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Anderson acceleration stability in NDA-accelerated k-eigenvalue problems

Anderson acceleration (AA) has been used to improve the stability and convergence rate of multiphysics iterative methods for reactor analysis. Most applications studied assume a tightly converged solution for the different physics problems, and AA is usually applied to state variables like temperature, density, and heat generation rate. In this paper, we study the theoretical performance of AA in NDA-accelerated k-eigenvalue problems. The problems and algorithms studied are simplified from the coupled iteration scheme adopted by MPACT and many other high-fidelity whole-core reactor codes. Compared to previous analyses of AA for these iteration schemes, we study the case with a partially converged neutronics solution and possibly partially converged nonlinear diffusion acceleration (NDA)/coarse mesh finite difference (CMFD) solutions. We observe that the performance of the iteration scheme with AA is very sensitive to the initial guess and is affected by the partially converged CMFD solutions. When the NDA solution is fully converged, using AA cannot achieve the optimal convergence rate in large-sized problems. Conversely, if the NDA solution is partially converged, the iteration scheme with AA can diverge or converge extremely slowly. It is found that the loss of robustness for AA is due to the fact that it is applied to the iterative subspace of state variables rather than the fundamental unknowns of the governing equations. To improve the robustness, the scalar flux should also be considered in the implementation of AA. After considering the residuals of flux, we observe that the stability is regardless of the partial convergence of NDA solutions. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

