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

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Influence of temporal variations in plasma conditions on the electric potential near self-organized dust chains

Self-organization of dust grains into stable filamentary dust structures (or “chains”) largely depends on dynamic interactions between individual charged dust grains and complex electric potential arising from the distribution of charges within a local plasma environment. Recent studies have shown that the positive column of the gas discharge plasma in the Plasmakristall-4 (PK-4) experiment at the International Space Station supports the presence of fast-moving ionization waves, which lead to variations of plasma parameters by up to an order of magnitude from the average background values. The highly variable environment resulting from ionization waves may have interesting implications for the dynamics and self-organization of dust particles, particularly concerning the formation and stability of dust chains. Here, we investigate the electric potential surrounding dust chains in the PK-4 experiment by employing a molecular dynamics model of the dust and ions with boundary conditions supplied by a particle-in-cell with Monte Carlo collision simulation of the ionization waves. The model is used to examine the effects of the plasma conditions within different regions of the ionization wave and compare the resulting dust structure to that obtained by employing the time-averaged plasma conditions. Here, the comparison between simulated dust chains and experimental data from the PK-4 experiment shows that the time-averaged plasma conditions do not accurately reproduce observed results for dust behavior, indicating that more careful treatment of plasma conditions in the presence of ionization waves is required. It is further shown that commonly used analytic forms of the electric potential do not accurately describe the electric potential near charged dust grains under these plasma conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Characterization of turbulence under different stability conditions using lidar scanning data

The spatiotemporal scales of turbulence in the boundary layer flow vary with the static stability of the atmosphere. For example, turbulence structures in unstable conditions are often found to be large and coherent, whereas the turbulent structures in stable conditions are relatively small and sporadic. To better understand the behavior of such turbulent structures under different atmospheric stability conditions in the lower atmosphere, herein, we use scanning lidar data collected over several months during the US Department of Energy's second Wind Forecast Improvement Project (WFIP 2) in 2016. The radial velocity data from scanning lidar were gathered along the horizontal plane (PPI mode) and were analyzed using proper orthogonal decomposition (POD) and spectral energy methods. The results from these analyses show that the turbulent structures in daytime unstable conditions are different from those present during nighttime stable conditions in terms of amount of energy and coherent structures. The POD energy is distributed more evenly in all the higher spatial modes in the daytime unstable case compared to the nighttime stable case. Besides characterizing the turbulence in the flow, the lidar data were also used to compare the simulated flow field generated from the WRF-LES framework (Weather Research and Forecasting - large-eddy simulation) with the scanning lidar data. The results from both simulated and lidar scanned data show similar structures orienting the streak-like structure along the mean wind. This indicates that the streak-like structures can exist in the real atmosphere during unstable atmospheric condition cases.

Rai, Raj K.↗
DOE OSTI2023

Evaluation of Atmospheric Conditions Leading to a Fumigation Event

During the afternoon of 30 January 2022, the Savannah River Site experienced unusual temperature conditions leading to a fumigation event that triggered safety alarms and caused considerable confusion about the cause of the event. Normally, it is assumed that fumigation events occur early in the day once surface heating has begun. While most fumigation events are related to the breakup of a nocturnal inversion, this event was related to synoptic atmospheric conditions, which provided a more unique scenario that led to the fumigation event. The unusual synoptic atmospheric conditions led to the downwash and fumigation of the elevated plume, causing a pollutant to mix rapidly to the surface. These conditions could have potentially harmed workers within the facility, since the plume was directed toward a building air intake system. Here, we seek to outline the conditions that led to this unusual fumigation event and provide results of two-dimensional (2D) wind modeling of the event to characterize these conditions for future operational guidance of the facility air intake systems. This work sets the groundwork for future high-resolution modeling to explore the mechanisms and thresholds affecting fumigation on the facility-specific short distance scales and improve forecasting of non-standard fumigation events to protect human health.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Neural conditional reweighting

