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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Advanced Unstructured Grid Generation for Complex Aerodynamic Applications

A new approach for distribution of grid points on the surface and in the volume has been developed. In addition to the point and line sources of prior work, the new approach utilizes surface and volume sources for automatic curvature-based grid sizing and convenient point distribution in the volume. A new exponential growth function produces smoother and more efficient grids and provides superior control over distribution of grid points in the field. All types of sources support anisotropic grid stretching which not only improves the grid economy but also provides more accurate solutions for certain aerodynamic applications. The new approach does not require a three-dimensional background grid as in the previous methods. Instead, it makes use of an efficient bounding-box auxiliary medium for storing grid parameters defined by surface sources. The new approach is less memory-intensive and more efficient computationally. The grids generated with the new method either eliminate the need for adaptive grid refinement for certain class of problems or provide high quality initial grids that would enhance the performance of many adaptation methods.

Pirzadeh, Shahyar↗
NASA NTRS2011

Grid Fin Stabilization of the Orion Launch Abort Vehicle

Wind tunnel tests were conducted by Nielsen Engineering & Research (NEAR) and Rose Engineering & Research (REAR) in conjunction with the NASA Engineering & Safety Center (NESC) on a 6%-scale model of the Orion launch abort vehicle (LAV) configured with four grid fins mounted near the base of the vehicle. The objectives of these tests were to 1) quantify LAV stability augmentation provided by the grid fins from subsonic through supersonic Mach numbers, 2) assess the benefits of swept grid fins versus unswept grid fins on the LAV, 3) determine the effects of the LAV abort motors on grid fin aerodynamics, and 4) generate an aerodynamic database for use in the future application of grid fins to small length-to-diameter ratio vehicles similar to the LAV. The tests were conducted in NASA Ames Research Center's 11x11-foot transonic wind tunnel from Mach 0.5 through Mach 1.3 and in their 9x7-foot supersonic wind tunnel from Mach 1.6 through Mach 2.5. Force- and moment-coefficient data were collected for the complete vehicle and for each individual grid fin as a function of angle of attack and sideslip angle. Tests were conducted with both swept and unswept grid fins with the simulated abort motors (cold jets) off and on. The swept grid fins were designed with a 22.5deg aft sweep angle for both the frame and the internal lattice so that the frontal projection of the swept fins was the same as for the unswept fins. Data from these tests indicate that both unswept and swept grid fins provide significant improvements in pitch stability as compared to the baseline vehicle over the Mach number range investigated. The swept fins typically provide improved stability as compared to the unswept fins, but the performance gap diminished as Mach number was increased. The aerodynamic performance of the fins was not observed to degrade when the abort motors were turned on. Results from these tests indicate that grid fins can be a robust solution for stabilizing the Orion LAV over a wide range of operating conditions.

Pruzan, Daniel A.↗
NASA NTRSDate not supplied

Micro-grid for Future Planetary Surface Needs

Under the current Artemis Program, the National Aeronautics and Space Administration (NASA) will send its next set of astronauts (first woman and next man) to the Moon by 2024 and establish a sustainable presence on the lunar surface by 2028. The challenge of creating a sustained lunar surface presence is significantly different than previous efforts. Lunar surface operations will require access to continuous and highly reliable power to support mission needs, such as to support ISRU operations. Adding to this challenge, the lunar surface operations are not going to be established over a single effort, rather the system and operations will evolve and grow over time (years). The first initial loads that arrive on the lunar surface will be integrated to their own dedicated power sources. As the lunar surface operations grow, so will the demand for power and at some point these individual loads will require more power than can be generated with any single power device. This power demand drives the need for inter-connecting the loads and power devices to share power between them, resulting in a micro-grid. One of the advantages of developing a lunar surface micro-grid is that allows lunar surface operations to resemble electrical utility operations on Earth; it allows power to be generated where it is convenient and allows power to be consumed where it is convenient, rather than negotiating between generation and consumption. The micro-grid concept also provides another benefit of affording the ability to increase overall system reliability by integrating dissimilar power generation and energy storage devices together, for example modifying the power generation strategy to include both solar arrays and nuclear. Creating a lunar surface micro-grid has its advantages, however there are significant challenges associated with an evolvable micro-grid concept. The challenges include how to efficiently transmit large amounts of power (10kW+) long distances (1kW+), how to effectively integrate dissimilar power generation and energy storage devices to maximize power consumption and minimize downtime, and how to physically connect these devices together with a connector that can survive the lunar environment (dust, extreme cold temperatures) and is capable of both astronaut and robotic operation. The basic components of the micro-grid have to be designed to ensure the system is sustainable, modular, and reconfigurable. An interface to the micro-grid has to be designed that allows for additional technologies, some of which may not yet be fully designed, to easily integrate into the micro-grid concept. This presentation discusses these lunar challenges in some more depth and offers a path forward in designing an evolvable micro-grid to meet the needs of the lunar surface operations and proposes a Universal Micro-grid Interface Converter to connect these dissimilar power sources and mission loads to the micro-grid.