TRAILS Output Files

Overview This data repository contains ZIP files that store compressed versions of the output of running the WaterPaths utility planning and management tool in the DU Re-Evaluation mode (to download the tool, please see this GitHub repository). The tool was used to simulate the six-utility North Carolina Research Triangle problem. Details on the contents of each ZIP file can be seen below. Data details Temporal range: Weekly data for 2,344 weeks from 2015 to 2060 (45 years). Spatial range: Six water utilities in the North Carolina Research Triangle region (0: Chapel Hil/OWASA, 1: Durham, 2: Cary, 3: Raleigh, 4: Pittsboro, and 5: Chatham) File types: CSV and OUT Different solutions available The solution numbers correspond to the different pathway strategies (henceforth referred to as "solutions") discussed in paper's main and supporting text (abstract and link to the paper here). They are as follows: Sol92: The Durham-focused pathway strategy Sol132: The Raleigh-focused pathway strategy Sol140: The regionally-robust pathway strategy Objectives files These files can be accessed by unzipping solXX_objectives_pathways.zip that contains 1,000 Objectives_RDMXX_solsXX_to_XX.csv files. Each CSV file will consist of a row representing all the objective values for that specific solution, while every six columns represents the reliability, restriction frequency, infrastructure net present value ($ mil), peak financial cost, worst-case cost, and unit cost ($ per MG; in that order) for each of the six utilities. There will be 1,000 such files, denoting the performance of the six utilities across the 1,000 deeply uncertain states of the world (DU SOWs). Pathway files These files can be accessed by unzipping solXX_objectives_pathways.zip that contains 1,000 Pathways_sXX_RDMXX.out file. Each OUT corresponds to the set of infrastructure being triggered in a specific DU SOW, and each file will have the name file will consist of four tab-delimited columns that are described as follows: Realization: The realization in which an infrastructure options being triggered utility: The utility currently triggering infrastructure week: The week in which a specific infrastructure option is being triggered infra.: The infrastructure option being triggered If the OUT file contains only the header line, no infrastructure was triggered for that specific DU SOW. Policies files These files can be obtained by unzipping Policies.zip. Each of the 1,000 CSV files within the unzipped folder will contain weekly water use restriction policies for all 1,000 hydroclimatic realizations within a specific DU SOW. The column structure is as follows: 0rest_m: restriction multiplier for utility 0 (values between 0 and 1) 1rest_m: restriction multiplier for utility 1 (values between 0 and 1) 2rest_m: restriction multiplier for utility 2 (values between 0 and 1) 3rest_m: restriction multiplier for utility 3 (values between 0 and 1) 4rest_m: restriction multiplier for utility 4 (values between 0 and 1) 5rest_m: restriction multiplier for utility 5 (values between 0 and 1) 0transf: transfer volume for utility 0 (in MGD) 1transf: transfer volume for utility 1 (in MGD) 2transf: transfer volume for utility 2 (in MGD) 3transf: transfer volume for utility 3 (in MGD) 4transf: transfer volume for utility 4 (in MGD) 5transf: transfer volume for utility 5 (in MGD) Water Sources files These files can be obtained by unzipping WaterSources_subset.zip. Each of the 100 CSV files within the unzipped folder will contain weekly state variables at each water source for all 1,000 hydroclimatic realizations within a specific DU SOW. The column structure is as follows: Xvolume: available water volume from source X (in MGD) Xs_area: surface area of source X (in ACF) Xdemand: demand drawn from a water source from source X (in MGD) Xup_spill: upstream spillage from source X (in MGD) Xww_inflow: wastewater inflow from source X (in MGD) Xcatch_inflow: upstream catchment inflow to source X (in MGD) Xevap: evaporation multiplier for source X (values between 0 and 1) Xds_spill: downstream spillage from source X (in MGD) X_Y_alloc_cap: the allocated capacity from source X to utility Y (values between 0 and 1) X_Y_alloc_dem: the allocated demand from source X to utility Y (values between 0 and 1) Xtrmt_alloc_Y: the allocated treatment capacity from source X to utility Y (values between 0 and 1) Utilities files These files can be obtained by unzipping Utilities_subset.zip. Each of the 100 CSV files within the unzipped folder will contain weekly state variables at each utility for all 1,000 hydroclimatic realizations within a specific DU SOW. The column structure is as follows: Xst_vol: total available storage volume of utility X (in MG) Xcapacity: total storage capacity of utility X (in MG) Xnet_inf: : net inflow for all storage infrastructure for utility X (in MGD) Xst_rof: short term ROF for utility X (values between 0 and 1) Xst_stor_rof: short-term storage ROF for utility X (values between 0 and 1) Xst_trmt_rof: short-term treatment ROF for utility X (values between 0 and 1) Xlt_rof: long-term ROF for utility X (values between 0 and 1) Xlt_stor_rof: long-term storage ROF for utility X (values between 0 and 1) Xlt_trmt_rof: long-term treatment ROF for utility X (values between 0 and 1) Xrest_demand: restricted demand for utility X (in MGD) Xunrest_demand: unrestricted demand for utility X (in MGD) Xunfulf_demand: unfulfilled demand for utility X (in MGD) Xwastewater: wastewater return for utility X (in MGD) Xtreat_capacity: total treatment capacity for utility X (in MG) Xcont_fund: reserve (contingency) fund balance for utility X Xins_pout: insurance payout for utility X (% annual volumetric revenue) Xins_price: insurance price for utility X (% annual volumetric revenue) Xinfra_npv: infrastructure net present value for utility ($mil) Xst_vol: total available storage volume of utility X (in MG) Xdebt_serv: debt service for utility X (usually once per year if the infrastructure is triggered; % annual volumetric revenue) Xstor_vol: total stored volume (in MGD) Xobs_ann_dem: observed annual demand for utility X (in MGD) Xproj_dem: projected annual demand for utility X (in MGD) Xpv_debt_serv: present value of debt service payments for utility X (% annual volumetric revenue) Xgross_rev: gross revenue for utility X ($mil) Acknowledgment IM3 is a multi-institutional effort led by Pacific Northwest National Laboratory and supported by the U.S. Department of Energy's Office of Science as part of research in MultiSector Dynamics, Earth and Environmental Systems Modeling Program.

Artificial Intelligence↗

A Small Temperate Lake in the 21st Century: Dynamics of Water Temperature, Ice Phenology, Dissolved Oxygen, and Chlorophyll a

It is unclear how small temperate lakes will evolve physically and biologically in the whole water column under future climate because previous modeling studies usually focused on only one or two physical or biological state variables in the surface waters. To fill this gap, we used a well-validated lake biogeochemistry model driven with different climate scenarios to predict the dynamics of ice phenology, water temperature, dissolved oxygen (DO) and chlorophyll in a small Canadian temperate lake during the 21st century, considering the influence of catchment hydrology. We find that the ice season and ice thickness of the lake would shrink substantially, resulting in a positive energy feedback between climate and the lake. Due to the reduced heat diffusion and water mixing, the dynamics of water temperature in surface waters and deep waters are considerably different, with surface waters warmed dramatically but deep waters muted to warming. The lake DO concentrations would be depleted by warming in the whole column but the controlling processes are depth dependent. The chlorophyll concentration in the lake is inertia to climate change, mainly due to the mismatch of the timings of peak solar radiation and thermal and nutrient optima. Our analysis indicates that the influence of catchment hydrology is large on the dynamics of DO, but not on other state variables we have examined. Finally, this study suggests that small temperate lakes could be sensitive to climate change but their physical and biological responses could be diverse.

