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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Efficient Topology Assessment for Integrated Transmission and Distribution Network with 10,000+ Inverter-based Resources

The renewable energy proliferation calls upon the grid operators and planners to systematically evaluate the potential impacts of distributed energy resources (DERs). Considering the significant differences between various inverter-based resources (IBRs), especially the different capabilities between grid-forming inverters and grid-following inverters, it is crucial to develop an efficient and effective assessment procedure besides available co-simulation framework with high computation burdens. This paper presents a streamlined graph-based topology assessment for the integrated power system transmission and distribution networks. Graph analyses were performed based on the integrated graph of modified miniWECC grid model and IEEE 8500-node test feeder model, high performance computing platform with 40 nodes and total 2400 CPUs has been utilized to process this integrated graph, which has 100,000+ nodes and 10,000+ IBRs. The node ranking results not only verified the applicability of the proposed method, but also revealed the potential of distributed grid forming (GFM) and grid following (GFL) inverters interacting with the centralized power plants.

Graph Analysis, Topology evaluation, Infrastructur↗
DOE OSTI2021

Electromagnetic Transient (EMT) Simulation Algorithm for Evaluation of Photovoltaic (PV) Generation Systems

Use of inverter-based resources facilitating renewable energy resources such as photovoltaic (PV) generation is increasing rapidly with decreasing costs and reduced emissions associated. To accommodate such rapid growth of inverter-based resources like PV systems, electromagnetic transient (EMT) simulation models of both PV systems and grids are required to analyze the interaction of PVs in the grid (like the post-event analysis). In addition, the EMT simulation would help with the planning of future power grid with a large number of PVs as well as other inverter-based distributed generation systems. In this paper, the EMT simulation models of PV systems and grids are developed based on the differential algebraic equations (DAEs) representing their EMT dynamics. Furthermore, advanced simulation algorithms including numerical stiffness-based hybrid discretization, DAE clustering and aggregation, multi-order integration, and matrix splitting approaches are applied to accelerate the EMT simulation. The proposed algorithm was applied to 125 PV inverters within 52-bus medium-voltage (MV) distribution grid.

Choi, Jongchan↗
DOE OSTI2021

Probabilistic Voltage Sensitivity based Preemptive Voltage Monitoring in Unbalanced Distribution Networks

With increasing penetration of renewable energy and active consumers, control and management of power distribution networks has become challenging. Renewable energy sources can cause random voltage fluctuations as their output power depends on weather conditions. Conventional voltage control schemes such as tap changers and capacitor banks lack the foresight required to quickly alleviate voltage violations. Thus, there is an urgent need for effective approaches for predicting and mitigating voltage violations as a result of random fluctuations in power injections. This work proposes a novel voltage monitoring approach based on low-complexity, data-driven probabilistic voltage sensitivity analysis. The usefulness of this work is not only in predicting voltage violations in unbalanced distribution grids, but also in opening up the door for optimal voltage control. Using system data and forecasts, the proposed approach predicts the distribution of system node voltages which is then used to to identify nodes that may violate the nominal operational limits with high probability. The method is tested on the IEEE 37 node distribution system considering integrated distributed solar energy sources. The method is validated against the classic load flow based method and offers over 95% accuracy in predicting voltage violations.

