time, while fast neutron absorption (above ~1 MeV) results in 133m Xe ~50% of the time. To optimize the production of 133m Xe via neutron absorption in 132 Xe in the thermal TRIGA reactor, spectral tuning using an irradiation chamber is required to maximize the fraction of fast neutrons being absorbed and minimize the number of thermal neutrons interacting with the 132 Xe. We used MCNP to tally 132 Xe absorptions with the isotopic tally function, flux tallies and neutron attenuation to estimate the number of neutrons reaching the 132 Xe through the irradiation chamber, and the adjoint importance function to improve the source strength estimate. Additionally, we performed a heat transfer analysis for safety considerations. It was determined that the use of a 96% enriched 10 B boron carbide chamber, placed next to the fuel elements in reactor position D8, increases the 133m Xe/ 133 Xe activity ratio from a baseline value of 0.3 to 1.0, a 233% increase. Additionally, it was determined that the alpha heating produced in the boron does not become an unmanageable problem in the Washington State University reactor.

37 - INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL C↗

DOE OSTI2018

Normal-mode-based analysis of electron plasma waves with second-order Hermitian formalism

The classic problem of the dynamic evolution and Landau damping of linear Langmuir electron waves in a collisionless plasma with Maxwellian background is cast as a second-order, self-adjoint problem with a continuum spectrum of real and positive squared frequencies. The corresponding complete basis of singular normal modes is obtained, along with their orthogonality relation. This yields easily the general expression of the time-reversal-invariant solution for any initial-value problem. Examples are then given for specific initial conditions that illustrate different behaviors of the Landau-damped macroscopic moments of the perturbations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

Guidelines for effective radiation transport for cable SGEMP modeling

This report describes experiences gained in performing radiation transport computations with the SCEPTRE radiation transport code for System Generated ElectroMagnetic Pulse (SGEMP) applications. SCEPTRE is a complex code requiring a fairly sophisticated user to run the code effectively, so this report provides guidance for analysts interested in performing these types of calculations. One challenge in modeling coupled photon/electron transport for SGEMP is to provide a spatial mesh that is sufficiently resolved to accurately model surface charge emission and charge deposition near material interfaces. The method that has been most commonly used to date to compute cable SGEMP typically requires a sub-micron mesh size near material interfaces, which may be difficult for meshing software to provide for complex geometries. We present here an alternative method for computing cable SGEMP that appears to substantially relax this requirement. The report also investigates the effect of refining the energy mesh and increasing the order of the angular approximation to provide some guidance on determining reasonable parameters for the energy/angular approximation needed for x-ray environments. Conclusions for γ-ray environments may be quite different and will be treated in a subsequent report. In the course of the energy-mesh refinement studies, a bug in the cross-section generation software was discovered that may cause underprediction of the result by as much as an order of magnitude for the test problem studied here, when the electron energy group widths are much smaller than those for the photons. Results will be presented and compared using cross sections generated before and after the fix. We also describe adjoint modeling, which provides sensitivity of the total charge drive to the source energy and angle of incidence, which is quite useful for comparing the effect of changing the source environment and for determining most stressing angle of incidence and source energy. This report focusses on cable SGEMP applications, but many of the conclusions will be directly applicable for box Internal ElectroMagnetic Pulse (IEMP) modeling as well.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2024

Adjoint Waveform Tomography for Crustal and Upper Mantle Structure of the Middle East and Southwest Asia for Improved Waveform Simulations Using Openly Available Broadband Data