54 ENVIRONMENTAL SCIENCES↗

Production of cold beams of ND{sub 3} with variable rotational state distributions by electrostatic extraction of He and Ne buffer-gas-cooled beams

The measurement of the rotational state distribution of a velocity-selected, buffer-gas-cooled beam of ND{sub 3} is described. In an apparatus recently constructed to study cold ion-molecule collisions, the ND{sub 3} beam is extracted from a cryogenically cooled buffer-gas cell using a 2.15 m long electrostatic quadrupole guide with three 90° bends. (2+1) resonance enhanced multiphoton ionization spectra of molecules exiting the guide show that beams of ND{sub 3} can be produced with rotational state populations corresponding to approximately T{sub rot} = 9–18 K, achieved through manipulation of the temperature of the buffer-gas cell (operated at 6 K or 17 K), the identity of the buffer gas (He or Ne), or the relative densities of the buffer gas and ND{sub 3}. The translational temperature of the guided ND{sub 3} is found to be similar in a 6 K helium and 17 K neon buffer-gas cell (peak kinetic energies of 6.92(0.13) K and 5.90(0.01) K, respectively). The characterization of this cold-molecule source provides an opportunity for the first experimental investigations into the rotational dependence of reaction cross sections in low temperature collisions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Data-Driven Closures and Assimilation for Stiff Multiscale Random Dynamics

Here, we introduce a data-driven and physics-informed framework for propagating uncertainty in stiff, multiscale random ordinary differential equations (RODEs) driven by correlated (colored) noise. Unlike systems subjected to Gaussian white noise, a deterministic equation for the joint probability density function (PDF) of RODE state variables does not exist in closed form. Moreover, such an equation would require as many phase-space variables as there are states in the RODE system. To alleviate this curse of dimensionality, we instead derive exact, albeit unclosed, reduced-order PDF (RoPDF) equations for low-dimensional observables/quantities of interest. The unclosed terms take the form of state-dependent conditional expectations, which are directly estimated from data at sparse observation times. However, for systems exhibiting stiff, multiscale dynamics, data sparsity introduces regression discrepancies that compound during RoPDF evolution. This is overcome by introducing a kinetic-like defect term to the RoPDF equation, which is learned by assimilating in sparse, low-fidelity RoPDF estimates. Two assimilation methods are considered, namely nudging and deep neural networks, which are successfully tested against Monte Carlo simulations.

97 MATHEMATICS AND COMPUTING↗

Converging towards atomic and nuclear pressures (Final Report)

his report details the development of transformational tools and techniques, allowing the accurate characterization of matter at the most extreme conditions yet studied in the high energy density (HED) domain. Before this work, most experiments quantitatively mapping the nature of matter in the HED realm were performed using planar geometry, which allows for the isolation and measurement of variables in a single thermodynamic state. Such measurements include equation of state variables, optical conductivity, heat transport and more. However, due to a variety of plasma processes, such experiments are limited to below ~10 TPa (100 Mbar) pressures. To achieve higher pressures, convergent experiments are needed. Historically, convergent experiments have not been used for benchmark data because they are integral measurements. That is each part of a convergent target undergoes a time dependent wide range of states, making it difficult to accurately isolate any particular quantity for a given thermodynamic state. This effort developed innovative convergent HED platforms and techniques enabling the exploration of matter from atomic to nuclear scale pressures. This effort also performed pioneering experiments that yielded the first rigorous benchmark data at these extreme conditions. This funding award began with the overarching goal to understand the behavior of matter at extreme (atomic-to-nuclear scale) pressures. The motivation for these goals lie in the fact that every time scientists explore matter beyond the threshold of an atomic unit, there is a fundamental shift in science. The atomic unit for energy, mass, charge, length, and time have each been explored, and each time such a threshold was crossed, a new sequence of discoveries was made resulting in significant awards such as the Nobel Prize. The only unexplored atomic unit is pressure, and this effort set the course for exploring matter at and beyond such pressures. That most of the recently discovered extrasolar planets and stars, as well as matter in the late implosion stages of inertial fusion targets, have deep internal pressures at and beyond atomic pressures amplifies the importance of this effort. Much of the initial work in developing techniques to create these atomic-to-nuclear pressures already existed within the HED community, predominantly at large scale laser facilities such as the National Ignition Facility (NIF) and the Omega60 laser the University of Rochester and although these experiments were routinely performed the ability to extract information about the underlying physical states and processes remained elusive due to the complexity of the experiments, extreme scales in both time and space, and the integrated nature of all the measurements. This work built a rigorous framework so such measurements can routinely be made. This was done in part through the introduction of Bayesian inference techniques into the field of HED science. These techniques allow for the self-consistent extraction of the relevant variables and their explicit and implicit correlations, so as to make use of integrated experimental data to constrain physical models and provide accurate uncertainty bounds for the data. The techniques developed here are fully transparent and proved immediately useful providing quantitative rigorous benchmarks for physical states and processes at some of the most extreme conditions yet explored on Earth. This funding is directly or partly responsible for 7 publications in major peer-reviewed scientific journals, a doctoral thesis, 3 invited talks at major conferences, and the training of a post-doc, 2 graduate students, and 1 undergraduate student. Beyond the effort supported by this award launched the introduction of Bayesian inference into the HED physics community and helped push the usage if modern data-science techniques within the physics community at large.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Bayesian Optical Heterodyne Tomography