Abujubbeh, Mohammad↗
DOE OSTI2020

Vadose Zone Model for B-3A/B Pond for Composite Analysis

The objectives of the vadose modeling for the updated Hanford Site composite analysis (CA) are to simulate the flow and transport of water and radionuclide releases from the surface to the water table and to provide radionuclide transfer rates for the plateau to river (P2R) model, version 8.3 (CP-57037, Model Package Report: Plateau to River Groundwater Model, Version 8.3). Water additions include natural recharge and water discharged to the ground as a result of industrial processes associated with Hanford Site operations. Contaminant sources include radionuclides in water discharged to the ground during operations and radionuclides disposed “dry” in solid waste burial grounds or other means. The following 16 radionuclides were selected for this modeling effort; carbon-14 (C-14), chlorine-36 (Cl-36), tritium (H-3), iodine-129 (I-129), neptunium-237 (Np-237), rhenium-187 (Re-187), strontium-90 (Sr-90), technetium-99 (Tc-99), uranium-232 (U-232), uranium-233 (U-233), uranium-234 (U-234), uranium-235 (U-235), uranium-236 (U-236), uranium-238 (U-238), radium-226 (Ra-226), and thorium-230 (Th-230). The simulation time starts in 1943 and ends at 12070, which is 10,000 years after assumed Hanford Site closure in 2070. The parallel version of the Subsurface Transport Over Multiple Phases (STOMP) simulator officially named the exascale Subsurface Transport Over Multiple Phases (eSTOMP), is used to simulate flow and transport for the vadose models. The documentation for the STOMP code is comprehensive. The theoretical and numerical approaches applied in the STOMP code are documented in a published theory guide (PNNL-12030, STOMP Subsurface Transport Over Multiple Phases Version 2.0 Theory Guide). The code has undergone a rigorous verification procedure against analytical solutions, laboratory-scale experiments, and field-scale demonstrations. The application guide (PNNL-11216, STOMP Subsurface Transport Over Multiple Phases Application Guide) provides instructive examples in the application of the code to classical groundwater problems. The user’s guide (PNNL-15782, STOMP: Subsurface Transport Over Multiple Phases Version 4.0: User’s Guide) describes the general use, input file formatting, compilation, and execution of the code. The primary output of the vadose zone modeling is radionuclide transfer rates to the groundwater for input into the P2R model. The rates will be summed over the 100 by 100 m P2R grid cells that fall within the vadose zone model source domain. The Hanford Site Central Plateau was subdivided into 26 individual vadose zone models, with 13 in the 200 East Area and 13 in the 200 West Area. Waste sites that have a completed performance assessment (PA) or past-leak analysis were not included as sources of radionuclides. Instead the vadose zone to groundwater transfer rates of the Environmental Restoration Disposal Facility, Integrated Disposal Facility, US Ecology, and Waste Management Area C (WMA C) PAs and the past-leak analysis for WMA C were used as direct input to the P2R model. Each of the vadose zone models is documented in separate environmental calculation files (ECFs). This ECF describes the B-3A/B Ponds model. The scope of this ECF is to document the development and results of the B-3 A/B Ponds vadose zone model. CP-63515, Model Package Report: Central Plateau Vadose Zone Models, describes the approach, assumptions, process of determining the number of models required and domain of each model, input data, and processing common to all the models.

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

Vadose Zone Model for SALDS for Composite Analysis

The objectives of the vadose modeling for the updated Hanford Site composite analysis (CA) are to simulate the flow and transport of water and radionuclide releases from the surface to the water table and to provide radionuclide transfer rates for the plateau to river (P2R) model, version 8.3 (CP-57037, Model Package Report: Plateau to River Groundwater Model, Version 8.3). Water additions include natural recharge and water discharged to the ground as a result of industrial processes associated with Hanford Site operations. Contaminant sources include radionuclides in water discharged to the ground during operations and radionuclides disposed “dry” in solid waste burial grounds or other means. The following 16 radionuclides were selected for this modeling effort: carbon-14 (C-14), chlorine-36 (Cl-36), tritium (H-3), iodine-129 (I-129), neptunium-237 (Np-237), rhenium-187 (Re-187), strontium-90 (Sr-90), technetium-99 (Tc-99), uranium-232 (U-232), uranium-233 (U-233), uranium-234 (U-234), uranium-235 (U-235), uranium-236 (U-236), uranium-238 (U-238), radium-226 (Ra-226), and thorium-230 (Th-230). The simulation time starts in 1943 and ends at 12070, which is 10,000 years after assumed Hanford Site closure in 2070. The parallel version of the Subsurface Transport Over Multiple Phases (STOMP1) simulator, officially named the exascale Subsurface Transport Over Multiple Phases (eSTOMP) is used to simulate flow and transport for the vadose models. The documentation for the STOMP code is comprehensive. The theoretical and numerical approaches applied in the STOMP code are documented in a published theory guide (PNNL-12030, STOMP Subsurface Transport Over Multiple Phases Version 2.0 Theory Guide). The code has undergone a rigorous verification procedure against analytical solutions, laboratory-scale experiments, and field-scale demonstrations. The application guide (PNNL-11216, STOMP Subsurface Transport Over Multiple Phases Application Guide) provides instructive examples in the application of the code to classical groundwater problems. The user’s guide (PNNL-15782, STOMP: Subsurface Transport Over Multiple Phases Version 4.0: User’s Guide) describes the general use, input file formatting, compilation, and execution of the code. The primary output of the vadose zone modeling is radionuclide transfer rates to the groundwater for input into the P2R model. The rates will be summed over the 100 by 100 m P2R grid cells that fall within the vadose zone model source domain. The Hanford Site Central Plateau was subdivided into 26 individual vadose zone models, with 13 in the 200 East Area and 13 in the 200 West Area. Waste sites that have a completed performance assessment (PA) or past-leak analysis were not included as sources of radionuclides. Instead the vadose zone to groundwater transfer rates of the Environmental Restoration Disposal Facility, Integrated Disposal Facility, US Ecology, and Waste Management Area C (WMA C) PAs and the past-leak analysis for WMA C were used as direct input to the P2R model. Each of the vadose zone models is documented in separate environmental calculation files (ECFs). This ECF describes the State-Approved Land Disposal Site (SALDS) model. The scope of this ECF is to document the development and results of the SALDS vadose zone model. CP-63515, Model Package Report: Central Plateau Vadose Zone Models, describes the approach, assumptions, process of determining the number of models required and domain of each model, input data, and processing common to all the models.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS1987