Jeffrey Csank↗
NASA NTRSDate not supplied

Automatic Boundary-Layer Adaptation of Structured Grids in VULCAN-CFD

In supersonic and hypersonic flow computations, well-resolved boundary layers are essential for accurate quantification of surface heating and transition prediction, particularly via linear stability analysis. Grid design for hypersonic flows with shocks, boundary-layer separation, and/or complex mean flow features incorporating spanwise/azimuthal inhomogeneities is a difficult issue. In comparison to a manual grid adaptation procedure, an autonomous grid adaptation technique offers significant improvements in computing time and solution quality. The VULCAN-CFD solver already includes a validated procedure for automatic adaption of structured grids to the bow shock. The present focus is on implementing an automatic boundary-layer adaptation capability in VULCAN-CFD that adapts structured, multiblock grids to both the bow shock and the boundary layer at the same time. The boundary-layer adaptation algorithm allows the user to specify the number of cells within the boundary layer, along with the input parameters used for detecting the edge of the boundary layer, namely, the variable used in the edge detection criterion,the edge detection method, the detection direction, and the relaxation factor used during the morphing of the grid. The algorithm automatically distributes grid points along the wall-normal direction to achieve a smooth variation in grid spacing from the edge of the boundary layer to a"junction" location within the outer part of the grid. Illustrative results are presented for three different high-speed configurations: the two-dimensional flow over a cylinder at Mach 17.6 and unit Reynolds number of Re=0.38x10^6 m^-1, the axisymmetric flow over a cone-cylinder-flare model at Mach 6.0 and Re = 10.5×10^6 m^-1, and the three-dimensional flow over a blunt, 7-degree half-angle cone at 5-degree angle of attack in a Mach 9.79 flow with Re = 17.1×10^6 m^-1. The automated boundary-layer adaptation is shown to provide an adequate grid topology that is aligned with the bow shock in the outer part of the grid and also resolves the viscous boundary-layer region close to the surface.

boundary layer transition↗
DOE OSTI2021

Building Energy Codes and Grid-Interactive Efficient Buildings: How building energy codes can enable a more dynamic and energy-efficient built environment

This report considers the role of national model codes to promote grid-interactive efficient buildings (GEBs) as part of the modernization of the U.S. electricity grid. It introduces GEBs, describes their ability to support a clean, resilient grid, and considers challenges and approaches for incorporating GEB measures into national model energy codes and standards. Desirable traits of GEB include being low energy, low peaking, and responsive to grid needs, and minimizing the curtailment of renewable energy resources. In addition, the future grid incurs a time and locational value on these types of building services. Accounting for these considerations in future code development requires a continuation and expansion of code-minimum energy efficiency requirements and inclusion of demand responsive and load flexibility measures while ensuring annual use and cost reductions. Also, efforts to include GEB measures in codes will be limited until they are fully developed into an American National Standards Institute (ANSI)-approved standard. Then it would be straightforward to address GEB measures through points or packages and/or scoring requirements. Otherwise, the building code would have to describe each specific grid responsive strategy. This document reviews topics pertinent to considering codes in this context. Specifically, the study presents the status and direction of current building energy codes, the future smart grid, low-energy buildings, and grid-integrated buildings. The report concludes with recommendations for future code development activities to support low-energy, grid-interactive buildings in order to provide added value to building owners, the grid, and society.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Macroscopic Nonuniformities in Metal Grids Formed by Cracked Film Lithography Result in 19.3% Efficient Solar Cells