Here we present a new model of radially anisotropic seismic wavespeeds for the crust and upper mantle of a broad region of the Middle East and Southwest Asia (MESWA) derived from adjoint waveform tomography. The new model enables fully 3D simulations of complete three-component waveforms and provides improved fits that were not possible with previous models. We inverted over 32,000 waveforms from 192 earthquakes recorded by over 1000 openly available broadband seismic stations from permanent and temporary networks in the region with highly uneven coverage. Inversion iterations proceeded from the period band 50–100 s in six stages and 54 total iterations reducing the minimum period to 30 s. Our final model, MESWA, improves waveform fits compared to the starting and other models for both the data used in the inversion and an independent validation set of 66 events. Restitution tests indicate that the model resolves features in the central part of the model to depths of about 150 km. The new model reveals tectonic features imaged by other studies and methods but in a new holistic model of anisotropic shear and compressional wavespeeds (V S and V P , respectively) covering a larger domain with smaller scale length and amplified features. Examples include low crustal V S in the Tethyan belt and low mantle VS following divergent (Gulf of Aden, Red Sea) and transform (Dead Sea fault) margins of the Arabian plate. Low V S is imaged below Cenozoic volcanic centers of the Mecca–Madina–Nafud Line, Arabian Peninsula, and the Türkiye–Iran border region. Elevated V S tracks Makran subduction under southeast Iran with near vertical dip. MESWA could be used as a starting model for further improvements, say, using waveforms from in-country seismic networks that are not currently openly available and/or smaller-scale studies targeting a shorter period. The model could be used to improve earthquake hazard studies and nuclear explosion monitoring.

58 GEOSCIENCES↗

DOE OSTI2022

Invertible Neural Networks for Aerodynamic Design of Wind Turbine Blades

The state-of-the-practice methods for aerodynamic design of wind turbine blads use linearized blade element momentum theory (BEM) to optimize the twist and chord profiles from a pre-selected set of 2D airfoil shapes. In this work, we apply invertible neural network (INN) tools to enable the rapid inverse aerodynamic design of wind turbine blades including component airfoils. The INN is trained on data obtained through the use of robust automated mesh generation and the HAMSTR computational fluid dynamics solver with advanced turbulence and transition models validated for turbine applications. Our design technique is a significant improvement over the state-of-the-practice linearized blade element momentum (BEM) techniques in capturing 3D nonlinear aerodynamic effects that are critical for optimal design of the rotors. This is made possible by developing sparse, invertible neural networks (INNs) for inverse design and optimization that realize a 100x cost reduction compared to adjoint-based computational fluid dynamics (CFD) approaches, while enabling increased robustness of the final design. We demonstrate the INN tool for design of a section of the NREL 5-MW blade. All generated shapes satisfy the desired aerodynamic characteristics, demonstrating the success of the INN approach for inverse design of wind turbine blades.

aerodynamic design↗

NASA NTRSDate not supplied

Cartesian Mesh Simulations for the Third AIAA Sonic Boom Prediction Workshop

Simulation results are presented for all cases from the Third AIAA Sonic Boom Prediction Workshop. An inviscid, embedded-boundary Cartesian-mesh flow solver is used in conjunction with adjoint-based mesh adaptation to compute nearfield pressure signatures. Specialized techniques are applied to maximize accuracy and minimize cost on Cartesian meshes. The Richardson-based error estimate highlights regions of the signatures most sensitive to mesh refinement. Timing results and coarse, medium, and fine mesh sizes for nearfield cases demonstrate that the parallel decomposition approach is efficient in both computational time and wall-clock. Pressure signals are propagated to the ground using an augmented Burgers’ equation solver to predict boom carpets. Ground signatures and loudness metrics are presented for a standard atmosphere as well as more realistic atmospheric profiles, which affect overall noise levels and can significantly widen the boom carpet. Mesh convergence studies show that high sampling frequencies, around 500 kHz, are required for propagation, and the sampling frequency increases at large off-track angles with longer acoustic ray paths and propagation times. The numerical methods yield accurate results for predicting low sonic boom signatures while being among the least computationally expensive of the workshop.