Variational four-dimensional analysis using quasi-geostrophic constraints

A variational four-dimensional analysis technique using quasi-geostrophic models as constraints is examined using gridded fields as data. The analysis method uses a standard iterative nonlinear minimization technique to find the solution to the constraining forecast model which best fits the data as measured by a predefined functional. The minimization algorithm uses the derivative of the functional with respect to each of the initial condition values. This derivative vector is found by inserting the weighted differences between the model solution and the inserted data into a backwards integrating adjoint model. The four-dimensional analysis system was examined by applying it to fields created from a primitive equations model forecast and to fields created from satellite retrievals. The results show that the technique has several interesting characteristics not found in more traditional four-dimensional assimilation techniques. These features include a close fit of the model solution to the observations throughout the analysis interval and an insensitivity to the frequency of data insertion or the amount of data. The four-dimensional analysis technique is very versatile and can be extended to more complex problems with little theoretical difficulty.

Derber, John C.↗
NASA NTRS1992

A case study of analyzed versus satellite-derived water vapor distributions over the Atlantic Ocean

The paper compares two estimates (one derived from the ECMF analysis and the other from the DMSP Special Sensor Microwave/Imager, SSM/I) of precipitable water content (PWC) over the North Atlantic Ocean during a period of intense cyclone and frontal activity between September 20 and 29, 1987, when two tropical cyclones, Dennis and Emily, moved into midlatitudes and took on extratropical characteristics. The values from the ECMWF analyses consisted of vertical integrals of specific humidity from 1000-300 mb, on a 2.5-deg latitude/longitude grid. The PWC values from the SSM/I were computed using the technique described by Wentz (1983) and were based on retrievals at increments of 25 km. The two distributions of PWC showed very good agreement with each other and with the synoptic patterns depicted.

Vincent, Dayton G.↗
NASA NTRS2005

A Regional, Integrated Monitoring System for the Hydrology of the Pan-Arctic Land Mass

Work under this NASA contract developed a system for monitoring and historical analysis of the major components of the pan-Arctic terrestrial water cycle. It is known as Arctic-RIMS (Regional Integrated Hydrological Monitoring System for the Pan-Arctic Landmass). The system uses products from EOS-era satellites, numerical weather prediction models, station records and other data sets in conjunction with an atmosphere-land surface water budgeting scheme. The intent was to compile operational (at 1-2 month time lags) gridded fields of precipitation (P), evapotranspiration (ET), P-ET, soil moisture, soil freeze/thaw state, active layer thickness, snow extent and its water equivalent, soil water storage, runoff and simulated discharge along with estimates of non-closure in the water budget. Using "baseline" water budgeting schemes in conjunction with atmospheric reanalyses and pre-EOS satellite data, water budget fields were conjunction with atmospheric reanalyses and pre-EOS satellite data, water budget fields were compiled to provide historical time series. The goals as outlined in the original proposal can be summarized as follows: 1) Use EOS data to compile hydrologic products for the pan-Arctic terrestrial regions including snowcover/snow water equivalent (SSM/A MODIS, AMSR) and near-surface freeze/thaw dynamics (Sea Winds on QuikSCAT and ADEOS I4 SSMI and AMSR). 2) Implement Arctic-RIMS to use EOS data streams, allied fields and hydrologic models to produce allied outputs that fully characterize pan-Arctic terrestrial and aerological water budgets. 3) Compile hydrologically-based historical products providing a long-term baseline of spatial and temporal variability in the water cycle.

