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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

AttentionFire_v1.0: interpretable machine learning fire model for burned-area predictions over tropics

Abstract. African and South American (ASA) wildfires account for more than 70 % of global burned areas and have strong connection to local climate for sub-seasonal to seasonal wildfire dynamics. However, representation of the wildfire–climate relationship remains challenging due to spatiotemporally heterogenous responses of wildfires to climate variability and human influences. Here, we developed an interpretable machine learning (ML) fire model (AttentionFire_v1.0) to resolve the complex controls of climate and human activities on burned areas and to better predict burned areas over ASA regions. Our ML fire model substantially improved predictability of burned areas for both spatial and temporal dynamics compared with five commonly used machine learning models. More importantly, the model revealed strong time-lagged control from climate wetness on the burned areas. The model also predicted that, under a high-emission future climate scenario, the recently observed declines in burned area will reverse in South America in the near future due to climate changes. Our study provides a reliable and interpretable fire model and highlights the importance of lagged wildfire–climate relationships in historical and future predictions.

58 GEOSCIENCES↗
DOE OSTI2021

Machine Learning Analysis of Hydrologic Exchange Flows and Transit Time Distributions in a Large Regulated River

Hydrologic exchange between river channels and adjacent subsurface environments is a key process that influences water quality and ecosystem function in river corridors. High-resolution numerical models were often used to resolve the spatial and temporal variations of exchange flows, which are computationally expensive. In this study, we adopt Random Forest (RF) and Extreme Gradient Boosting (XGB) approaches for deriving reduced order models of hydrologic exchange flows and associated transit time distributions, with integrated field observations (e.g., bathymetry) and hydrodynamic simulation data (e.g., river velocity, depth). The setup allows an improved understanding of the influences of various physical, spatial, and temporal factors on the hydrologic exchange flows and transit times. The predictors also contain those derived using hybrid clustering, leveraging our previous work on river corridor system hydromorphic classification. The machine learning-based predictive models are developed and validated along the Columbia River Corridor, and the results show that the top parameters are the thickness of the top geological formation layer, the flow regime, river velocity, and river depth; the RF and XGB models can achieve 70% to 80% accuracy and therefore are effective alternatives to the computational demanding numerical models of exchange flows and transit time distributions. Each machine learning model with its favorable configuration and setup have been evaluated. The transferability of the models to other river reaches and larger scales, which mostly depends on data availability, is also discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Attend and Decode: 4D fMRI Task State Decoding Using Attention Models

Source code for Brain Attend and Decode paper. Functional magnetic resonance imaging (fMRI) is a neuroimaging modality that captures the blood oxygen level in a subject's brain while the subject either rests or performs a variety of functional tasks under different conditions. Given fMRI data, the problem of inferring the task, known as task state decoding, is challenging due to the high dimensionality (hundreds of million sampling points per datum) and complex spatio-temporal blood flow patterns inherent in the data. In this work, we propose to tackle the fMRI task state decoding problem by casting it as a 4D spatiotemporal classification problem. We present a novel architecture called Brain Attend and Decode (BAnD), that uses residual convolutional neural networks for spatial feature extraction and self-attention mechanisms for temporal modeling. We achieve significant performance gain compared to previous works on a 7-task benchmark from the large-scale Human Connectome Project-Young Adult (HCP-YA) dataset. We also investigate the transferability of BAnD's extracted features on unseen HCP tasks, either by freezing the spatial feature extraction layers and retraining the temporal model, or finetuning the entire model. The pre-trained features from BAnD are useful on similar tasks while finetuning them yields competitive results on unseen tasks/conditions.