We introduce a complete workflow for Bayesian quantum state tomography of generic continuous-variable states. We also summarize experimental results applying this workflow to the tomographic reconstruction of thermal and coherent states of light.

Chapman, Joseph↗

ML-based Dimension Reduction Strategies

Deep learning (DL)--based surrogate models have achieved success in various applications in carbon capture and storage (CCS). However, the model training on high-dimensional spaces is computationally expensive and impractical for large-scale and complex geological models, because the models usually contain hundreds of thousands to millions of grid cells, each with a set of parameters. Furthermore, the high cost of generating training data with sufficient variation is another limitation of model training on high-dimensional spaces, which may result in overfitting and reduce the model efficiency and prediction performance. We proposed the workflow incorporating dimension reduction methods and deep learning models, which aim to extract the latent variables of input parameters and output state variables, and then build the mapping function at the latent spaces. The proposed workflow can significantly reduce the computational complexity in solving both forward and inverse problems compared to models trained on high-dimensional spaces. Dimensionality reduction models showed great potential in workflows for fast reservoir simulation, history matching, prior model generation, visualization, and more, ultimately enhancing DL model performance in related SMART Work Packages.

Hosseini, Seyyed↗

Dynamic parameter estimation of generators

Various examples are provided extended Kalman filtering estimators for generators. In one example, among others an extended Kalman filtering estimator includes a dynamics estimator configured to calculate an estimated variable such as an estimated dynamic state or an estimated parameter of a generator, a geometry estimator configured to estimate generator values, and a Kalman filter component configured to determine a correction to the estimated state variable.

Miao, Zhixin↗

Electrochemical state and internal variables estimation using a reduced-order physics-based model of a lithium-ion cell and an extended Kalman filter

This paper addresses the problem of estimating the present value of electrochemical internal variables in a lithium-ion cell in real time, using readily available measurements of cell voltage, current, and temperature. The variables that can be estimated include any desired set of reaction flux and solid and electrolyte potentials and concentrations at any set of one-dimensional spatial locations, in addition to more standard quantities such as state of charge. The method uses an extended Kalman filter along with a one-dimensional physics-based reduced-order model of cell dynamics. Simulations show excellent and robust predictions having dependable error bounds for most internal variables. (C) 2014 Elsevier B.V. All rights reserved.

Stetzel, KD↗

Tracking the Sun: Pricing and Design Trends for Distributed Photovoltaic Systems in the United States (2023 Edition) [Slides]

Berkeley Lab’s annual Tracking the Sun report describes trends among grid-connected, distributed solar photovoltaic (PV) and paired PV+storage systems in the United States. For the purpose of this report, distributed solar includes residential systems, roof-mounted non-residential systems, and ground-mounted systems up to 5 MW-AC. Ground-mounted systems larger than 5 MW-AC are covered in Berkeley Lab’s companion annual report, Utility-Scale Solar. The latest edition of the report is based on 3.2 million systems installed through year-end 2022, representing more than 80% of systems installed to date. The report describes and discusses key trends related to: -Project characteristics, including system size, module efficiencies, prevalence of paired PV with storage, use of module-level power electronics, third-party ownership, mounting configurations, panel orientation, and non-residential customer segmentation ownership -Median installed-price trends, both nationally and by state -Variability in pricing according to system size, state, installer, equipment type, and other factors, relying on both descriptive and econometric analysis The report also includes a multi-variate regression analysis to estimate the effects of key pricing drivers for residential systems installed in 2022.

