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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Multigrid method for stability problems

The problem of calculating the stability of steady state solutions of differential equations is treated. Leading eigenvalues (i.e., having maximal real part) of large matrices that arise from discretization are to be calculated. An efficient multigrid method for solving these problems is presented. The method begins by obtaining an initial approximation for the dominant subspace on a coarse level using a damped Jacobi relaxation. This proceeds until enough accuracy for the dominant subspace has been obtained. The resulting grid functions are then used as an initial approximation for appropriate eigenvalue problems. These problems are being solved first on coarse levels, followed by refinement until a desired accuracy for the eigenvalues has been achieved. The method employs local relaxation on all levels together with a global change on the coarsest level only, which is designed to separate the different eigenfunctions as well as to update their corresponding eigenvalues. Coarsening is done using the FAS formulation in a non-standard way in which the right hand side of the coarse grid equations involves unknown parameters to be solved for on the coarse grid. This in particular leads to a new multigrid method for calculating the eigenvalues of symmetric problems. Numerical experiments with a model problem demonstrate the effectiveness of the method proposed. Using an FMG algorithm a solution to the level of discretization errors is obtained in just a few work units (less than 10), where a work unit is the work involved in one Jacobi relization on the finest level.

Taasan, Shlomo↗
DOE OSTI2025

Plug-in Electric Vehicle Charging Response Characterization for Grid Integration: Implications for Smart Charge Management

The rapid expansion of plug-in electric vehicles (PEVs) has created a unique challenge for electrical grids due to their significant power demand. At the same time, PEVs also create a unique opportunity to ease their own burden on the power grid, as they create a growing fleet of distributed energy resources capable of providing grid services such as demand response, frequency regulation, and renewable balancing. For aggregators and grid operators to effectively integrate PEVs into grid management, it is essential to first understand and characterize how they would respond in such situations. This study examines 25 models of PEVs across 25 makes, spanning model years from 2013 to 2025, to characterize their responses to the basic controls used in vehicle-grid integration (VGI): stopping, starting, and modulating the charge rate. Each vehicle was tested in a controlled laboratory setting to evaluate its performance in response to varying the maximum allowable current via the SAE J1772 control pilot signal, as well as its response to wake-up commands outlined in SAE J1772. Results show measurable differences across vehicle makes in the accuracy, latency, and precision with which PEVs respond to changes in ampacity, as well as varying sleep and wake-up behavior. The test results show that all vehicles respond to changes in ampacity, though with varying accuracy, precision, latency, and resolution. Wake-up behavior also differs across makes and models. These findings indicate that effective grid integration strategies must account for these differences. The results provide a foundation for understanding current vehicle behavior and advancing smart-charging methods while also highlighting the need for further testing, broader standardization, and manufacturer collaboration to ensure the successful integration of PEVs into the electrical grid.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

EV Charging Infrastructure Energization An Overview of Approaches for Simplifying and Accelerating Timelines to Processing EV Charging Load Service Requests