There is a growing use of neural network classifiers as unbinned, high-dimensional (and variable-dimensional) reweighting functions. To date, the focus has been on marginal reweighting, where a subset of features are used for reweighting while all other features are integrated over. There are some situations, though, where it is preferable to condition on auxiliary features instead of marginalizing over them. Here, we introduce neural conditional reweighting, which extends neural marginal reweighting to the conditional case. This approach is particularly relevant in high-energy physics experiments for reweighting detector effects conditioned on particle-level truth information. Furthermore we leverage a custom loss function that not only allows us to achieve neural conditional reweighting through a single training procedure, but also yields sensible interpolation even in the presence of phase space holes. As a specific example, we apply neural conditional reweighting to the energy response of high-energy jets, which could be used to improve the modeling of physics objects in parametrized fast simulation packages.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Distributionally Robust Decision Making Leveraging Conditional Distributions

Distributionally robust optimization (DRO) is a powerful tool for decision making under uncertainty. It is particularly appealing because of its ability to leverage existing data. However, many practical problems call for decision-making with some auxiliary information, and DRO in the context of conditional distributions is not straightforward. We propose a conditional kernel distributionally robust optimization (CKDRO) method that enables robust decision making under conditional distributions through kernel DRO and the conditional mean operator in the reproducing kernel Hilbert space (RKHS). In particular, we consider problems where there is a correlation between the unknown variable y and an auxiliary observable variable x. Given past data of the two variables and a queried auxiliary variable, CKDRO represents the conditional distribution P(y|x) as the conditional mean operator in the RKHS space and quantifies the ambiguity set in the RKHS as well, which depends on the size of the dataset as well as the query point. To justify the use of RKHS, we demonstrate that the ambiguity set defined in RKHS can be viewed as a ball under a metric that is similar to the Wasserstein metric. The DRO is then dualized and solved via a finite dimensional convex program. The proposed CKDRO approach is applied to a generation scheduling problem and shows that the result of CKDRO is superior to common benchmarks in terms of quality and robustness.

Chen, Yuxiao↗
DOE OSTI2020

Cut–and–chip harvester material capacity and fuel performance on commercial-scale willow fields for varying ground and crop conditions

Shrub willow (Salix spp.) is capable of producing commercially attractive amounts of biomass in short rotations, but harvesting costs and logistics remain a concern. There is a particular need for information about harvesting operations on larger, commercial short–rotation woody crop systems. Another recent issue on commercial fields in northern New York is commercial growers conducting harvests during the growing season rather than the recommended dormant season when fields may be too wet to harvest. This study evaluated and modeled the in–field performance of a cut–and–chip harvester for almost 700 wagonloads of chips operating in commercial willow fields in a wider array of crop and field conditions than have been previously reported. Analysis indicated that the time of harvest (leaf–on or leaf–off) and whether site conditions were wet or dry affected the harvester's material capacity. Mean material capacity was greatest for leaf–off, dry conditions (71.8 Mg/hr) and lowest for leaf–on harvests, which were similar for wet (30.4 Mg/hr) and dry conditions (29.7 Mg/hr). Mean crop specific fuel consumption ranged between 1.3 and 3.3 L/Mg, but can get considerably higher for standing biomasses below 40 Mg/ha. Wet ground conditions and leaf–on harvests tend to decrease material capacity and increase fuel consumption as the harvester has to divert power to forward movement and material processing. Relationships for material capacity and fuel consumption based on standing biomass, time of harvest and ground conditions will be essential for evaluating and modeling the economic and environmental impacts of commercial–scale willow operations.

09 BIOMASS FUELS↗
DOE OSTI2021

Inverse Design of Two-Dimensional Airfoils Using Conditional Generative Models and Surrogate Log-Likelihoods

Abstract This paper shows how to use conditional generative models in two-dimensional (2D) airfoil optimization to probabilistically predict good initialization points within the vicinity of the optima given the input boundary conditions, thus warm starting and accelerating further optimization. We accommodate the possibility of multiple optimal designs corresponding to the same input boundary condition and take this inversion ambiguity into account when designing our prediction framework. To this end, we first employ the conditional formulation of our previous work BézierGAN–Conditional BézierGAN (CBGAN)—as a baseline, then introduce its sibling conditional entropic BézierGAN (CEBGAN), which is based on optimal transport regularized with entropy. Compared with CBGAN, CEBGAN overcomes mode collapse plaguing conventional GANs, improves the average lift-drag (Cl/Cd) efficiency of airfoil predictions from 80.8% of the optimal value to 95.8%, and meanwhile accelerates the training process by 30.7%. Furthermore, we investigate the unique ability of CEBGAN to produce a log-likelihood lower bound that may help select generated samples of higher performance (e.g., aerodynamic performance). In addition, we provide insights into the performance differences between these two models with low-dimensional toy problems and visualizations. These results and the probabilistic formulation of this inverse problem justify the extension of our GAN-based inverse design paradigm to other inverse design problems or broader inverse problems.

