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NASA NTRS2022

How Well do Multisatellite Products Capture the Space-Time Dynamics of Precipitation? Part II: Building an Error Model Through Spectral System Identification

Satellite precipitation products, as all quantitative estimates, come with some inherent degree of uncertainty. To associate a quantitative value of the uncertainty to each individual estimate, error modeling is necessary. Most of the error models proposed so far compute the uncertainty as a function of precipitation intensity only, and only at one specific spatio-temporal scale. We propose a spectral error model which accounts for the neighboring space-time dynamics of precipitation into the uncertainty quantification. Systematic distortions of the precipitation signal and random errors are characterized distinctively in every frequency-wavenumber band in the Fourier domain, to accurately characterize error across scales. The systematic distortions are represented as a deterministic space-time linear filtering term. The random errors are represented as a non-stationary additive noise. The spectral error model is applied to the IMERG multi satellite precipitation product and its parameters are estimated empirically through a system identification approach using the GV-MRMS gauge-radar measurements as reference (“truth”) over the eastern United States. The filtering term is found to be essentially low-pass. While traditional error models attribute most of the error variance to random errors, it is found here that the systematic filtering term explains 48% of the error variance at the native resolution of IMERG. This fact confirms that, at high resolution, filtering effects in satellite precipitation products cannot be ignored, and that the error cannot be represented as a purely random additive or multiplicative term. An important consequence is that precipitation estimates derived from totally different sources shall not be expected to automatically have statistically independent errors.

Precipitation↗

NASA NTRS1998

Fractal Characterization of Multitemporal Scaled Remote Sensing Data

Scale is an "innate" concept in geographic information systems. It is recognized as something that is intrinsic to the ingestion, storage, manipulation, analysis, modeling, and output of space and time data within a GIS purview, yet the relative meaning and ramifications of scaling spatial and temporal data from this perspective remain enigmatic. As GISs become more sophisticated as a product of more robust software and more powerful computer systems, there is an urgent need to examine the issue of scale, and its relationship to the whole body of spatiotemporal data, as imparted in GISS. Scale is fundamental to the characterization of geo-spatial data as represented in GISS, but we have relatively little insight on the effects of, or how to measure the effects of, scale in representing multiscaled data; i.e., data that are acquired in different formats (e.g., map, digital) and exist in varying spatial, temporal, and in the case of remote sensing data, radiometric, configurations. This is particularly true in the emerging era of Integrated GISs (IGIS), wherein spatial data in a variety of formats (e.g., raster, vector) are combined with multiscaled remote sensing data, capable of performing highly sophisticated space-time data analyses and modeling. Moreover, the complexities associated with the integration of multiscaled data sets in a multitude of formats are exacerbated by the confusion of what the term "scale" is from a multidisciplinary perspective; i.e., "scale" takes on significantly different meanings depending upon one's disciplinary background and spatial perspective which can lead to substantive confusion in the input, manipulation, analyses, and output of IGISs (Quattrochi, 1993). Hence, we must begin to look at the universality of scale and begin to develop the theory, methods, and techniques necessary to advance knowledge on the "Science of Scale" across a wide number of spatial disciplines that use GISs.

Quattrochi, Dale A.↗

NASA NTRS1999

Computation of Steady and Unsteady Laminar Flames: Theory

In this paper we describe the numerical analysis underlying our efforts to develop an accurate and reliable code for simulating flame propagation using complex physical and chemical models. We discuss our spatial and temporal discretization schemes, which in our current implementations range in order from two to six. In space we use staggered meshes to define discrete divergence and gradient operators, allowing us to approximate complex diffusion operators while maintaining ellipticity. Our temporal discretization is based on the use of preconditioning to produce a highly efficient linearly implicit method with good stability properties. High order for time accurate simulations is obtained through the use of extrapolation or deferred correction procedures. We also discuss our techniques for computing stationary flames. The primary issue here is the automatic generation of initial approximations for the application of Newton's method. We use a novel time-stepping procedure, which allows the dynamic updating of the flame speed and forces the flame front towards a specified location. Numerical experiments are presented, primarily for the stationary flame problem. These illustrate the reliability of our techniques, and the dependence of the results on various code parameters.