Ng, BrendaM.↗
DOE OSTI2023

A TCN-Based Hybrid Forecasting Framework for Hours-Ahead Utility-Scale PV Forecasting

This paper presents a Temporal Convolutional Network (TCN) based hybrid PV forecasting framework for enhancing hours-ahead utility-scale PV forecasting. The hybrid framework consists of two forecasting models: a physics-based trend forecasting (TF) model and a data-driven fluctuation forecasting (FF) model. Three TCNs are integrated in the framework for: i) blending the inputs from different Numerical Weather Prediction sources for the TF model to achieve superior performance on forecasting hourly PV profiles, ii) capturing spatial-temporal correlations between detector sites and the target site in the FF model to achieve more accurate forecast of intra- hour PV power drops, and iii) reconciling TF and FF results to obtain coherent hours-ahead PV forecast with both hourly trends and intra-hour fluctuations well preserved. To automatically identify the most contributive neighboring sites for forming a detector network, a scenario-based correlation analysis method is developed, which significantly improves the capability of the FF model on capturing large power fluctuations caused by cloud movements. Here, the framework is developed, tested, and validated using actual PV data collected from 95 PV farms in North Carolina. Simulation results show that the performance of 6 hours ahead PV power forecasting is improved by 20% - 30% compared with state-of-the-art methods.

42 ENGINEERING↗
DOE OSTI2020

Application of the Recharge Estimation Tool (RET) to Prepare Spatially and Temporally Variable Recharge Boundary Conditions for Hanford Site Composite Analysis Vadose Zone Models

This environmental calculation file (ECF) describes the development of a tool for translating recharge estimates into readable input for STOMP© (Subsurface Transport Over Multiple Phases) vadose zone models primarily supporting the vadose zone (VZ) facets of the updated Hanford Site Composite Analysis (CA) and the Hanford Site Cumulative Impact Evaluation (CIE). The recharge estimates are spatiotemporally variable and are produced by the Recharge Evolution Tool (RET) described in Hanford Site-wide Natural Recharge Boundary Condition for Groundwater Models (ECF-HANFORD-15-0019). Outputs from the RET are given in Esri’s™ feature class format with yearly estimates and associated metadata encapsulated in file geodatabase objects. For STOMP models, the translated output is a text file in the format of an input boundary condition card, consistent with STOMP software requirements. The text file contains assimilated spatiotemporal recharge estimates produced by the RET. The tool discussed in this document will be referred to as the “RET2STOMP” tool.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

Multizone Modeling of Black Hole Accretion and Feedback in 3D GRMHD: Bridging Vast Spatial and Temporal Scales

Simulating accretion and feedback from the horizon scale of supermassive black holes (SMBHs) out to galactic scales is challenging because of the vast range of scales involved. Elaborating on H. Cho et al., we describe and test a "multizone" technique, which is designed to tackle this difficult problem in three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulations. While short-timescale variability should be interpreted with caution, the method is demonstrated to be well-suited for finding dynamical steady states over a wide dynamic range. We simulate accretion on a nonspinning SMBH ($a\ast$ = 0) using initial conditions and the external galactic potential from a large-scale galaxy simulation and achieve a steady state over eight decades in radius. As found in H. Cho et al., the density scales with radius as ρ ∝ r –1 inside the Bondi radius R B , which is located at R B = 2 × 10 5 r g (≈60 pc for M87), where r g is the gravitational radius of the SMBH; the plasma-β is ~ unity, indicating an extended magnetically arrested state; the mass accretion rate $\dot{M}$ is ≈1% of the analytical Bondi accretion rate ${\dot{M}}_{{\rm{B}}};$ and there is continuous energy feedback out to ≈100R B (or beyond > kpc) at a rate $\approx 0.02\dot{M}{c}^{2}$. Surprisingly, no ordered rotation in the external medium survives as the magnetized gas flows to smaller radii, and the final steady solution is very similar to when the exterior has no rotation. Using the multizone method, we simulate GRMHD accretion over a wide range of Bondi radii, R B ~ 10 2 –10 7 r g , and find that $\dot{M}/{\dot{M}}_{{B}}\approx {({R}_{{B}}/6\,{r}_{g})}^{-0.5}$.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Development of an ERT‐Based Framework for Bentonite Buffers Monitoring From Laboratory Tests: 2. Quantitative Moisture Dynamics Estimation Model