ARMD↗

NASA NTRS2013

Analyzing Carbon Dioxide and Methane Emissions in California Using Airborne Measurements and Model Simulations

Greenhouse gas (GHG) concentrations have increased over the past decades and are linked to global temperature increases and climate change. These changes in climate have been suggested to have varying effects, and uncertain consequences, on agriculture, water supply, weather, sea-level rise, the economy, and energy. To counteract the trend of increasing atmospheric concentrations of GHGs, the state of California has passed the California Global Warming Act of 2006 (AB-32). This requires that by the year 2020, GHG (e.g., carbon dioxide (CO2) and methane (CH4)) emissions will be reduced to 1990 levels. To quantify GHG fluxes, emission inventories are routinely compiled for the State of California (e.g., CH4 emissions from the California Greenhouse Gas Emissions Measurement (CALGEM) Project). The major sources of CO2 and CH4 in the state of California are: transportation, electricity production, oil and gas extraction, cement plants, agriculture, landfills/waste, livestock, and wetlands. However, uncertainties remain in these emission inventories because many factors contributing to these processes are poorly quantified. To alleviate these uncertainties, a synergistic approach of applying air-borne measurements and chemical transport modeling (CTM) efforts to provide a method of quantifying local and regional GHG emissions will be performed during this study. Additionally, in order to further understand the temporal and spatial distributions of GHG fluxes in California and the impact these species have on regional climate, CTM simulations of daily variations and seasonality of total column CO2 and CH4 will be analyzed. To assess the magnitude and spatial variation of GHG emissions and to identify local “hot spots”, airborne measurements of CH4 and CO2 were made by the Alpha Jet Atmospheric eXperiment (AJAX) over the San Francisco Bay Area (SFBA) and San Joaquin Valley (SJV) in January and February 2013 during the Discover-AQ-CA study. High mixing ratios of GHGs were observed in-flight with a high degree of spatial variability. To provide an additional method to quantify GHG emissions, and analyze AJAX measurement data, the GEOS-Chem CTM is used to simulate SFBA/SJV GHG measurements. A nested-grid version of GEOS-Chem will be applied and utilizes varying emission inventories and model parameterizations to simulate GHG fluxes/emissions. The model considers CO2 fluxes from fossil fuel use, biomass/biofuel burning, terrestrial and oceanic biosphere exchanges, shipping and aviation, and production from the oxidation of carbon monoxide, CH4, and non-methane volatile organic carbons. The major sources of CH4 simulated in GEOS-Chem are domesticated animals, rice fields, natural gas leakage, natural gas venting/flaring (oil production), coal mining, wetlands, and biomass burning. Preliminary results from the comparison between available observations (e.g., AJAX and CALGEM CH4 emission maps) and GEOS-Chem results will be presented, along with a discussion of CO2 and CH4 source apportionment and the use of the GEOS-Chem-adjoint to perform inverse GHG modeling.

Johnson, Matthew S.↗

DOE OSTI2023

Fluoride-Cooled High-Temperature Pebble-Bed Reactor Reference Plant Model

In this report we present work performed in Fiscal Year 2022 that demonstrates the modeling and simulation of a fully coupled neutronics thermal hydraulics reference plant model for a fluoride-cooled high-temperature pebble-bed reactor. The multiphysics model is developed on the Nuclear Regulatory Commission’s Comprehensive Reactor Analysis Bundle (BlueCRAB) available on the Idaho National Laboratory’s high-performance computer, which natively and seamlessly couples Griffin, Pronghorn, and the BISON Multiphysics Object-Oriented Simulation Environment based applications. Griffin provides reactor physics capabilities, including depletion to the equilibrium core, k-eigenvalue, adjoint, and transient. The unique direct equilibrium core capability in Griffin is based on a streamline methodology to spatially deplete the pebbles into burnup groups. Pronghorn solves the porous medium equations for the fluid regions and conduction in the solid regions and incorporates a fluidic diode model to simulate the transition from forced to natural convection during accident scenarios. MOOSE modules solves thermal conduction problems for the pebbles and tristructural isotropic in the pebble-bed core, thus providing the fuel and moderator spatial fields for each pebble burnup group. The neutronics feedback relies primarily on fuel, moderator, and reflector temperatures as as well as the FLiBe salt density. Here, we present results for the uncoupled equilibrium core and perform comparisons to equivalent Monte Carlo models. The power distributions and kinetic parameters obtained with Griffin are consistent with those computed with Griffin. We demonstrate a noticeable improvement with the use of discrete ordinates method (SN) transport. The coupled steady-state equilibrium core provides the initial condition for two time-dependent problems: a control rod withdrawal event and an unprotected loss of flow event. In both cases, the reactor design is self-stabilizing and the solutions are consistent with the expected physics. Although this model is prototypical regarding BlueCRAB’s capabilities, its results are consistent with published work by Kairos Power and other research entities. Significant improvements to the model are planned in future work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