Hagstrom, Thomas↗

NASA NTRS1990

Three-dimensional flux-split Euler schemes involving unstructured dynamic meshes

Improved algorithms for the solution of the 3-D time dependent Euler equations are presented for aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves either an explicit time integration scheme using a multistage Runge-Kutta procedure or an implicit time integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. With the implicit Gauss-Seidel procedure, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady flow results are presented for both the NACA 0012 airfoil and the ONERA M6 wing to demonstrate applications of the new Euler solvers. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

Batina, John T.↗

NASA NTRS1995

Clouds and the Earth's Radiant Energy System (CERES) algorithm theoretical basis document: Determination of surface and atmosphere fluxes and temporally and spatially averaged products (subsystems 5-12) - volume 4

The theoretical bases for the Release 1 algorithms that will be used to process satellite data for investigation of the Clouds and the Earth's Radiant Energy System (CERES) are described. The architecture for software implementation of the methodologies is outlined. Volume 4 details the advanced CERES techniques for computing surface and atmospheric radiative fluxes (using the coincident CERES cloud property and top-of-the-atmosphere (TOA) flux products) and for averaging the cloud properties and TOA, atmospheric, and surface radiative fluxes over various temporal and spatial scales. CERES attempts to match the observed TOA fluxes with radiative transfer calculations that use as input the CERES cloud products and NOAA National Meteorological Center analyses of temperature and humidity. Slight adjustments in the cloud products are made to obtain agreement of the calculated and observed TOA fluxes. The computed products include shortwave and longwave fluxes from the surface to the TOA. The CERES instantaneous products are averaged on a 1.25-deg latitude-longitude grid, then interpolated to produce global, synoptic maps to TOA fluxes and cloud properties by using 3-hourly, normalized radiances from geostationary meteorological satellites. Surface and atmospheric fluxes are computed by using these interpolated quantities. Clear-sky and total fluxes and cloud properties are then averaged over various scales.

Wielicki, Bruce A.↗

DOE OSTI2024

Nonsteady Load Responses of Wind Turbines to Atmospheric and Mountain-Generated Turbulence Eddies, With Impacts on the Main Bearing: A Validation Study

Previous computational and field experiments identify three characteristic time scales in the aerodynamic responses of utility-scale wind turbine loads to atmospheric boundary layer (ABL) turbulence: a 30-90 second time scale for the passage of high/low speed "streaks" through the rotor plane, the blade and rotor rotation time scales (approximately 1 to 5 seconds), and a sub-second time scale created by blade rotation through gradients within eddy coherent structure. In the current study we compare aerodynamic load responses from daytime ABL turbulence quantified with large-eddy simulation and a actuator line model of the NREL 5 MW wind turbine with analysis of field data from the NREL/GE 1.5 MW wind turbine 5 kilometers east of the Rocky Mountain Front Range in Colorado. In addition, we contrast the responses to the passage of the mountain-generated eddies embedded within the westerly winds with the ABL eddies embedded within northerly/southerly winds. These analyses are in context with the nonsteady forcing of the main bearing by the aerodynamic generation of nontorque bending moments on the main shaft. Potentially relevant to main bearing failure mechanisms, both computational and field data show that the magnitudes of turbulence-generated nontorque bending moments, that we show generate nonsteady force on the main bearing, are of order, and often larger than, torque (which underlies power). However, the temporal variations in these two responses are uncorrelated, implying that the aerodynamic mechanisms that drive power and main bearing response are fundamentally different. We find this to be the case in the field with both mountain-generated eddies (westerly winds) and ABL-generated eddies (northerly/southerly winds). Whereas the time and length scales are comparable, the mountain eddies were somewhat more energetic than the northerly/southerly ABL eddies. Interestingly, however, the fluctuations in nontorque bending moment that force the main bearing were found to be stronger when forced by the ABL eddies than the mountain eddies. The field studies validate the key results from the computational study and show even stronger response in the nontorque bending moment than in the computer simulations. In all cases, the torque and nontorque bending moments are temporally uncorrelated, torque and power are driven by time variations in rotor-averaged horizontal wind velocity and nontorque bending moments are driven by time changes in the degree of nonuniformity in the distribution of velocity over the rotor plane. Thus the results generalize the mechanisms underlying nonsteady aerodynamic forcing to classes of turbulence eddy types with strength of order or stronger than ABL eddies with transverse scale of order the wind turbine rotor. These include atmospheric turbulence eddies, topography-generated turbulence eddies and, by extension, impacts of turbine-wake-scale turbulence eddies on downstream wind turbine rotors.