The United States has seen significant growth in electric vehicle (EV) adoption, leading to increased demand for EV charging infrastructure. Over the past decade, EV charging infrastructure site developers, site hosts, and electric distribution utilities have navigated the process to integrate chargers onto the electric grid. Site developers and site hosts have raised the alarm that the integration process for high-powered EV charging projects does not meet the needs of the EV market for timeliness or cost. High-powered charging stations typically require a load service request or an agreement with the local utility to connect to the grid. The process of energizing a new high-powered charging site can be complex and time-consuming, often taking up to 2 years. This timeline is the result of current utility energization processes having been designed for construction projects that take longer to build (i.e., buildings). The specific challenges stem from various factors, including compartmentalization in application processes, the integration of EV charging process approvals with other distributed energy resources (DERs), and the need to ensure grid reliability. The energization process needs to evolve to meet the growing demand for high-powered EV charging. This white paper compiles information gathered through various conversations with key stakeholders, including utilities, utility regulators, EV charging operators, site developers, and authorities having jurisdiction (AHJ) as well as through an extensive literature review. This document identifies the challenges and provides potential solutions to streamline the process of connecting EV charging infrastructure to the power grid in the United States, serving as a starting point for future conversations around these solutions. The solutions noted in this white paper require collaborative efforts among utilities, regulators, and EV charging infrastructure developers to streamline the grid connection process for EV charging infrastructure. They are broadly organized into four areas: 1. Increase data access and transparency: Develop automated load service request tools, integrate hosting capacity and load service request analyses, incorporate EV adoption forecasts, and provide transparency on the processing queue. 2. Improve energization processes and timing: Create fast-track options based on prescreening criteria, provide flexibility or phased approvals in the load service request/interconnection process, build internal knowledge within utilities about EV charging technologies, and provide standardized workforce training. 3. Promote economic efficiency: Right size distribution components to accurately reflect the load requirements of EV charging infrastructure, make proactive investments in grid infrastructure based on EV adoption forecasts and growth projections, and consider energy equity and environmental justice factors such as equitable access to EV charging when planning infrastructure. 4. Improve grid reliability and resilience: Use load management/power control systems (PCS) at EV charging stations, adopt and implement harmonized standards for communication protocols and information models between the EV charging and grid control infrastructure, and address cybersecurity considerations by implementing robust security measures and standards for EV charging infrastructure—with particular emphasis on clarifying the security requirements for the interface to the grid. The objective of the solutions proposed in this white paper is to accelerate the timeline and decrease costs associated with connecting EV charging infrastructure to the grid. Electric utilities, utility regulators, EV charging infrastructure developers, and site hosts will first need to understand which solutions are available in their service territory, and if warranted, which combination of solutions would support their specific needs. Through the successful implementations of solutions at scale detailed here, industry will demonstrate a new and innovative ecosystem where timely deployment and energization of EV charging infrastructure with greater grid resiliency and reliability is a reality.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Securing Grid Communications Infrastructure: Addressing Gaps Beyond NERC CIP Facility Perimeters

The North American electric grid relies on a complex communications infrastructure that extends beyond facility perimeters traditionally covered by NERC Critical Infrastructure Protection (CIP) standards. While CIP requirements have significantly strengthened cybersecurity within Electronic Security Perimeters, many operational communications—such as those between control centers, substations, and third-party networks—fall outside current regulatory scope. As grid modernization introduces new technologies and connectivity models, these external pathways present evolving security challenges. This brief explores the nature of these challenges, including emerging attack vectors and supply chain considerations, and highlights how ongoing grid transformation increases exposure to sophisticated threats. It outlines practical strategies and policy options to complement existing standards, such as expanding secure communications practices, enhancing supply chain transparency, and fostering collaboration among federal, state, and industry stakeholders. Near-term actions like encryption, authentication, and contractual safeguards can help reduce risk while longer-term frameworks are developed to ensure resilient and secure grid operations.

24 - POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Graph-Based Attention Mechanisms for Solving the AC Optimal Power Flow Problem in Electrical Power Networks

With the increasing complexity and data availability in modern power systems, learning-based approaches to AC Optimal Power Flow (AC OPF) have garnered significant attention. In particular, the structure of smart grids lends itself naturally to graph-based representations, where Graph Neural Networks (GNNs) can capture spatial and relational dependencies. This paper investigates attention-based GNN architectures tailored to heterogeneous graph representations of electric grids. We evaluate two major paradigms: relational attention, which distinguishes between edge types during message passing, and meta-path attention, which captures high-level semantics through multi-hop, typed paths. Using a large corpus of public AC OPF scenarios, we benchmark representative models of each type of attention. Our results demonstrate the benefits of heterogeneous attention-based models in accurately capturing grid dynamics; heterogeneous attention models achieve superior performance in both standard and perturbed settings. The findings highlight the importance of semantic-aware architectures for improving prediction robustness and interpretability in power system applications.

Trigui, Ali [Qubit Engineering Inc.]↗
DOE OSTI2025

Real Time Phasor Analytics (RTPA) and RTPA-SCR System Strength Online Tool

This presentation showcases the Real-Time Phasor Analytics (RTPA) framework for monitoring inertia and assessing system strength in power grids. RTPA is an open-source tool designed to standardize access to data from Power Management Units (PMUs) and Phasor Data Concentrators (PDCs). It facilitates real-time connectivity to multiple PDCs in accordance with the IEEE C37.118-2 standard and supports asynchronous data stream integration. Additionally, RTPA can simulate a PDC server streaming C37.118-2 data and provides Python bindings for seamless interaction with the framework, eliminating the need for direct Rust programming.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Energy Storage Siting and Permitting Outreach Workshop Report