Engineering↗
DOE OSTI2023

Membrane Pretreatment and Cell Conditioning for Proton Exchange Membrane Water Electrolysis

As the research community studying proton exchange membrane water electrolysis (PEMWE) grows, it is important to develop methods that achieve transparent, reproducible research. Reproducibility of performance and durability is a challenge facing the PEMWE field, as the published literature includes a wide spread of results obtained with nominally similar materials. Prior round-robin performance benchmarking efforts [1] have identified inadequate cell conditioning as a major source of variation in apparent cell performance. Inadequate pre-treatment and conditioning can lead to instability in initial performance and adds ambiguity to durability measurements. However, excessively prolonged conditioning procedures limit the throughput of testing and the pace of research. Pretreatment and conditioning methods vary significantly across the research literature, but little systematic investigation is available into the mechanisms of these procedures or how procedural differences may impact results. This presentation will discuss investigations into the effects of membrane pre-treatment and operating procedures during cell conditioning on initial performance and catalyst-specific accelerated stress tests, with the aim of recommending procedures to enable clear, reproducible, and high-throughput research. Methods investigated include the use of hydrogen peroxide, acids, and hydration at elevated temperature for membrane pretreatment, and conditioning procedures such as current or voltage holds and cycling. The investigations cover both the impacts of these procedures on cell performance and stability as well as underlying mechanisms and processes taking place in the cell materials.

cell↗
DOE OSTI2025

Experiment to Investigate the On-set of Transient Fission Gas Release Under Simulated LOCA Conditions

Continuing efforts to better understand the phenomenon of transient fission gas release in irradiated commercial light water reactor fuel undergoing a simulated loss of coolant accident (LOCA) will be discussed in this work. During heating associated with LOCA conditions there is an additional release of fission gas beyond what is typically released during steady state operation. The exact timing of this release could impact the cladding balloon and rupture as the LOCA progresses in an actual accident. Recent experiments performed on the upgraded Severe Accident Test Station at Oak Ridge National Laboratory have expanded the current assessment of transient fission gas release. This system evaluates fission gas release by sweeping fission gas out of the LOCA test furnace and into cryogenically cooled cold traps where radioactive noble gas fission products are measured by gamma spectrometry. Additionally, the sweep gas can be monitored by a gas mass spectrometer to provide additional data on noble gas release and changes in the sweep gas atmosphere during heating. Several different conditions have been evaluated that explored the response of irradiated fuel to different thermal ramp conditions and different overpressure conditions. This further confirmed the impact of an overpressure in suppressing transient fission gas release. Further experiments are planned to evaluate the on-set temperature of transient fission gas release under a known overpressure. This test will progressively step through different temperature conditions while maintaining hydrostatic pressure on the fuel that is representative of high burnup fuel conditions. The available results from this type of testing will be discussed. Post-test microscopy will be compared to other transient fission gas release and standard LOCA tests to further understand the microstructural source of transient fission gas release.

Harp, Jason [ORNL] (ORCID:0000000253458440)↗
DOE OSTI2023

FUN-PROSE: A deep learning approach to predict condition-specific gene expression in fungi

mRNA levels of all genes in a genome is a critical piece of information defining the overall state of the cell in a given environmental condition. Being able to reconstruct such condition-specific expression in fungal genomes is particularly important to metabolically engineer these organisms to produce desired chemicals in industrially scalable conditions. Most previous deep learning approaches focused on predicting the average expression levels of a gene based on its promoter sequence, ignoring its variation across different conditions. Here we present FUN-PROSE—a deep learning model trained to predict differential expression of individual genes across various conditions using their promoter sequences and expression levels of all transcription factors. We train and test our model on three fungal species and get the correlation between predicted and observed condition-specific gene expression as high as 0.85. We then interpret our model to extract promoter sequence motifs responsible for variable expression of individual genes. We also carried out input feature importance analysis to connect individual transcription factors to their gene targets. A sizeable fraction of both sequence motifs and TF-gene interactions learned by our model agree with previously known biological information, while the rest corresponds to either novel biological facts or indirect correlations.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Oceanographic Conditions. 2007 - 2040. North Slope Alaska.