Cracked film lithography (CFL) is an emerging method for patterning transparent conductive metal grids. CFL can be vacuum- and Ag-free, and it forms more durable grids than nanowire approaches. In spite of CFL’s promising transmittance/grid sheet resistance/wire spacing tradeoffs, previous solar cell demonstrations have had relatively low performance. This work introduced macroscopic nonuniformities in the grids to improve the short-circuit current density/fill factor tradeoff in small area Cu(In,Ga)Se2 cells. Furthermore, the performance of optimized baseline grids was matched by CFL grids with microscopic openings and macroscopic patterns, culminating in a 19.3%-efficient cell. Simulations show that uniform CFL grids are enhanced by patterning because it leads to better balance among shadowing, grid resistance and transparent conductive oxide resistance losses. Thin-film module efficiency calculations were performed to highlight the performance gains that metal grids can enable by eliminating the transparent conductive oxide losses and widening monoliths. Adding the patterned CFL grids demonstrated in this work to CIGS modules is predicted to reach 0.7% higher efficiency (absolute) than screen-printed grids.

14 SOLAR ENERGY↗
DOE OSTI2019

Efficient Modeling of HIL Multi-Grid System for Scalability & Concurrency in CPS Security Testbed

Cyber-event-triggered power grid blackout compels utility operators to intensify cyber-aware and physics-constrained recovery and restoration process. Recently, coordinated cyber attacks on the Ukrainian grid witnessed such a cyber-event-triggered power system blackout. Various cyber-physical system (CPS) testbeds have attempted with multitude designs to analyze such interdependent events and evaluate remedy measures. However, resource constraints and modular integration designs have been significant barriers while modeling large-scale grid models (scalability) and multi-grid isolated models (concurrency) under a single real-time execution environment for the hardware-in-the-loop (HIL) CPS security testbeds. This paper proposes a meticulous design and effective modeling for simulating large-scale grid models and multi-grid isolated models in a HIL realtime digital simulator environment integrated with industry-grade hardware and software systems. We have used our existing HIL CPS security testbed to demonstrate scalability by the realtime performance of a Texas-2000 bus US synthetic grid model and concurrency by the real-time performance of simultaneous ten IEEE-39 bus grid models and an IEEE-118 bus grid model. The experiments demonstrated significant results by 100% realtime performance with zero overruns, low latency while receiving and executing control signals from SEL Relays via IEC-61850 protocol and low latency while computing and transmitting grid data streams including stability measures via IEEE C37.118 synchrophasor data protocol to SEL Phasor Data Concentrators.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

LA100 Equity Strategies. Chapter 12: Distribution Grid Upgrades for Equitable Resilience and Solar, Storage, and Electric Vehicle Access

The LA100 Equity Strategies project integrates community guidance with robust research, modeling, and analysis to identify strategy options that can increase equitable outcomes in Los Angeles' clean energy transition. As Los Angeles transitions toward clean energy, existing distribution grid infrastructure will need to be updated and expanded to support reliable service during routine operations, enable interconnection with distributed energy resources and electrified loads, and provide access to energy-related services during disasters. This chapter focuses on equity in distribution grid upgrades, reliability, and resilience in Los Angeles. Specifically, NREL performed grid upgrade and resilience analyses using a detailed model of the distribution grid and income-differentiated household load profiles, electric vehicle (EV) adoption patterns, distributed solar adoption, and grid reliability to explore two key questions to inform how the City of Los Angeles can ensure a resilient and reliable distribution grid for all communities during the clean energy transition: Where can distribution system upgrades can be prioritized to enable equitable access to, and adoption of, clean energy technologies and how can Los Angeles provide equitable, resilient access to electricity-related services (e.g., health care, food) during disaster events like earthquakes and flooding? The electric distribution system is the "last mile" of the grid, linking the multistate bulk power system with customers; new loads, including EVs; and distributed energy resources, such as customer and community solar and storage. This analysis focuses on the 4.8-kilovolt (kV) system, including service transformers that represent the utility-side of the grid connection for most residential customers. Chapter 17 looks at the customer-side of the grid connection with a focus on electric panel upgrade needs. The transition toward clean energy can put additional stress on the distribution system from distributed energy resources and electrification - especially EVs and increased use of electricity for heating, cooling, cooking, and hot water. This stress, measured here as the number of equipment overloads and voltage violations, correlates strongly to grid reliability and therefore is used as a proxy for understanding additional upgrades needed and to help ensure equitable access to electrification and distributed energy resources. NREL also conducted community resilience analysis to examine customer-level access to both electricity and a larger range of services, such as hospitals and grocery stores during a disaster. This analysis explicitly considers equity to understand differences in current resilience and resilience strategies to effectively improve critical services access for all Angelenos. Research was guided by input from the community engagement process, and associated equity strategies are presented in alignment with that guidance.