On March 24th, 2026, under the sponsorship of the U.S. Department of Energy’s Office of Electricity, Pacific Northwest National Laboratory (PNNL) staff hosted the Energy Storage Siting & Permitting Outreach Workshop at PNNL’s Grid Storage Launchpad (GSL) facility in Richland, Washington. The workshop convened a cohort of state and regional stakeholders from across the country to build a shared understanding of energy storage technologies, regulatory frameworks, and best practices for engaging in the permitting process. Participants left with a deeper understanding of energy storage technologies, grid uses and benefits, interconnection and regulatory processes, battery safety standards and risk management, and local engagement strategies and approaches. The workshop concluded with a guided tour of the GSL for hands-on exposure to energy storage research and development. The workshop had 17 external participants. The attendees represented a range of backgrounds, including state and local governments, nonprofits or other local organizations, project developers, and utility stakeholders.

Battery Energy Storage↗
NASA NTRS1994

Comparison and analysis of aircraft measurements and mesoscale atmospheric chemistry model simulations of tropospheric ozone

The Regional Acid Deposition Model (RADM) has been applied to several of the field experiments which were part of the Acid Models Operational and Diagnostic Evaluation Study (Acid MODES). The experiment which was of particular interest with regards to ozone photochemistry involved horizontal zig-zag flight patterns (ZIPPER) over an area from the eastern Ohio River valley to the Adirondacks of New York. Model simulations by both the standard resolution RADM (delta x = 80 km) and the nested grid RADM (delta x = 26.7 km) compare well to measurements in the low emission regions in central Pennsylvania and upstate New York, but underestimate in the high emission upper Ohio River valley. The nested simulation does considerably better, however, than the coarse grid simulation in terms of horizontal pattern and concentration magnitudes. Analysis of NO(x) and HO(x) concentrations and photochemical products rates of ozone show that the model's response to large point source emissions is very unsystematic both spatially and temporally. This is due to the models instability to realistically simulate the small scale (subgrid) gradients in precursor concentrations in and around large point source plumes.

Pleim, Jonathan E.↗
NASA NTRS2014

SpaceCube v2.0 Space Flight Hybrid Reconfigurable Data Processing System

This paper details the design architecture, design methodology, and the advantages of the SpaceCube v2.0 high performance data processing system for space applications. The purpose in building the SpaceCube v2.0 system is to create a superior high performance, reconfigurable, hybrid data processing system that can be used in a multitude of applications including those that require a radiation hardened and reliable solution. The SpaceCube v2.0 system leverages seven years of board design, avionics systems design, and space flight application experiences. This paper shows how SpaceCube v2.0 solves the increasing computing demands of space data processing applications that cannot be attained with a standalone processor approach.The main objective during the design stage is to find a good system balance between power, size, reliability, cost, and data processing capability. These design variables directly impact each other, and it is important to understand how to achieve a suitable balance. This paper will detail how these critical design factors were managed including the construction of an Engineering Model for an experiment on the International Space Station to test out design concepts. We will describe the designs for the processor card, power card, backplane, and a mission unique interface card. The mechanical design for the box will also be detailed since it is critical in meeting the stringent thermal and structural requirements imposed by the processing system. In addition, the mechanical design uses advanced thermal conduction techniques to solve the internal thermal challenges.The SpaceCube v2.0 processing system is based on an extended version of the 3U cPCI standard form factor where each card is 190mm x 100mm in size The typical power draw of the processor card is 8 to 10W and scales with application complexity. The SpaceCube v2.0 data processing card features two Xilinx Virtex-5 QV Field Programmable Gate Arrays (FPGA), eight memory modules, a monitor FPGA with analog monitoring, Ethernet, configurable interconnect to the Xilinx FPGAs including gigabit transceivers, and the necessary voltage regulation. The processor board uses a back-to-back design methodology for common parts that maximizes the board real estate available. This paper will show how to meet the IPC 6012B Class 3A standard with a 22-layer board that has two column grid array devices with 1.0mm pitch. All layout trades such as stack-up options, via selection, and FPGA signal breakout will be discussed with feature size results. The overall board design process will be discussed including parts selection, circuit design, proper signal termination, layout placement and route planning, signal integrity design and verification, and power integrity results. The radiation mitigation techniques will also be detailed including configuration scrubbing options, Xilinx circuit mitigation and FPGA functional monitoring, and memory protection.Finally, this paper will describe how this system is being used to solve the extreme challenges of a robotic satellite servicing mission where typical space-rated processors are not sufficient enough to meet the intensive data processing requirements. The SpaceCube v2.0 is the main payload control computer and is required to control critical subsystems such as autonomous rendezvous and docking using a suite of vision sensors and object avoidance when controlling two robotic arms.