Complete representations of oceanographic conditions require spatial and temporal information about the significant wave height (Hs), peak wave period (Tp), wind speed, wind direction, wave direction, water level, salinity, and temperature. This data develops location-independent typologies to reduce the number of boundary conditions needed to assess nearshore oceanographic environments in both a Historical (2007-2019) and Future (2020-2040) timespan along the Alaskan North Slope. Wave information for both time spans were generated from WaveWatch III, Delft3D-FLOW, and Delft3D-WAVE simulations forced by wind conditions from reanalysis data (e.g., ASRv2 and ERA5) for the historical simulations while projected conditions were obtained from downscaled GFDL-CM3 forced under RCP8.5 conditions. Salinity was generated from GOFS 3.1 for the years between 2008-2015 and skin temperature of the ocean was obtained from ASRv2 reanalysis data for the years between 2007-2016. To identify generalized oceanographic typologies, K-means clustering was applied to the energy-weighted joint-probability distribution of Hs and Tp at six sites along the North Slope of Alaska. Distributions of wave and wind direction, wind speed, and water level associated with locaiton-indepndent centroids were assigned single values to describe a reduced order, typological rendition of offshore oceanographic conditions. These final typologies and their constituent data are provided here and can be used to evaluate the change in ocean energy over the next two decades in response to climate change and provide insight into expected consequences such as coastal erosion and flooding. A full assessment of the findings and techniques developed can be found in: Eymold, W.K., Flanary, C., Erikson, L., Nederhoff, K., Chartrand, C.C., Jones, C., Kasper, J., and Bull, D.L. Typological Representation of the Offshore Oceanographic Environment along the Alaskan North Slope. Continental Shelf Research (2022). 10.1016/j.csr.2022.104795

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Computational Characterization and Boundary Condition Models of a Jet Interaction Fluidic Oscillator

Fluidically oscillating jet actuators that generate sweeping jets when supplied with a pressurized fluid have been used to mitigate separation and reduce drag in a range of flow control applications. Their implementation in future flight vehicles would require fundamental understanding and accurate predictive techniques of the physics of their internal flow and jet formation. The present investigations focus on high-fidelity, time-accurate simulations to characterize the flow physics of the actuator in quiescent conditions. An important element of the present simulations is to demonstrate the ability of the computational fluid dynamics (CFD) solver to predict the jet characteristics and provide a basis for the development of improved boundary conditions (BC) without entirely resolving the geometrical features of the fluidic device. The CFD-predicted oscillation frequencies of the engendered jets were found to be in excellent agreement with experiments, even on two-dimensional meshes. The study revealed that three-dimensional simulations are required to capture some of the flow features of the sweeping jet such as the double peak in time-averaged velocity distributions downstream of the actuator’s orifice that were measured in experiments. Furthermore, several approaches for modeling the actuator were implemented and assessed in quiescent conditions. The evaluation of a boundary condition at the device throat, based on the phase-averaged flow variables, provides the basis for devising surface-based boundary conditions. The influence and necessity of including turbulent characteristics as part of the boundary conditions have also been identified.

42 ENGINEERING↗
DOE OSTI2024

Iron dissolution from Patagonian dust in the Southern Ocean: under present and future conditions