17 WIND ENERGY↗

NASA NTRS2018

GMI-IPS: Python Processing Software for Aircraft Campaigns

NASA's Atmospheric Tomography Mission (ATom) seeks to understand the impact of anthropogenic air pollution on gases in the Earth's atmosphere. Four flight campaigns are being deployed on a seasonal basis to establish a continuous global-scale data set intended to improve the representation of chemically reactive gases in global atmospheric chemistry models. The Global Modeling Initiative (GMI), is creating chemical transport simulations on a global scale for each of the ATom flight campaigns. To meet the computational demands required to translate the GMI simulation data to grids associated with the flights from the ATom campaigns, the GMI ICARTT Processing Software (GMI-IPS) has been developed and is providing key functionality for data processing and analysis in this ongoing effort. The GMI-IPS is written in Python and provides computational kernels for data interpolation and visualization tasks on GMI simulation data. A key feature of the GMI-IPS, is its ability to read ICARTT files, a text-based file format for airborne instrument data, and extract the required flight information that defines regional and temporal grid parameters associated with an ATom flight. Perhaps most importantly, the GMI-IPS creates ICARTT files containing GMI simulated data, which are used in collaboration with ATom instrument teams and other modeling groups. The initial main task of the GMI-IPS is to interpolate GMI model data to the finer temporal resolution (1-10 seconds) of a given flight. The model data includes basic fields such as temperature and pressure, but the main focus of this effort is to provide species concentrations of chemical gases for ATom flights. The software, which uses parallel computation techniques for data intensive tasks, linearly interpolates each of the model fields to the time resolution of the flight. The temporally interpolated data is then saved to disk, and is used to create additional derived quantities. In order to translate the GMI model data to the spatial grid of the flight path as defined by the pressure, latitude, and longitude points at each flight time record, a weighted average is then calculated from the nearest neighbors in two dimensions (latitude, longitude). Using SciPya's Regular Grid Interpolator, interpolation functions are generated for the GMI model grid and the calculated weighted averages. The flight path points are then extracted from the ATom ICARTT instrument file, and are sent to the multi-dimensional interpolating functions to generate GMI field quantities along the spatial path of the flight. The interpolated field quantities are then written to a ICARTT data file, which is stored for further manipulation. The GMI-IPS is aware of a generic ATom ICARTT header format, containing basic information for all flight campaigns. The GMI-IPS includes logic to edit metadata for the derived field quantities, as well as modify the generic header data such as processing dates and associated instrument files. The ICARTT interpolated data is then appended to the modified header data, and the ICARTT processing is complete for the given flight and ready for collaboration. The output ICARTT data adheres to the ICARTT file format standards V1.1. The visualization component of the GMI-IPS uses Matplotlib extensively and has several functions ranging in complexity. First, it creates a model background curtain for the flight (time versus model eta levels) with the interpolated flight data superimposed on the curtain. Secondly, it creates a time-series plot of the interpolated flight data. Lastly, the visualization component creates averaged 2D model slices (longitude versus latitude) with overlaid flight track circles at key pressure levels. The GMI-IPS consists of a handful of classes and supporting functionality that have been generalized to be compatible with any ICARTT file that adheres to the base class definition. The base class represents a generic ICARTT entry, only defining a single time entry and 3D spatial positioning parameters. Other classes inherit from this base class; several classes for input ICARTT instrument files, which contain the necessary flight positioning information as a basis for data processing, as well as other classes for output ICARTT files, which contain the interpolated model data. Utility classes provide functionality for routine procedures such as: comparing field names among ICARTT files, reading ICARTT entries from a data file and storing them in data structures, and returning a reduced spatial grid based on a collection of ICARTT entries. Although the GMI-IPS is compatible with GMI model data, it can be adapted with reasonable effort for any simulation that creates Hierarchical Data Format (HDF) files. The same can be said of its adaptability to ICARTT files outside of the context of the ATom mission. The GMI-IPS contains just under 30,000 lines of code, eight classes, and a dozen drivers and utility programs. It is maintained with GIT source code management and has been used to deliver processed GMI model data for the ATom campaigns that have taken place to date.