Abstract The long‐term containment of high‐level radioactive waste in geological disposal repositories relies on Engineered Barrier Systems (EBS), with bentonite clay emerging as a candidate material due to its unique properties. Understanding moisture dynamics within bentonite buffers is crucial for EBS performance, as it directly influences the material's swelling capacity, thermal and hydraulic conductivity, mechanical properties, and long‐term evolution under complex thermal‐hydrological‐mechanical (THM) processes. This study develops an advanced Electrical Resistivity Tomography (ERT)‐based framework to quantitatively monitor moisture dynamics under THM conditions. Our framework extends the Waxman‐Smits model to incorporate the coupled effects of temperature, water content, fluid chemistry, and mechanical changes on bentonite's electrical properties. Utilizing HotBENT‐Lab data from our companion paper, which includes electrical conductivity, CT density, and thermocouple measurements, this study offers a novel methodological framework bridging different scales of the model. Our results show that the extended model can estimate water content from ERT data, capturing spatial and temporal variations in moisture distribution within bentonite columns. However, the model tends to overestimate water content compared to CT density‐derived measurements. We address this discrepancy by incorporating a simplified swelling effect model, which improves agreement between ERT and CT density‐based water content estimates. We also discuss model limitations, including simplified treatment of swelling and micropore effects, and propose a conceptual framework for transitioning from laboratory to field applications, addressing challenges such as parameter scalability, field validation methods, and integration of diverse data sources. This ERT‐based framework can potentially advance real‐world moisture monitoring of bentonite‐based EBS in nuclear waste repositories. Plain Language Summary Safely containing high‐level radioactive waste depends on barriers made from materials like bentonite clay, which is effective because it swells and seals in the waste. To ensure these barriers work well over time, it's important to understand how moisture moves through the clay. Our study developed a new method using ERT to monitor moisture levels in bentonite under conditions that mimic those in actual storage sites, including changes in temperature, water content, and mechanical stress. This study improved an existing model to better account for how these factors affect the clay, allowing us to create more accurate moisture maps. Initially, the proposed model overestimated the amount of water in the clay, but its accuracy was improved by factoring in how the clay swells when wet. This study also identified some limitations of the model and suggested ways to adapt it for use in real‐world waste storage sites. This new approach could lead to better monitoring and safety checks for nuclear waste storage systems, helping to ensure long‐term containment. Key Points This work develops an ERT‐based framework extending the Waxman‐Smits model to monitor bentonite moisture dynamics during coupled THM processes The extended model accurately estimates water content from Electrical Resistivity Tomography data, incorporating swelling effects to improve precision This work proposes a conceptual framework for transitioning from laboratory to field applications, advancing EBS monitoring in nuclear waste repositories

Chen, Hang↗
DOE OSTI2023

Large inflationary logarithms in a nontrivial nonlinear sigma model

Loops of inflationary gravitons are known to induce large temporal and spatial logarithms that can cause perturbation theory to break down. Nonlinear sigma models possess the same kind of derivative interactions and induce the same sorts of large logarithms, without the complicated index structure and potential gauge problem. Previous studies have examined models with zero field space curvature that can be reduced to free field theories by local, invertible field redefinitions. Here we study a model that cannot be so reduced and still shows the same sorts of large logarithms. Additionally, we compute the evolution of the background at 1-loop and 2-loop orders, and we find the 1-loop β and γ functions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Applying Gaussian Process Machine Learning and Modern Probabilistic Programming to Satellite Data to Infer CO 2 Emissions

Satellite data provides essential insights into the spatiotemporal distribution of CO 2 concentrations. However, many atmospheric inverse models fail to adequately incorporate the spatial and temporal correlations inherent in satellite observations and often lack rigorous methods for estimating parameters like spatial length scales. We introduce an inference model that processes the spatiotemporal covariance in satellite data and estimates hyperparameters such as covariance length scales. Our approach uses the Gaussian process (GP) machine learning (ML) and modern probabilistic programming languages (PPLs) to perform atmospheric inversions of emissions from satellite data. We develop a GP ML inversion system based on modern PPLs and the GEOS-Chem chemical transport model, simulating atmospheric CO 2 concentrations corresponding to the Orbiting Carbon Observatory-2/3 (OCO-2/3) data for July 2020. In our supervised learning framework, we treat the GEOS-Chem simulated data set as the target, with predictors derived by scaling the target with sector-specific factors hidden from the GP machine. Our results show that the GP model, combined with GPU-enabled PPLs, effectively retrieves true emission scaling factors and infers noise levels concealed within the data. This suggests that our method could be applied over larger areas with more complex covariance structures, enabling comprehensive analysis of the spatiotemporal patterns observed in OCO-2/3 and similar satellite data sets.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

gdess: A framework for evaluating simulated atmospheric CO 2 in Earth System Models