14 SOLAR ENERGY↗
DOE OSTI2024

Network Security Challenges and Countermeasures for Software-Defined Smart Grids: A Survey

The rise of grid modernization has been prompted by the escalating demand for power, the deteriorating state of infrastructure, and the growing concern regarding the reliability of electric utilities. The smart grid encompasses recent advancements in electronics, technology, telecommunications, and computer capabilities. Smart grid telecommunication frameworks provide bidirectional communication to facilitate grid operations. Software-defined networking (SDN) is a proposed approach for monitoring and regulating telecommunication networks, which allows for enhanced visibility, control, and security in smart grid systems. Nevertheless, the integration of telecommunications infrastructure exposes smart grid networks to potential cyberattacks. Unauthorized individuals may exploit unauthorized access to intercept communications, introduce fabricated data into system measurements, overwhelm communication channels with false data packets, or attack centralized controllers to disable network control. An ongoing, thorough examination of cyber attacks and protection strategies for smart grid networks is essential due to the ever-changing nature of these threats. Previous surveys on smart grid security lack modern methodologies and, to the best of our knowledge, most, if not all, focus on only one sort of attack or protection. This survey examines the most recent security techniques, simultaneous multi-pronged cyber attacks, and defense utilities in order to address the challenges of future SDN smart grid research. The objective is to identify future research requirements, describe the existing security challenges, and highlight emerging threats and their potential impact on the deployment of software-defined smart grid (SD-SG).

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2018

Generating a Grid for Unstructured RANS Simulations of Jet Flows

A study has been performed to determine best practices for generating unstructured grids for Reynolds-Averaged Navier-Stokes (RANS) simulations of jet flows. The Axisymmetric Near-Sonic Jet Case from the Turbulence Modeling Resource was used for this study: a Mach 0.985 flow through the 2-in. diameter Acoustic Reference Nozzle (ARN2). Simulations were run with FUN3D and used the Menter Shear Stress Transport (SST-V), Spalart-Allmaras (S-A), and k-kL turbulence models. The axial velocity and turbulent kinetic energy fields in the jet plume of the unstructured grid solutions were compared to those of the baseline structured grid solution provided by the Turbulence Modeling Resource. Only solutions using grids with structured-like elements in the jet plume showed good agreement with the baseline structured grid solution. Using the SST-V turbulence model, the fully unstructured grid solutions predicted the jet potential core to decay upstream of the baseline solution. With the S-A turbulence model, the unstructured grid solutions predicted the jet potential core to decay upstream of the baseline solution. The solutions using the k-kL turbulence model seemed less sensitive to grid topology. Nozzle massflow and thrust performance were also compared for all simulations. Based on the results of this study, it is currently recommended that structured-like grid elements are used in the plumes of jet flows; unstructured grid elements can be used elsewhere.

RANS Simulations; Unstructured Grids; Jet Flows↗
DOE OSTI2020

A Stabilizer based Predictive Control Scheme for Smart Inverters in Weak Grid

This paper presents a self-stabilization mechanism based on finite-set model predictive control (FCS-MPC) framework for smart inverters operating in weak grid conditions. As weak grid’s large parasitic impedance and low short-circuitratio (SCR) challenge the stable operation of grid-connected inverters. Specifically, the inverter may experience frequencies that might excite the LCL filter resonance phenomenon. The inverter stability collapses if this LCL resonance is triggered. To address this issue, a robust predictive controller is proposed that features a self-stabilization mechanism for smart inverters interacting with a weak grid. The proposed methodology utilizes the idea that in stiff grid conditions the grid current feedback (GCF) is stable and in weak grid conditions the inverter current feedback (ICF) is stable. Therefore, the proposed FCS-MPC toggles between GCF and ICF to achieve inherent LCL filter resonance damping. The toggling action between GCF and ICF is leveraged by comparing the moving RMS grid current with threshold current as a constrained in the proposed FCS-MPC cost function. The theoretical analyses are verified by several case studies for a single-phase grid-connected inverter. The analysis and results demonstrated that the proposed FCS-MPC operates well under weak, ultra-weak and stiff grid conditions.