14 SOLAR ENERGY↗

Tracking the Sun: Pricing and Design Trends for Distributed Photovoltaic Systems in the United States, 2024 Edition [Slides]

Berkeley Lab’s annual Tracking the Sun report describes trends among grid-connected, distributed solar photovoltaic (PV) and paired PV+storage systems in the United States. For the purpose of this report, distributed solar includes residential systems, roof-mounted non-residential systems, and ground-mounted systems up to 5 MW-AC. Ground-mounted systems larger than 5 MW-AC are covered in Berkeley Lab’s companion annual report, Utility-Scale Solar. The latest edition of the report is based on 3.7 million systems installed through year-end 2023, representing close to 80% of systems installed to date. The report describes and discusses key trends related to: -Project characteristics, including system size, module efficiencies, roof-coverage ratios, prevalence of paired PV with storage, use of module-level power electronics, third-party ownership, mounting configurations, panel orientation, and customer segmentation -Median installed-price trends, both nationally and by state -Variability in pricing according to system size, state, installer, equipment type, and other factors, relying on both descriptive analysis and a multi-variate regression to estimate the effects of key pricing drivers for residential systems installed in 2023.

14 SOLAR ENERGY↗

Identifying Characteristics of Wildfire Towers and Troughs

Wildfire behavior is dictated by the complex interaction of numerous physical phenomena including dynamic ambient and fire-induced winds, heat transfer, aerodynamic drag on the wind by the fuel and combustion. These phenomena create complex feedback effects between the fire and its surroundings. In this study, we aim to study the mechanisms by which buoyant flame dynamics along with vortical motions and instabilities control wildfire propagation. Specifically, this study employs a suite of simulations conducted with the physics-based coupled fire-atmosphere behavior model (FIRETEC). The simulations are initialized with a fire line and the fires are allowed to propagate on a grass bed, where the fuel heights and wind conditions are varied systematically. Flow variables are extracted to identify the characteristics of the alternating counter-rotational vortices, called towers and troughs, that drive convective heat transfer and fire spread. These vortices have previously been observed in wildfires and laboratory fires, and have also been observed to arise spontaneously in FIRETEC due to the fundamental physics incorporated in the model. However, these past observations have been qualitative in nature and no quantitative studies can be found in the literature which connected these coherent structures fundamental to fire behavior with the constitutive flow variables. To that end, a variety of state variables are examined in the context of these coherent structures under various wind profile and grass height conditions. Identification of various correlated signatures and fire-atmosphere feedbacks in simulations provides a hypothesis that can be tested in future observational or experimental efforts, potentially assisting experimental design, and can aid in the interpretation of data from in situ detectors.

54 ENVIRONMENTAL SCIENCES↗

SU-D-BRB-05: Quantum Learning for Knowledge-Based Response-Adaptive Radiotherapy

Purpose: There is tremendous excitement in radiotherapy about applying data-driven methods to develop personalized clinical decisions for real-time response-based adaptation. However, classical statistical learning methods lack in terms of efficiency and ability to predict outcomes under conditions of uncertainty and incomplete information. Therefore, we are investigating physics-inspired machine learning approaches by utilizing quantum principles for developing a robust framework to dynamically adapt treatments to individual patient’s characteristics and optimize outcomes. Methods: We studied 88 liver SBRT patients with 35 on non-adaptive and 53 on adaptive protocols. Adaptation was based on liver function using a split-course of 3+2 fractions with a month break. The radiotherapy environment was modeled as a Markov decision process (MDP) of baseline and one month into treatment states. The patient environment was modeled by a 5-variable state represented by patient’s clinical and dosimetric covariates. For comparison of classical and quantum learning methods, decision-making to adapt at one month was considered. The MDP objective was defined by the complication-free tumor control (P{sup +}=TCPx(1-NTCP)). A simple regression model represented state-action mapping. Single bit in classical MDP and a qubit of 2-superimposed states in quantum MDP represented the decision actions. Classical decision selection was done using reinforcement Q-learning and quantum searching was performed using Grover’s algorithm, which applies uniform superposition over possible states and yields quadratic speed-up. Results: Classical/quantum MDPs suggested adaptation (probability amplitude ≥0.5) 79% of the time for splitcourses and 100% for continuous-courses. However, the classical MDP had an average adaptation probability of 0.5±0.22 while the quantum algorithm reached 0.76±0.28. In cases where adaptation failed, classical MDP yielded 0.31±0.26 average amplitude while the quantum approach averaged a more optimistic 0.57±0.4, but with high phase fluctuations. Conclusion: Our results demonstrate that quantum machine learning approaches provide a feasible and promising framework for real-time and sequential clinical decision-making in adaptive radiotherapy.