Atmospheric carbon dioxide (CO 2 ) plays a key role in the global carbon cycle and global warming. Climate-carbon feedbacks are often studied and estimated using Earth System Models (ESMs), which couple together multiple model components—including the atmosphere, ocean, terrestrial biosphere, and cryosphere—to jointly simulate mass and energy exchanges within and between these components. Despite tremendous advances, model intercomparisons and benchmarking are aspects of ESMs that warrant further improvement (Fer et al., 2021; Smith et al., 2014). Such benchmarking is critical because comparing the value of state variables in these simulations against observed values provides evidence for appropriately refining model components; moreover, researchers can learn much about Earth system dynamics in the process (Randall et al., 2019). We introduce `gdess` (a.k.a., Greenhouse gas Diagnostics for Earth System Simulations), which parses observational datasets and ESM simulation output, combines them to be in a consistent structure, computes statistical metrics, and generates diagnostic visualizations. In its current incarnation, `gdess` facilitates evaluating a model's ability to reproduce observed temporal and spatial variations of atmospheric CO 2 . The diagnostics implemented modularly in `gdess` support more rapid assessment and improvement of model-simulated global CO 2 sources and sinks associated with land and ocean ecosystem processes. We intend for this set of automated diagnostics to form an extensible, open source framework for future comparisons of simulated and observed concentrations of various greenhouse gases across Earth system models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Advancing stream temperature prediction with a generalizable large-sample framework across CONUS river reaches

Accurately predicting stream temperature in ungauged basins remains a critical challenge for water resource management, thermoelectric power plant cooling, and ecosystem conservation. Large-sample machine learning models trained on hundreds of well-monitored river basins have shown remarkable performance; however, such models have yet to be developed solely using forcing data that can be readily extracted to simulate stream temperatures anywhere in the contiguous United States (CONUS). In this study, we present a scalable, large-sample deep learning framework using Long Short-Term Memory (LSTM) networks to simulate daily stream temperatures in ungauged basins across the CONUS. The framework leverages both modeled reanalysis of meteorological and streamflow inputs as well as static attributes available for all 2.7 million CONUS river reaches in the National Hydrography Dataset Plus (NHDPlusV2). By generating dynamical inputs from predefined thermally relevant upstream contributing areas, rather than the entire upstream basin, the model also offers improvements in very large basins where full-basin averaging can dilute the most important influences on stream temperature. Evaluated across 300 basins, the model achieves a median Mean Absolute Error (MAE) of 1.1 °C and a Nash-Sutcliffe Efficiency (NSE) of 0.95 on temporally and spatially distinct test folds—comparable to models trained exclusively using meteorological and streamflow observational data. The flexible, high-performing framework generalizes to any unmonitored river reach without significant regulation or unnatural thermal input immediately upstream, substantially expanding predictive capabilities in data-scarce regions.

Hydrology↗
DOE OSTI2022

High-Resolution Wind Resource Data Set of the Greater Puerto Rico Region

In February 2022, the U.S. Department of Energy and six national laboratories launched the Puerto Rico Grid Resilience and Transitions to 100% Renewable Energy Study (PR100). PR100 aims to provide a comprehensive analysis of possible pathways for Puerto Rico's energy future, with a goal of 100% renewable energy by 2050. As a part of the renewable energy potential assessment in this project, we developed 20 years (2001-2020) of data using a numerical weather prediction (NWP) model for onshore and offshore wind resource assessment for the Puerto Rico. The research steps in developing the long-term wind resource data sets based on the NWP model were: 1. Model wind resource based on the Weather Research and Forecasting (WRF) model. 2. Develop WRF model configurations for Puerto Rico. 3. Test WRF with 11 different physics parameterizations for planetary boundary layer (PBL). 4. Assess WRF output from the different PBL schemes against observations. 5. Select a final model configuration which can produce the modeled wind speed with sufficient accuracy. 6. Produce 20 years wind resource data sets for Puerto Rico region. In the first stage of our framework for developing wind resource data, we developed a WRF model configuration using two nested domains (9 km and 3 km) to cover Puerto Rico and U.S. Virgin Islands and downscale the ERA5 reanalysis data (0.25 degrees x 0.25 degrees; hourly interval) to a 3-km domain. For the second stage, we implemented one-year simulations focused on using 11 different PBL physics parameterizations to find a combination of WRF physics parameterizations that could provide accurately modeled wind speed for Puerto Rico. We also analyzed the sensitivity of the modeled wind speed to PBL schemes for onshore and offshore locations. The WRF output resulting from the 11 WRF experiments using different PBL parameterizations were evaluated against observations obtained from the National Data Buoy Center (NDBC) as well as at hub height for a location for which measurements were available. A final model setup selected through the validation with observational data was used to produce 20 years of data with 3-km spatial and 5-minute temporal resolution. The WRF model output was post-processed to include wind profiles and basic atmospheric variables in a format that can be easily used for downstream modeling. The 20 years of wind resource data will be made available through NREL and support the estimation of wind energy development costs for the PR100 study.