Xilinx FPGA↗
NASA NTRSDate not supplied

Publishing Variables Archived at GES DISC to Earth System Grid Federation (ESGF)

We present a straightforward and low-cost approach to publish variables archived at NASA Goddard Earth Sciences Data and Information Services Center (GES DISC) to the Earth System Grid Federation (ESGF). An ESGF publication requires a single standard-name variable aggregated over time to facilitate data inter-comparison. It also contains significant metadata to enable searching in ESGF. We look up standard names on high demand in ESGF search history, and using OPeNDAP and NcML technologies we aggregate the corresponding variables available in the GES DISC archive with augmented metadata required by CMIP6 and obs4MIPs Data Specification version 2.1. At this writing 10 variables from a standard product of the Atmospheric Infrared Sounder along with the Tech Notes are published in ESGF by NASA Center for Climate Simulation (NCCS). Users can view, analyze, and subset remotely, and download these aggregated variables via links in any ESGF node after searching. We plan to work on and publish more variables and data from different NASA missions and experiments in our archive.

Fan Fang↗
NASA NTRS1993

GGOT total pressure loss control concept evaluation

Total pressure loss is one of the most important parameters in the design of a turbine. This parameter effects not only the turbine performance, but consequently the engine power balance and engine performance. Computational Fluid Dynamics (CFD) can be an effective tool in predicting turbine total pressure loss, and also for performing sensitivity studies to achieve an optimal design with respect to pressure loss. In the present study, the AEROVISC code was used to predict the total pressure loss in the Turbine Technology Team Gas Generator Oxidizer Turbine (GGOT). The objectives in this study are two-fold. It is first necessary to determine an optimal methodology in predicting total pressure loss. The type of grid, grid density and distribution are parameters which may affect the loss prediction. Also, the effect of using a standard K-epsilon turbulence model with wall functions versus a two-layer turbulence model needs to be investigated. The use of grid embedding to resolve areas with high flow gradients needs to be explored. The second objective of the study is to apply the optimal methodology toward evaluating different tip leakage control concepts.

Blumenthal, R. F.↗
NASA NTRS2020

Evaluating China's fossil-fuel CO2 emissions from a comprehensive dataset of nine inventories

China's fossil-fuel CO2 (FFCO2) emissions accounted for approximately 28 % of the global total FFCO2 in 2016. An accurate estimate of China's FFCO2 emissions is a prerequisite for global and regional carbon budget analyses and the monitoring of carbon emission reduction efforts. However, significant uncertainties and discrepancies exist in estimations of China's FFCO2 emissions due to a lack of detailed traceable emission factors (EFs) and multiple statistical data sources. Here, we evaluated China's FFCO2 emissions from nine published global and regional emission datasets. These datasets show that the total emissions increased from 3.4 (3.0–3.7) in 2000 to 9.8 (9.2–10.4) Gt CO2 per yr in 2016. The variations in these estimates were largely due to the different EF (0.491–0.746 t C per t of coal) and activity data. The large-scale patterns of gridded emissions showed a reasonable agreement, with high emissions being concentrated in major city clusters, and the standard deviation mostly ranged from 10 % to 40 % at the provincial level. However, patterns beyond the provincial scale varied significantly, with the top 5 % of the grid level accounting for 50 %–90 % of total emissions in these datasets. Our findings highlight the significance of using locally measured EF for Chinese coal. To reduce uncertainty, we recommend using physical CO2 measurements and use these values for dataset validation, key input data sharing (e.g., point sources), and finer-resolution validations at various levels.