Umar, Muhammad Farooq↗
DOE OSTI2022

Caldera_Grid

Caldera Grid is part of Caldera software platform, a suite of collective, open-source tools that was developed to improve the state of the art in modeling the impacts of Electric Vehicle (EV) charging on the grid. Caldera Grid is a co-simulation framework implemented using Hierarchical Engine for Large scale Infrastructure Co-Simulation (HELICS). The framework facilitates the co-simulation of EV charging and Smart Charge Management (SCM) strategies in Caldera Infrastructure Charge Model (ICM) with distribution level grid models in OpenDSS. Vehicle energy needs and charge session requirements generated using Caldera Charge Decision Module (CDM) are fed in as input to Caldera Grid. The EV charging models in Caldera ICM simulates both the uncontrolled charging loads as well as loads modified by the SCM strategies to develop distributed load profiles for each grid node hosting an Electric Vehicle Supply Equipment (EVSE) – also known as chargers. These loads were simulated in OpenDSS alongside existing distribution feeder loads. Each of these models are co-simulated in a HELICS federate. The HELICS co-simulation framework facilitates communication and synchronization between the federates. By co-simulating EV loads and distribution feeder loads, Caldera Grid can assess the potential grid impacts of EV charging on distribution feeders under various grid conditions. A control strategy federate is implemented with an interface where control strategies based on feedback from EV charging status and grid conditions can be developed and implemented. The platform can also support multiple control strategies in a single co-simulation.

Sundarrajan, ManojKumar Cebol↗
DOE OSTI2021

An unstructured C-grid type variational formulation for the sea ice dynamics

Historically, B-grid formulations of sea ice dynamics have been dominant because they have matched the grid type used by ocean models. The reason for the grid match is simple – it facilitates penetration of the curl of ice-ocean stress into the deep ocean with minimal numerical diffusivity because sea ice and ocean velocity are co-located. In recent years, as ocean models have increasingly progressed to C-grids, sea ice models have followed suit on quadrilateral meshes, but the implementation of an unstructured C-grid sea ice models is new. We present an unstructured C-grid discretization of the Elastic Viscous Plastic (EVP) rheology, where the velocity unknowns are discretized at the edges of the mesh cells with n-sides, where typically n is greater than or equal to four, rather than at the vertices, as in the B-grid. Our framework of choice is the Model for Prediction Across Scales (MPAS) within E3SM, the climate model of the U.S. Department of Energy, although our approach is general and could be applied to other models as well. While MPAS-Seaice is currently defined on a B-grid, MPAS-Ocean runs on a C-grid, hence interpolation operators are heavily used when coupled simulations are performed. In this work, we describe a mathematical formulation to transition the dynamics of MPAS-Seaice to a C-grid, in order to ultimately facilitate the coupling with MPAS-Ocean and reduce numerical errors associated with this communication. Numerical results are reported to highlight the features of the method.

58 GEOSCIENCES↗
DOE OSTI2022

Emerging Trends and Systemic Issues Influencing Today’s U.S. Electric Grid

With increasing shifts from vertically integrated to horizontally structured operations and from centralized to distributed electric power delivery, today’s electric power grid (the “grid”) operators and designers face the challenge of creating an architecture that accommodates a host of diverse requirements. The grid’s modes of operation must address concerns of reliability and stability, new deployments of renewable energy sources, threats from cyber-attacks and natural disasters, and increasingly distributed system operations. Grid modernization calls for a reliable, affordable, sustainable, agile, secure, and resilient grid. However, the modernization of the U.S. power grid is hampered by mounting complexity and diverging objectives from owners and operators and is consequently risky and fraught with potential missteps. Flawed architecture, design, and implementation will lead to stranded investments and lost opportunities. A principled approach to minimize risk and develop a robust grid of the future is to begin with a sound architecture for the grid to inform the design process. Architecture development starts with the context of influencing factors that provide constraints as well as driving goals. This report provides the context of emerging trends and cross-cutting systemic issues in the U.S. electric power grid and serves as a vital input for grid architecture development.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