17 WIND ENERGY↗
DOE OSTI2023

Stochastic Models, Indices & Optimization Algorithms for Pricing & Hedging Reliability Risks in Modern Power Grids: Data Plan - Princeton

We collected and cleaned the synthetic grid data produced by NREL for the Texas and New York synthetic grids. We developed a high dimensional joint stochastic model for load at the zone level, and solar and wind power productions at the asset level, capturing the spatial and temporal dependencies between all the variables, and demonstrated how such a model could be fitted to historical data. We designed and implemented a simulation engine which can produce Monte Carlo scenarios for the hourly day-ahead values of load, and solar and wind power productions at the spatial and temporal resolutions of the historical data used to fit the model. Finally we developed an open-source Python package which can, from an input grid model, efficiently use forecasts and large numbers of Monte Carlo scenarios to provide unit commitment and economic dispatch for each of these scenarios. The high dimensional stochastic model and the subsequent Monte Carlo simulation engine were implemented in the package PGscen and the corresponding UC and ED optimization programs in the package Vatic.

14 SOLAR ENERGY↗
DOE OSTI2021

Substantial hysteresis in emergent temperature sensitivity of global wetland CH4 emissions

Abstract Wetland methane (CH 4 ) emissions ( $${F}_{{{CH}}_{4}}$$ F C H 4 ) are important in global carbon budgets and climate change assessments. Currently, $${F}_{{{CH}}_{4}}$$ F C H 4 projections rely on prescribed static temperature sensitivity that varies among biogeochemical models. Meta-analyses have proposed a consistent $${F}_{{{CH}}_{4}}$$ F C H 4 temperature dependence across spatial scales for use in models; however, site-level studies demonstrate that $${F}_{{{CH}}_{4}}$$ F C H 4 are often controlled by factors beyond temperature. Here, we evaluate the relationship between $${F}_{{{CH}}_{4}}$$ F C H 4 and temperature using observations from the FLUXNET-CH 4 database. Measurements collected across the globe show substantial seasonal hysteresis between $${F}_{{{CH}}_{4}}$$ F C H 4 and temperature, suggesting larger $${F}_{{{CH}}_{4}}$$ F C H 4 sensitivity to temperature later in the frost-free season (about 77% of site-years). Results derived from a machine-learning model and several regression models highlight the importance of representing the large spatial and temporal variability within site-years and ecosystem types. Mechanistic advancements in biogeochemical model parameterization and detailed measurements in factors modulating CH 4 production are thus needed to improve global CH 4 budget assessments.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Comparison of temporal resolution selection approaches in energy systems models

Capacity expansion models for the power sector are used to project future decisions over the coming decades by simulating investment and operation decisions for the use of electricity. Due to model performance constraints, these models typically do not explicitly simulate every hour within a year, but instead simulate representative time segments (groups of hours). This paper evaluates different approaches for selecting time segments across three methods: sequential, categorical, and clustering, across a wide range of time-segment quantities, for a total of 204 temporal profiles. To measure the performance of each profile's ability to accurately represent data, the root-mean-square-error of each profile's time segments are compared to the data's original hourly data. The temporal alignment across regions is also measured (i.e., how often windy days align across regions). Different spatial resolutions were applied for a subset of the temporal selection methods to investigate the impact spatial resolution has on performance. This paper provides a framework for measuring the value of different temporal selection methods and of adding more granular data to energy system models. Overall, multi-criteria clustering yields the lowest root-mean-square-error across all datasets evaluated and provides a holistic view of the intertwined relationships between renewable generation and electricity demand.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2020