Pengfei Han↗
NASA NTRS2002

Estimate of Top-of-Atmosphere Albedo for a Molecular Atmosphere over Ocean using Clouds and the Earth's Radiant Energy System (CERES) Measurements

The shortwave broadband albedo at the top of a molecular atmosphere over ocean between 40deg N and 40deg S is estimated using radiance measurements from the Clouds and the Earth's Radiant Energy System (CERES) instrument and the Visible Infrared Scanner (VIRS) aboard the Tropical Rainfall Measuring Mission (TRMM) satellite. The albedo monotonically increases from 0.059 at a solar zenith angle of 10deg to 0.107 at a solar zenith angle of 60deg. The estimated uncertainty in the albedo is 3.5 x 10(exp -3) caused by the uncertainty in CERES-derived irradiances, uncertainty in VIRS-derived aerosol optical thicknesses, variations in ozone and water vapor, and variations in surface wind speed. The estimated uncertainty is similar in magnitude to the standard deviation of 0.003 that is derived from 72 areas divided by 20deg latitude by 20deg longitude grid boxes. The empirically estimated albedo is compared with the modeled albedo using a radiative transfer model combined with an ocean surface bidirectional reflectivity model. The modeled albedo with standard tropical atmosphere is 0.061 and 0.111 at the solar zenith angles of 10deg and 60deg, respectively. This empirically estimated albedo can be used to estimate the direct radiative effect of aerosols at the top of the atmosphere over oceans.

Kato, S.↗
DOE OSTI2026

California Price Response Potential Study

California's energy landscape is undergoing a significant transformation, driven by the increasing integration of renewable energy sources, the increased adoption of distributed energy resources, the electrification of end-use loads, and the growing need for grid efficiency. To address these challenges, recent revisions to the State’s Load Management Standards (LMS) require all of California’s large utilities and community choice aggregators (CCAs) to offer dynamic electricity pricing options to customers by 2027. Dynamic pricing, which involves varying electricity rates based on real-time supply and demand conditions, offers a promising solution for optimizing grid operations, reducing costs, and incentivizing efficient use of grid capacity. Effective implementation of dynamic pricing requires understanding the potential impacts on customer bills, system load, and the cost-effectiveness of automation technologies. This study aims to evaluate the load response of various end-use devices to hourly dynamic prices. The end-uses studied here are space cooling, space heating, water heating, crop irrigation, pool and spa pumps, and electric vehicle (EV) charging, all for both residential and commercial applications, except for crop irrigation. In 2030, these end uses are forecasted to account for 18% of annual electricity demand in the state, but 40% of demand in the peak net load hour. By modeling possible price-responsive load dispatch algorithms and assessing the resulting impacts on both individual bills and the overall grid, we seek to inform policymakers and utilities about the potential benefits and challenges associated with dynamic pricing, and considerations for the design of dynamic pricing tariffs. Additionally, we will explore the cost effectiveness of adopting automation technologies to enable devices to respond more effectively to real-time price signals. This study considers a range of price profiles, accounting for differences across utilities and customer classes, and presents scenarios for dynamic price design via variation in the percentage of total customer electric costs that are allocated dynamically (versus constituting a fixed portion of the hourly volumetric price). We present results focused primarily on 2030, forecasting electricity prices under both low and high-cost scenarios, to inform longer-term tariff design considerations. We design tariffs by starting with 2019 prices that were calculated according to CalFUSE guidance (CPUC, 2022) and that have been used in recent studies; these prices are all-in volumetric rates that vary by utility and are revenue-neutral to each customer class. They are developed by considering six electricity cost components that are allocated hourly based on system load indicators (gross and net load, and wholesale prices). These prices are forecasted to 2030 for low and high cost scenarios, considering recent trends in total electricity costs with and without years of substantial wildfire mitigation investments. These tariffs, which allocate all costs on an hourly basis, are considered our “Full” dynamic tariff design scenario, while two additional scenarios explore allocating a portion of costs as a flat volumetric charge: the “Medium” scenario allocates 50% of revenue dynamically (and keeps 50% flat), while the “Mild” scenario allocates 20% of revenue dynamically. The 20% dynamic allocation on the Mild scenario aims to represent a case where only the marginal operating costs of the grid are included in the dynamic price.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRS1983