60 APPLIED LIFE SCIENCES↗

Multilevel Conditional Disturbance Rejection Control for Satellite Attitude Tracking

Recently, the conditional disturbance rejection controller (CDRC) was proposed to improve control performance by leveraging disturbances that have beneficial effects on the system. However, it only considers disturbances acting on the state variable directly influenced by them. Although fast convergence of this state can be achieved with the CDRC, it may unintentionally affect the convergence of the output (i.e., the primary state). Here, in this article, a multilevel CDRC is proposed to enhance satellite attitude control performance by accounting for the effect of disturbances on both attitude (output) and angular velocity. The extended state observer is employed to estimate the lumped disturbance, including the modeling errors and external disturbances. Then, a backstepping-based controller with the multilevel disturbance rejection law (ML-DRL) is designed for attitude tracking. The ML-DRL is developed to improve the control performance by using a disturbance with a damping effect on both attitude and velocity. Faster convergence of attitude and velocity can be achieved by conditionally compensating for the disturbance. The stability of the proposed control method is analyzed by demonstrating that the errors are bounded as time tends to infinity. The attitude control performance of the proposed method is evaluated through numerical examples conducted using the MATLAB/Simulink Multibody tool.

Active disturbance rejection control (ADRC)↗

Multi-Timescale Integrated Dynamic and Scheduling Model (MIDAS-Solar)

Solar photovoltaic (PV) installations have experienced unprecedented growth in the United States. PV will become not only an energy producer but also a necessary provider of ancillary services at multiple timescales. Conventional methods to simulate power system operations - such as long-term production simulation (which typically considers schedules from hours to minutes by using an optimization framework) and short-term transient studies (which simulate dynamics from seconds to sub-seconds using state variables and differential equations) are not sufficient for studying the multiple-timescale variation of solar generation and its impact on system reliability. Long-term system economics and short-term system dynamics are highly coupled, particularly when the penetration level of renewable generation is extremely high, because the uncertainty and variability of solar generation will impact both power systems steady-state and dynamic performance. This project helps meet and exceed the Solar Energy Technologies Office goal of systems integration by directly addressing this stability and reliability challenge for electric grid planning and operation. This will be accomplished by developing temporally comprehensive, closed-loop simulation models that seamlessly simulate power systems operations from economic scheduling (day-ahead to hours) to dynamic response analysis (seconds to sub-seconds). Both a multi-timescale grid model and an integrated PV model will be developed in this project to accurately study the impacts of PV variability and uncertainty on system reliability at multiple timescales. Using quasi-dynamic simulation methods and data-driven security assessment (DSA) criteria will allow the dynamic characteristics of PV to be fed forward into longer-timescale scheduling models for a complete understanding of the effect of short-term PV dynamics on bulk systems operations (e.g., reserve scheduling and deployment). Upon completion of the proposed model, this project will help operators accurately assess system reliability by deploying energy and reserve scheduling under critical contingency conditions and studying interactions among all types of essential reliability services provided by modern PV power plants.

14 SOLAR ENERGY↗

Empirical correlations between the function of entropy ( Z S ) and net artificial viscous work in a shock physics hydrocode

Entropy is a state variable that may be obtained from any thermodynamically complete equation of state (EOS). However, hydrocode calculations that output the entropy often contain numerical errors; this is not because of the EOS, but rather the solution techniques that are used in hydrocodes (especially Eulerian) such as convection, remapping, and artificial viscosity. Here, in this work, empirical correlations are investigated to reduce the errors in entropy without altering the solution techniques for the conservation of mass, momentum, and energy. Specifically, these correlations are developed for the function of entropy Z S , and they depend upon the net artificial viscous work, as determined via Sandia National Laboratories’ shock physics hydrocode CTH. These results are a continuation of a prior effort to implement the entropy-based CREST reactive burn model in CTH, and they are presented here to stimulate further interest from the shock physics community. Future work is planned to study higher-dimensional shock waves, shock wave interactions, and possible ties between the empirical correlations and a physical law.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