Serreze, Mark↗
DOE OSTI2020

Recent Developments at the U.S. Navy Wave Energy Test Site.

The U.S. Navy’s Wave Energy Test Site (WETS) in Hawaii has hosted two wave energy conversion (WEC) devices since its June 2015 commissioning – the Fred. Olsen BOLT Lifesaver and the Northwest Energy Innovations (NWEI) Azura – each for two deployments. Several additional devices will be tested in the coming years, beginning with the Ocean Energy device in summer 2019. The Hawaii Natural Energy Institute (HNEI) provides research and logistics support to WETS. We will provide an overview of three major activities that we have recently undertaken in this capacity. First, we will discuss results from a project in which modifications were made to the hull and float of the Azura, aimed at improving power performance for a second WETS deployment. Second, HNEI undertook a redeployment of Lifesaver beginning in October 2018, with the dual intent of achieving improvements in reliability and power performance, while also conducting an important demonstration of the use of wave power for non-grid applications. HNEI partnered with the University of Washington to integrate their Adaptable Monitoring Package (AMP) into the hull of BOLT Lifesaver. Included for this deployment was a subsea inductive charging capability from WiBotic, Inc.. These systems are powered entirely by electricity generated by the Lifesaver itself. Finally, HNEI has undertaken design improvements for the deeper berth moorings at WETS, with principal engineering guidance from DNV GL. This has included extensive numerical analysis of strength and fatigue aimed at establishing moorings that can persist for as long as possible. The resulting design will be discussed.

Wave energy conversion devices, Alternative market↗
DOE OSTI2024

Nuclear Integrated Hydrogen Production Analysis Tool

This is an Excel-based time-independent discount cash flow calculator for LWR-HTSE systems. The tool incorporates (1) discounted cash flow and levelized cost of hydrogen (LCOH) analysis, (2) sensitivity analysis with respect to select financial performance metrics with output ‘tornado’ charts, (3) profitability analysis represented by heat maps using the two most sensitive parameters, (4) electricity versus hydrogen production preference analysis by comparing change in net present value (?NPV) between NPP-HTSE and business-as-usual electricity production for the grid, and (5) competitiveness analysis by comparing the calculated LCOH for NPP-HTSE with that of steam methane reforming, which is the conventional process to produce hydrogen.

Cheng, WenChi [Idaho National Laboratory (INL), Id↗
DOE OSTI2025

ASEAN Technical Exchange Workshop for System Operators, Regulators, and Policymakers

This presentation provides an in-depth exploration of power system planning, cross-border electricity trading, and battery energy storage systems (BESS), offering actionable insights for system operators, regulators, and policymakers. The first section delves into power system planning and analysis, focusing on capacity expansion models and resource adequacy studies, including their role in optimizing system efficiency, managing emissions, and addressing system reliability risks. Key considerations, such as integration of transmission into generation planning and the forecasting versus optimization of customer distributed energy resources (DER) technologies, are explored. The session highlights critical trade-offs in spatial granularity and model runtimes, as well as the feasibility of aligning distribution investments with capacity expansion efforts. The second section examines cross-border electricity trading, with an emphasis on resource adequacy concepts such as reliability targets, loss of load expectation (LOLE), and planning reserve margins (PRM). Case studies on reserve market design and coordination across US regions provide insights into improving reserve deliverability and managing interregional power balance and congestion. This section also addresses market-to-market congestion management, including advanced strategies for high-voltage direct current (HVDC) optimization and ancillary service delivery. Finally, the presentation covers the rapid evolution of Battery Energy Storage Systems (BESS), highlighting their operational growth, regulatory frameworks, and use cases in grid flexibility, energy storage, and reliability. The discussion focuses on the benefits of BESS for system stability, resilience, and integration of renewable energy, offering insights into its role as a vital component in the transition toward a more sustainable and flexible grid. Key performance parameters, such as throughput, round-trip efficiency, and state of charge, are also examined.