Damon, M. R.↗

DOE OSTI2025

Hybrid learning techniques for scientific data reduction with performance guarantees

The research initiatives supported by the U.S. Department of Energy (DOE) Grant DE-SC0022265 are fundamentally aimed at pioneering advanced machine learning (ML) techniques for scientific data compression within high-performance computing (HPC) environments. This comprehensive body of work addresses the critical challenge posed by the exponential growth of data generated by scientific simulations in domains such as fusion energy, climate modeling, and computational fluid dynamics (CFD). A core objective is to develop compression algorithms that achieve substantial data reduction—often by orders of magnitude—while rigorously ensuring the fidelity of both the primary data (PD) and scientifically crucial derived quantities of interest (QoI). The methodologies deployed under this grant integrate sophisticated deep learning architectures, prominently featuring autoencoders, advanced generative models like conditional diffusion, and hybrid learning techniques. Key innovations include the development of Guaranteed Autoencoders (GAE) and the Guaranteed Conditional Diffusion with Tensor Correction (GCDTC) framework, which provide explicit, instance-level error bounds on reconstructed data. Furthermore, specialized strategies such as nonlinear constraint satisfaction are employed to preserve the integrity of QoI, a vital requirement for the trustworthiness of downstream scientific analyses. This research also focuses on the design and implementation of scalable, GPU-accelerated software pipelines that seamlessly integrate into existing HPC workflows, ensuring both computational efficiency and practical applicability. The CAESAR framework, for example, unifies foundation and generative models to create an adaptive and efficient compression solution for spatio-temporal scientific data. Collectively, these efforts represent a significant advancement in mitigating the scientific data deluge, enabling more effective data management, accelerated scientific discovery, and optimized utilization of HPC resources.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2009

Spatial Modulation Improves Performance in CTIS

Suitably formulated spatial modulation of a scene imaged by a computed-tomography imaging spectrometer (CTIS) has been found to be useful as a means of improving the imaging performance of the CTIS. As used here, "spatial modulation" signifies the imposition of additional, artificial structure on a scene from within the CTIS optics. The basic principles of a CTIS were described in "Improvements in Computed- Tomography Imaging Spectrometry" (NPO-20561) NASA Tech Briefs, Vol. 24, No. 12 (December 2000), page 38 and "All-Reflective Computed-Tomography Imaging Spectrometers" (NPO-20836), NASA Tech Briefs, Vol. 26, No. 11 (November 2002), page 7a. To recapitulate: A CTIS offers capabilities for imaging a scene with spatial, spectral, and temporal resolution. The spectral disperser in a CTIS is a two-dimensional diffraction grating. It is positioned between two relay lenses (or on one of two relay mirrors) in a video imaging system. If the disperser were removed, the system would produce ordinary images of the scene in its field of view. In the presence of the grating, the image on the focal plane of the system contains both spectral and spatial information because the multiple diffraction orders of the grating give rise to multiple, spectrally dispersed images of the scene. By use of algorithms adapted from computed tomography, the image on the focal plane can be processed into an image cube a three-dimensional collection of data on the image intensity as a function of the two spatial dimensions (x and y) in the scene and of wavelength (lambda). Thus, both spectrally and spatially resolved information on the scene at a given instant of time can be obtained, without scanning, from a single snapshot; this is what makes the CTIS such a potentially powerful tool for spatially, spectrally, and temporally resolved imaging. A CTIS performs poorly in imaging some types of scenes in particular, scenes that contain little spatial or spectral variation. The computed spectra of such scenes tend to approximate correct values to within acceptably small errors near the edges of the field of view but to be poor approximations away from the edges. The additional structure imposed on a scene according to the present method enables the CTIS algorithms to reconstruct acceptable approximations of the spectral data throughout the scene.