Although the input of desert dust as a key source of trace metals in the Southern Ocean (SO) has been previously studied, the dissolution process of metals in surface waters, particularly iron (Fe), remain poorly understood. Given the crucial role of Fe in primary production and the biological carbon pump in the SO, we focused on experimental estimations of Fe dissolution from Patagonian dust, the primary natural dust source in the SO. Our study considered both current and projected future conditions, encompassing sea-surface warming, acidification, increased photosynthetically active radiation, and doubled dust inputs. Through controlled laboratory experiments using filtered SO seawater, conducted over 7 days, we assessed changes in particulate Fe (pFe) concentrations, Fe redox speciation (Fe(II)/Fe(III)), and in the mineralogy of Fe-bearing dust in abiotic condition. The predominant minerals in the dust included quartz and aluminosilicates, with silicon (Si), aluminum (Al), and Fe as the major elements. No significant alterations in the mineralogy and the elemental composition of the dust were recorded during the dissolution experiments, neither under present nor under projected future conditions. The particulate Fe(II)/Fe(III) ratio remained consistently at 0.25 during the experiments, unaffected by changed conditions. Consequently, changes in environmental conditions in the SO would therefore not significantly alter the mineralogy and redox speciation of pFe in the Patagonian dust. On the contrary, pFe exhibited a dissolution rate of 3.8% and 1.6% per day under present and future conditions, respectively. The environmental changes anticipated for 2100 in the SO will likely to result in a decrease in the dissolution rate of pFe. Thus, even though a doubling of dust input by 2100 is anticipated, it will unlikely provide significantly more dissolved Fe (dFe) in seawater in the SO. Consequently, the future intensification of Patagonian dust inputs may not alleviate the Fe limitation in the SO.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Ducted Fuel Injection Provides Consistently Lower Soot Emissions in Sweep to Full-Load Conditions

Earlier studies have proven how ducted fuel injection (DFI) substantially reduces soot for low- and mid-load conditions in heavy-duty engines, without significant adverse effects on other emissions. Nevertheless, no comprehensive DFI study exists showing soot reductions at high- and full-load conditions. This study investigated DFI in a single-cylinder, 1.7-L, optical engine from low- to full-load conditions with a low-net-carbon fuel consisting of 80% renewable diesel and 20% biodiesel. Over the tested load range, DFI reduced engine-out soot by 38.1–63.1% compared to conventional diesel combustion (CDC). This soot reduction occurred without significant detrimental effects on other emission types. Thus, DFI reduced the severity of the soot–NO x tradeoff at all tested conditions. While DFI delivered considerable soot reductions in thepresent study, previous DFI studies at low- and mid-load conditions delivered larger soot reductions (>90%) compared to CDC operation at the same conditions. Therefore, the DFI configuration used here has been deemed nonoptimal (in terms of parameters such as the injector-spray and piston geometries), and several improvements are recommended for future studies with high-load DFI. Further, these improvements include employing better spray-duct alignment, a deeper piston bowl with a smaller injector umbrella angle, and a fuel injector that opens and closes faster. The study also suggests future research to make DFI ready for commercialization, such as metal-engine tests to ensure desirable DFI performance over an engine’s complete speed/load map. Overall, this study supports the continued development and commercialization of DFI to meet upcoming emissions regulations for heavy-duty vehicles. Specifically, multicylinder engine experiments and CFD simulations should be utilized to optimize the performance and clarify the full potential of DFI.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2026

Idealized simulations of wind farm interactions with intermittent turbulence in stable boundary layer conditions

Stable atmospheric boundary layer conditions typically correspond to weak turbulence levels, but intermittent periods of elevated turbulence can occur during otherwise quiescent conditions. The interaction between intermittent turbulence and wind turbines is not well understood because of sparse observations, as well as the difficulty in realistically resolving small-scale turbulence during strongly stable conditions with numerical simulations. In this study, an explicit filtering and reconstruction approach for large-eddy simulation (LES) is used to simulate weakly and strongly stable conditions, with surface cooling rates of −0.2 and −2.0 K h −1 , respectively. This approach can sustain resolved background turbulence at relatively coarse grid spacing and stronger stratification compared to conventional closures, permitting more realistic intermittent stable boundary layer (SBL) turbulence. The idealized LES capability of the Weather Research and Forecasting model is employed with turbine rotors parameterized using generalized actuator disks to examine (1) how the presence of turbine wakes affects SBL evolution and (2) the effect of intermittent turbulence on power production and wake recovery. Wakes increase mixing and deepen the SBL, with a stronger effect under strongly stable conditions, primarily because the SBL is shallower and closer to the top of the wind turbine rotor layer. Intermittent turbulence does not have a significant impact on mean power generation and wake recovery because the relevant intermittent turbulent structures in this study only affect the bottom half of the rotor disk. Power production is, however, more variable during periods of elevated turbulence, demonstrating the impact of SBL intermittency. This study uses an idealized configuration, focusing on LES model performance and physical understanding, with the goal of informing future simulations of the conditions observed during the American Wake Experiment.