25 ENERGY STORAGE↗
DOE OSTI2025

Impact Analysis of Utility-Scale Energy Storage on the ERCOT Grid in Reducing Renewable Generation Curtailments and Emissions

This paper explores the solutions for minimizing renewable energy (RE) curtailment in the Texas Electric Reliability Council of Texas (ERCOT) grid. By utilizing current and future planning data from ERCOT and the System Advisor Model from the National Renewable Energy Laboratory, we examine how future renewable energy (RE) initiatives, combined with utility-scale energy storage, can reduce CO2 emissions while reshaping Texas’s energy mix. The study projects the energy landscape from 2023 to 2033, considering the planned phase-out of fossil fuel plants and the integration of new wind/solar projects. By comparing emissions under different load scenarios, with and without storage, we demonstrate storage’s role in optimizing RE utilization. The findings of this paper provide actionable guidance for energy stakeholders, underscoring the need to expand wind and solar projects with strategic storage solutions to maximize Texas's RE capacity and substantially reduce CO2 emissions.

14 SOLAR ENERGY↗
DOE OSTI2024

Coupling thermal energy storage with a thermally anisotropic building envelope for building demand-side management across various US climate conditions

Here, the thermally anisotropic building envelope (TABE) is a novel active building envelope that enhances energy efficiency and thermal comfort in buildings by transferring heat and cold between building envelopes and hydronic loops. When coupled with thermal energy storage (TES) units, the TABE + TES enables the storage of both heat and cold energy captured by the TABE roof or exterior walls. This stored energy can be later released by the TABE floor for indoor heating and cooling, benefiting both the grid and the end user. This paper evaluates the merits of TABE + TES for building demand-side management across various US climate conditions, focusing on peak load shaving, annual energy savings, and cost savings under time-of-use (TOU) electric rate schedules. Simulations were conducted by integrating time-of-day–informed, rule-based control strategies in MATLAB, TABE components and TES units in COMSOL Multiphysics, and whole-building energy analysis in EnergyPlus. A case study using the US Department of Energy’s prototype single-family detached house model in Birmingham, Alabama; Los Angeles, California; Oak Ridge, Tennessee; and Denver, Colorado, showed that the TABE + TES system achieved (1) 70 % peak load shaving in Los Angeles and Denver and 20 % in Birmingham and Oak Ridge; (2) significant peak electricity savings of 351–497 kWh, reducing peak energy consumption by 38 %–78 %; and (3) annual heating cost savings of 0.79 $\$$/m2–1.17 $\$$/m 2 and cooling cost savings of 0.60 $\$$/m 2 –1.17 $\$$/m 2 using a normal utility rate or low-TOU rate. The benefits of employing the TABE + TES system are even more significant under high TOU rates.

25 ENERGY STORAGE↗
NASA NTRS1995

CAE for thermal management of aerospace electronic boards using the BETAsoft program

Aerospace electronic boards require special attention to thermal management due to constraints such as their need to be light, small, and maintain high power densities. Also, cooling is mainly through conductive and radiative modes with minor or negligible convective cooling. Due to these particular requirements, thermal design has become an integrated part of the electronic design process in order to avoid expensive repeat prototyping and to ensure high reliability. To achieve high speed simulations, the BETAsoft code uses semi-empirical formulations and an advanced finite difference scheme that incorporates local adaptive grids. Detailed conduction, convection and radiation heat transfer is considered. Various benchmark verifications of the software simulation compared to infrared images typically prove to be within 10% of each other. The thermal analysis of a sample avionic card in a natural convection environment is shown. Then, the individual effects of attaching metal screws to the casing, increasing radiative emissivities of the casing, increasing the conductance of the wedge lock, adding an aluminum core to the board, adding metal strips in board layers, inserting conduction pads under components, and adding heat sinks to components are demonstrated.