A unified hp-HDG framework for Friedrichs' PDE systems

Here, this work proposes a unified hp-adaptivity framework for hybridized discontinuous Galerkin (HDG) method for a large class of partial differential equations (PDEs) of Friedrichs' type. In particular, we present unified hp-HDG formulations for abstract one-field and two-field structures and prove their well-posedness. In order to handle non-conforming interfaces we simply take advantage of HDG built-in mortar structures. With split-type mortars and the approximation space of trace, a numerical flux can be derived via Godunov approach and be naturally employed without any additional treatment. As a consequence, the proposed formulations are parameter-free. We perform several numerical experiments for time-independent and linear PDEs including elliptic, hyperbolic, and mixed-type to verify the proposed unified hp-formulations and demonstrate the effectiveness of hp-adaptation. Two adaptivity criteria are considered: one is based on a simple and fast error indicator, while the other is rigorous but more expensive using an adjoint-based error estimate. The numerical results show that these two approaches are comparable in terms of convergence rate even for problems with strong gradients, discontinuities, and singularities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Development of Adaptive Model Refinement (AMoR) for Multiphysics and Multifidelity Problems

This project investigated the development and utilization of Adaptive Model Refinement (AMoR) for nuclear systems simulation applications. AMoR refers to utilization of several models of physical phenomena which differ in prediction fidelity. If the highest fidelity model is judged to always provide or exceeded the desired fidelity, than if one can determine the difference in a Quantity of Interest (QoI) between the highest fidelity model and lower fidelity models, one could utilize the fidelity model that would just provide the magnitude of the QoI desired. Assuming lower fidelity models require less computational resources, in this manner computational efficiency can be realized provided the QoI value can be accurately and efficiently evaluated. This work utilized Generalized Perturbation Theory (GPT) to evaluate the QoI, by convoluting the GPT solution with the residual of the highest fidelity model determined using the solution from lower fidelity models. Specifically, a reactor core neutronics problem and thermal-hydraulics problem were studied to develop and utilize AMoR. The highest fidelity neutronics model was based upon the 3D space-time, two-group, nodal diffusion equations as solved in the NESTLE computer code. Added to the NESTLE code was the ability to determine the time-dependent GPT neutron flux. The lower fidelity neutronics model was based upon the point kinetics equations along with utilization of a prolongation operator to determine the 3D space-time, two-group flux. The highest fidelity thermal-hydraulics model was based upon the space-time equations governing fluid flow in a closed channel around a heat generating fuel rod. The Homogenous Equilibrium Mixture (HEM) model was used for the fluid and Finite Difference Method was applied to both the coolant and fuel pin energy conservation equations. The lower fidelity thermal-hydraulic model was based upon the same equations as used for the highest fidelity model but now with coarse spatial meshing, corrected somewhat by employing effective fuel heat conduction values. The effectiveness of switching between the highest fidelity model and lower fidelity model as a function of time was assessed using the neutronics problem. Based upon work completed to date, one concludes that the time switching is effective in annealing out differences between the highest and lower fidelity solutions. The effectiveness of using a lower fidelity GPT solution, along with a prolongation operator, to estimate the QoI was also assessed. The utilization of a lower fidelity GPT solution was done in an attempt to avoid the high computational burden associated with solving for the highest fidelity GPT solution. Based upon work completed to date, one concludes that the lower fidelity adjoint solution is not sufficiently accurate with regard to estimating the QoI; however, a formulation has been revealed that may provide a path for addressing this shortcoming.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