State of Common Grid Services Definitions

This document is prepared as part of the Department of Energy’s Grid Modernization Laboratory Consortium (GMLC) 2.5.2 project, whose goal is to develop and socialize a common set of grid service definitions relevant to grid-related interactions with distributed energy resources (DER: responsive generation, storage, and loads), and to advance the concept and requirements of the Energy Services Interface (ESI) to the point of launching related interface standards and guides that can be implemented in communication protocols and business process definitions. The notion of “grid services” is integral to the definition of an ESI because a key principle of the ESI is that it permits coordination between grid operators and DER facilities in a way that is service-oriented, with an understanding of performance expectations. This document reviews the current state of grid service definitions, including those actively used in the market today as well as new services that have been proposed for future implementation. The document describes grid services used in transmission as well as distribution systems. In defining grid services, this document also distinguishes between two fundamental concepts: an “operational objective” and a “grid service,” which describes a generator’s or customer’s expected physical performance in delivering power to or consuming power from the grid.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Common Grid Services: Terms and Definitions Report

This document is prepared as part of the Department of Energy’s Grid Modernization Laboratory Consortium (GMLC) 2.5.2 project, whose goal is to develop and socialize a common set of grid service definitions relevant to grid-related interactions with distributed energy resources (DER: responsive generation, storage, and loads) and to advance the concept and requirements of the Energy Services Interface (ESI) to the point of launching related interface standards and guides that can be implemented in communication protocols and business process definitions. The notion of grid services is associated with the definition of an ESI because a key principle of the ESI is that it permits coordination between grid operators and DER facilities in a way that is service-oriented with an understanding of performance expectations. The project investigated the current state of North American grid service definitions from various market operators and utilities, as well as the Federal Energy Regulatory Commission and the North American Electric Reliability Corporation, actively used today (Liu et al. 2022). This document builds on that work to propose terms and definitions for a set of grid service types that address operational objectives commonly found in power system operations. These grid service types derive from existing grid services used in bulk electric market operations, recognizing that each operational authority uses somewhat different names with variations on service performance parameters. Finding commonality at the wholesale or bulk system operation level will hopefully engender progress in seeking agreement on grid services for DER engagement at the distribution level in the emerging retail marketplace.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1972

Optimization of electrostatic dual-grid beam-deflection system

Tests were performed to minimize accelerator grid erosion of a 5-cm diameter Kaufman ion thruster due to direct beam impingement. Several different screen hole diameters, pillow-shape-square screen holes, and dished screen grids were tried. The optimization was accomplished by copper plating the accelerator grid before testing each grid configuration on a thruster for a 2-hour run. The thruster beam sputtered copper and molybdenum from the accelerator grid where the beam impinged. The observed erosion patterns and measured accelerator currents were used to determine how to modify the accelerator system. The lowest erosion was obtained for a 50-percent open area pillow-shape-square-aperture screen grid, dished 0.043 centimeter convex toward the accelerator grid, which was positioned with the center of the screen grid 0.084 centimeter from the accelerator grid. During this investigation the accelerator current was reduced from 120 to 55 microamperes and was also more uniformly distributed over the area of the accelerator grid.

Hudson, W. R.↗
NASA NTRS1974

Multi-off-grid methods in multi-step integration of ordinary differential equations

Description of methods of solving first- and second-order systems of differential equations in which all derivatives are evaluated at off-grid locations in order to circumvent the Dahlquist stability limitation on the order of on-grid methods. The proposed multi-off-grid methods require off-grid state predictors for the evaluation of the n derivatives at each step. Progressing forward in time, the off-grid states are predicted using a linear combination of back on-grid state values and off-grid derivative evaluations. A comparison is made between the proposed multi-off-grid methods and the corresponding Adams and Cowell on-grid integration techniques in integrating systems of ordinary differential equations, showing a significant reduction in the error at larger step sizes in the case of the multi-off-grid integrator.

Beaudet, P. R.↗