Energy - Wind↗
DOE OSTI2021

Assessing boundary condition and parametric uncertainty in numerical-weather-prediction-modeled, long-term offshore wind speed through machine learning and analog ensemble

To accurately plan and manage wind power plants, not only does the time-varying wind resource at the site of interest need to be assessed but also the uncertainty connected to this estimate. Numerical weather prediction (NWP) models at the mesoscale represent a valuable way to characterize the wind resource offshore, given the challenges connected with measuring hub-height wind speed. The boundary condition and parametric uncertainty associated with modeled wind speed is often estimated by running a model ensemble. However, creating an NWP ensemble of long-term wind resource data over a large region represents a computational challenge. Here, we propose two approaches to temporally extrapolate wind speed boundary condition and parametric uncertainty using a more convenient setup in which a mesoscale ensemble is run over a short-term period (1 year), and only a single model covers the desired long-term period (20 year). We quantify hub-height wind speed boundary condition and parametric uncertainty from the short-term model ensemble as its normalized across-ensemble standard deviation. Then, we develop and apply a gradient-boosting model and an analog ensemble approach to temporally extrapolate such uncertainty to the full 20-year period, for which only a single model run is available. As a test case, we consider offshore wind resource characterization in the California Outer Continental Shelf. Both of the proposed approaches provide accurate estimates of the long-term wind speed boundary condition and parametric uncertainty across the region (R 2 >0.75), with the gradient-boosting model slightly outperforming the analog ensemble in terms of bias and centered root-mean-square error. At the three offshore wind energy lease areas in the region, we find a long-term median hourly uncertainty between 10 % and 14 % of the mean hub-height wind speed values. Finally, we assess the physical variability in the uncertainty estimates. In general, we find that the wind speed uncertainty increases closer to land. Also, neutral conditions have smaller uncertainty than the stable and unstable cases, and the modeled wind speed in winter has less boundary condition and parametric sensitivity than summer.

17 WIND ENERGY↗
NASA NTRS1975

Analytic and experimental evaluation of flowing air test conditions for selected metallics in a shuttle TPS application

A detailed experimental and analytical evaluation was performed to define the response of TD nickel chromium alloy (20 percent chromium) and coated columbium (R512E on CB-752 and VH-109 on WC129Y) to shuttle orbiter reentry heating. Flight conditions important to the response of these thermal protection system (TPS) materials were calculated, and test conditions appropriate to simulation of these flight conditions in flowing air ground test facilities were defined. The response characteristics of these metallics were then evaluated for the flight and representative ground test conditions by analytical techniques employing appropriate thermochemical and thermal response computer codes and by experimental techniques employing an arc heater flowing air test facility and flat face stagnation point and wedge test models. These results were analyzed to define the ground test requirements to obtain valid TPS response characteristics for application to flight. For both material types in the range of conditions appropriate to the shuttle application, the surface thermochemical response resulted in a small rate of change of mass and a negligible energy contribution. The thermal response in terms of surface temperature was controlled by the net heat flux to the surface; this net flux was influenced significantly by the surface catalycity and surface emissivity. The surface catalycity must be accounted for in defining simulation test conditions so that proper heat flux levels to, and therefore surface temperatures of, the test samples are achieved.

Schaefer, J. W.↗
NASA NTRS1979

Boundary conditions for exterior acoustic problems

Problems of acoustics are generally posed in unbounded regions. Numerical computations require that the infinite regions be truncated with artificial finite boundaries. Boundary conditions must be developed at these artificial boundaries which approximate the conditions for outgoing waves. These conditions should be asymptotic in the distance of the boundaries from the source terms and should give rise to well posed problems interior to fairly arbitrary regions, which can be chosen on the basis of computational efficiency rather than for mathematical (i.e., well posedness) reasons. A family of such conditions is presented and their properties are discussed. These conditions can be thought of as extensions of the Sommerfeld radiation condition for outgoing waves.

Bayliss, A.↗