Bobish, Kimberly↗
NASA NTRS2002

CAPRI: Using a Geometric Foundation for Computational Analysis and Design

CAPRI (Computational Analysis Programming Interface) is a software development tool intended to make computerized design, simulation and analysis faster and more efficient. The computational steps traditionally taken for most engineering analysis (Computational Fluid Dynamics (CFD), structural analysis, etc.) are: Surface Generation, usually by employing a Computer Aided Design (CAD) system; Grid Generation, preparing the volume for the simulation; Flow Solver, producing the results at the specified operational point; Post-processing Visualization, interactively attempting to understand the results. It should be noted that the structures problem is more tractable than CFD; there are fewer mesh topologies used and the grids are not as fine (this problem space does not have the length scaling issues of fluids). For CFD, these steps have worked well in the past for simple steady-state simulations at the expense of much user interaction. The data was transmitted between phases via files. In most cases, the output from a CAD system could go IGES files. The output from Grid Generators and Solvers do not really have standards though there are a couple of file formats that can be used for a subset of the gridding (i.e. PLOT3D) data formats and the upcoming CGNS). The user would have to patch up the data or translate from one format to another to move to the next step. Sometimes this could take days. Instead of the serial approach to analysis, CAPRI takes a geometry centric approach. CAPRI is a software building tool-kit that refers to two ideas: (1) A simplified, object-oriented, hierarchical view of a solid part integrating both geometry and topology definitions, and (2) programming access to this part or assembly and any attached data. The connection to the geometry is made through an Application Programming Interface (API) and not a file system.

Haimes, Robert↗
NASA NTRS2022

Development and Evaluation of Ensemble Consensus Precipitation Estimates over High Mountain Asia

Precipitation estimates are highly uncertain in complex regions such as High-Mountain Asia (HMA), where ground measurements are very difficult to obtain, and atmospheric dynamics poorly understood. Though gridded products derived from satellite-based observations and/or reanalysis can provide temporally and spatially distributed estimates of precipitation, there are significant inconsistencies in these products. As such, to date, there is little agreement in the community on the best and most accurate gridded precipitation product in HMA, which is likely area dependent because of HMA’s strong heterogeneities and complex orography. Targeting these gaps, this article presents the development of a consensus ensemble precipitation product using three gridded precipitation datasets (the Integrated Multi-satellitE Retrieals for Global Precipitation Measurement IMERG, the Climate Hazards group Infrared Precipitation with Stations CHIRPS, and the ECMWF Reanalysis ERA5) with a localized probability matched mean (LPM) approach. We evaluate the performance of the LPM estimate along with a simple ensemble mean (EM) estimate to overcome the differences and disparities of the three selected constituent products on long-term averages and trends in HMA. Our analysis demonstrates that LPM reduces the high biases embedded in the ensemble members and provides more realistic spatial patterns compared to EM. LPM is also a good alternative for merging data products with different spatio-temporal resolutions. By filtering disparities among the individual ensemble members, LPM overcomes the problem of a certain product performing well only in a particular area and provides a consensus estimate with plausible temporal trends.

Fadji Z Maina↗
DOE OSTI2023

Quantitative analysis of cost savings and occupants’ preferences in grid-interactive smart home operation

Many utility companies in the United States have introduced time-of-use (TOU) rates for homeowners with the goal of regulating electricity consumption during peak hours. The electrical appliances in homes include various thermostatically controlled devices, such as air conditioners (AC) for thermal comfort, and nonthermostatically controlled devices such as clothes washers. As a result, homeowners face the complicated challenge of economically operating multiple electrical appliances in their homes while maintaining comfort and convenience. This is usually due to the lack of an explicit understanding of the correlation between cost saving and the users’ comfort. To understand the correlation, this article is designed to construct a framework by integrating three major components: a multi-objective optimization method accommodating multiple competing goals with different weights, a learning-based system modeling approach describing the dynamics and thermal coupling effects of appliances, and a novel comfort index method differentiating preferred and acceptable thermal comfort. Our proposed framework can allow the indoor air temperature to fall into the "preferred" range with a marginal cost increase. Furthermore, the simulation result shows that an additional 8 h for the preferred thermal comfort can be achieved with a cost increase of only 1.77%.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS1990

Temporal-adaptive Euler/Navier-Stokes algorithm for unsteady aerodynamic analysis of airfoils using unstructured dynamic meshes

A temporal adaptive algorithm for the time-integration of the two-dimensional Euler or Navier-Stokes equations is presented. The flow solver involves an upwind flux-split spatial discretization for the convective terms and central differencing for the shear-stress and heat flux terms on an unstructured mesh of triangles. The temporal adaptive algorithm is a time-accurate integration procedure which allows flows with high spatial and temporal gradients to be computed efficiently by advancing each grid cell near its maximum allowable time step. Results indicate that an appreciable computational savings can be achieved for both inviscid and viscous unsteady airfoil problems using unstructured meshes without degrading spatial or temporal accuracy.

Kleb, William L.↗