The value of residential photovoltaic systems: A comprehensive assessment

Utility-interactive photovoltaic (PV) arrays on residential rooftops appear to be a potentially attractive, large-scale application of PV technology. Results of a comprehensive assessment of the value (i.e., break-even cost) of utility-grid connected residential photovoltaic power systems under a variety of technological and economic assumptions are presented. A wide range of allowable PV system costs are calculated for small (4.34 kW (p) sub ac) residential PV systems in various locales across the United States. Primary factor in this variation are differences in local weather conditions, utility-specific electric generation capacity, fuel types, and customer-load profiles that effect purchase and sell-back rates, and non-uniform state tax considerations. Additional results from this analysis are: locations having the highest insolation values are not necessary the most economically attractive sites; residential PV systems connected in parallel to the utility demonstrate high percentages of energy sold back to the grid, and owner financial and tax assumptions cause large variations in break-even costs. Significant cost reduction and aggressive resolution of potential institutional impediments (e.g., liability, standards, metering, and technical integration) are required for a residential PV marker to become a major electric-grid-connected energy-generation source.

Borden, C. S.↗
NASA NTRS2015

Aeroacoustic Simulations of a Nose Landing Gear Using FUN3D on Pointwise Unstructured Grids

Numerical simulations have been performed for a partially-dressed, cavity-closed (PDCC) nose landing gear configuration that was tested in the University of Florida's open-jet acoustic facility known as the UFAFF. The unstructured-grid flow solver FUN3D is used to compute the unsteady flow field for this configuration. Mixed-element grids generated using the Pointwise(TradeMark) grid generation software are used for these simulations. Particular care is taken to ensure quality cells and proper resolution in critical areas of interest in an effort to minimize errors introduced by numerical artifacts. A hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/LES) turbulence model is used for these simulations. Solutions are also presented for a wall function model coupled to the standard turbulence model. Time-averaged and instantaneous solutions obtained on these Pointwise grids are compared with the measured data and previous numerical solutions. The resulting CFD solutions are used as input to a Ffowcs Williams-Hawkings noise propagation code to compute the farfield noise levels in the flyover and sideline directions. The computed noise levels compare well with previous CFD solutions and experimental data.

Vatsa, Veer N.↗
DOE OSTI2025

A novel approach for large-scale wind energy potential assessment

Increasing wind energy generation is central to grid decarbonization, yet methods to estimate wind energy potential are not standardized, leading to inconsistencies and even skewed results. This study aims to improve the fidelity of wind energy potential estimates through an approach that integrates geospatial analysis and machine learning (i.e., Gaussian process regression). We demonstrate this approach to assess the spatial distribution of wind energy capacity potential in the Contiguous United States (CONUS). We find that the capacity-based power density ranges from 1.70 MW/km2 (25th percentile) to 3.88 MW/km2 (75th percentile) for existing wind farms in the CONUS. The value is lower in agricultural areas (2.73 ± 0.02 MW/km2, mean ± 95 % confidence interval) and higher in other land cover types (3.30 ± 0.03 MW/km2). Notably, advancements in turbine manufacturing could reduce power density in areas with lower wind speeds by adopting low specific-power turbines, but improve power density in areas with higher wind speeds (>8.35 m/s at 120m above the ground), highlighting opportunities for repowering existing wind farms. Wind energy potential is shaped by wind resource quality and is regionally characterized by land cover and physical conditions, revealing significant capacity potential in the Great Plains and Upper Texas. The results indicate that areas previously identified as hot spots using existing approaches (e.g., the west of the Rocky Mountains) may have a limited capacity potential due to low wind resource quality. Improvements in methodology and capacity potential estimates in this study could serve as a new basis for future energy systems analysis and planning.

Dai, Tao↗
NASA NTRS1986

Uniformly high order accurate essentially non-oscillatory schemes 3

In this paper (a third in a series) the construction and the analysis of essentially non-oscillatory shock capturing methods for the approximation of hyperbolic conservation laws are presented. Also presented is a hierarchy of high order accurate schemes which generalizes Godunov's scheme and its second order accurate MUSCL extension to arbitrary order of accuracy. The design involves an essentially non-oscillatory piecewise polynomial reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell. The reconstruction algorithm is derived from a new interpolation technique that when applied to piecewise smooth data gives high-order accuracy whenever the function is smooth but avoids a Gibbs phenomenon at discontinuities. Unlike standard finite difference methods this procedure uses an adaptive stencil of grid points and consequently the resulting schemes are highly nonlinear.

Harten, A.↗