Patchy particle model of hydrated amorphous silica

Glasses corroded in static aqueous conditions typically reach a slow, residual rate of dissolution as a result of the complex interplay between multiple processes. While intrinsically suited to address this problem, Monte Carlo (MC) models developed to date have relied on lattices to describe the amorphous structure of glass and are thus unable to reproduce the residual rate of glass corrosion. A recently developed MC approach based on amorphous structures derived from molecular dynamics simulations offers a solution [Kerisit and Du J. Non-Cryst. Solids 522 (2019) 119601], but it requires a simple model that can rapidly relax the glass-water interface upon each dissolution/condensation event to retain the ability of MC simulations to reach large spatial and temporal scales. To this end, a patchy particle model of hydrated amorphous silica was developed and evaluated against atomistic simulations in this work. Models of water and amorphous silica were first developed separately, and cross terms were then defined to enable simulations of hydrated amorphous silica structures with varying water content. While the nature of its interaction potential prevents the patchy particle model from reproducing simultaneously the structure and dynamics of the systems of interest with a single set of parameters, it described well the connectivity of hydrated amorphous silica structures and the local coordination geometry of individual species. Therefore, this model opens the door to MC simulations of the residual rate of glass corrosion and offers an alternative to atomistic models to investigate the evolution of silica gels over large spatial and temporal scales.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Spatially and Temporally Explicit Life Cycle Environmental Impacts of Soybean Production in the U.S. Midwest

Quantifying the spatially and temporally explicit life cycle environmental impacts of crop production is critical for designing sustainable supply chains for biofuel and animal sectors. This study assessed life cycle environmental impacts of soybean production in around 1000 Midwest counties over 9 years. A combination of Environmental Policy Integrated Climate model and process-based life cycle assessment model was used to estimate the spatially and temporally explicit life cycle global warming (GW), eutrophication (EU) and acidification (AD) impacts. Sequentially, a machine learning approach was applied to identify the top influential factors among soil, climate and farming practices for spatially and temporally explicit life cycle environmental impacts. The results indicated that significant variations existed in life cycle environmental impacts among counties and across years. Life cycle GW impacts ranged from -11.4 to 22.0 kg CO2-eq. kg soybean-1, whereas life cycle EU and AD impacts varied by a factor of 302 and 44, respectively. Nitrogen application rates, temperature in March and soil texture were the top influencing factors for the spatial-temporal variations in life cycle GW impacts. In contrast, soil organic content and nitrogen application rate were the top influencing factors for the spatial-temporal variations in life cycle EU and AD impacts.

Soybean, life cycle analysis, sustainability, spat↗
DOE OSTI2025

Local conservation of energy in fully implicit PIC algorithms

We consider the issue of strict, fully discrete local energy conservation for a whole class of fully implicit local-charge- and global-energy-conserving particle-in-cell (PIC) algorithms. Earlier studies demonstrated these algorithms feature strict global energy conservation. However, whether a local energy conservation theorem exists (in which the local energy update is governed by a flux balance equation at every mesh cell) for these schemes is unclear. In this study, we show that a local energy conservation theorem indeed exists. We begin our analysis with the 1D electrostatic PIC model without orbit-averaging, and then generalize our conclusions to account for orbit averaging, multiple dimensions, and electromagnetic models (Darwin). In all cases, a temporally, spatially, and particle-discrete local energy conservation theorem is shown to exist, proving that these formulations (as originally proposed in the literature), in addition to being locally charge conserving and globally energy conserving, are strictly locally energy conserving as well. In contrast to earlier proofs of local conservation in the literature, which only considered continuum time, our result is valid for the fully implicit time-discrete version of all models considered, including important features such as orbit averaging. We demonstrate the local-energy-conservation property numerically with a paradigmatic numerical example.

97 MATHEMATICS AND COMPUTING↗