Bearman, Gregory H.↗

NASA NTRS1992

Methodologies for building robust schedules

COMPASS is the name of a Computer Aided Scheduling System designed and built for NASA. COMPASS can be used to develop schedule of activities based upon the temporal relationships of the activities and their resource requirements. COMPASS uses this information, and guided by the user, develops precise start and stop times for the activities. In actual practice however, it is impossible to know with complete certainty what the actual durations of the scheduled activities will really be. The best that one can hope for is knowledge of the probability distribution for the durations. This paper investigates methodologies for using a scheduling tool like COMPASS that is based upon definite values for the resource requirements, while building schedules that remain valid in the face of the schedule execution perturbations. Representations for the schedules developed by these methodologies are presented, along with a discussion of the algorithm that could be used by a computer onboard a spacecraft to efficiently monitor and execute these schedules.

Dean, John H.↗

DOE OSTI2024

Enriching OpenStreetMap network data for transportation applications: Insights into the impact of urban congestion on accessibility

OpenStreetMap (OSM) data is a valuable open-source resource for various transportation, traffic, and planning applications. However, OSM network data lack operating traffic speed information, which is critical for transport planning and operations. Addressing this shortcoming, this study leverages commercial vendor data (to serve as ground truth) with exogenous, open-source variables characterizing local transport infrastructure, land use, and demographic information to predict average congested traffic speeds on OSM networks. Three machine-learning models were tested and estimated for OSM links with and without speed limit information in the Denver metropolitan region. Among these, XGBoost performed best, with mean absolute errors of 3.27 and 3.62 mph for links with and without speed limits, respectively. The developed models accurately predicted traffic speeds for different hours and days of the week compared to ground truth data. Using these predicted speeds, drive accessibility scores were computed for the Denver region for different time periods using the Mobility Energy Productivity (MEP) metric to understand the impact of congestion on energy-efficient accessibility. Results show that congestion-adjusted drive accessibility can be significantly lower compared to accessibility calculated using free flow speeds. Specifically, weekday evening hours saw a 42 % drop in accessibility due to reduced speeds, particularly around downtown Denver. Across the Denver metro region, approximately half as many opportunities and jobs are accessible in under 20 min by car during the evening peak period relative to free flow conditions. These findings underscore the importance of using congestion-adjusted operating speeds rather than speed limits in accessibility calculations, as reliance on speed limits can substantially overestimate energy-efficient drive accessibility in large, car-centric cities susceptible to significant congestion. In conclusion, the methodology presented here could further enrich OSM network data, making them useful for an even broader range of transportation applications.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2025

FLAMES─Fast, Low-Storage, Accurate, and Memory-Efficient Adaptive Sampling─Approach to Resolve Spatially Dependent Dynamics of Molecular Liquids

Many critical phenomena in soft matter occur at large length scales, necessitating the resolution of their structure and dynamics at low wavenumbers. However, resolving wavenumber-dependent dynamics computationally via molecular dynamics simulations presents significant challenges, as these phenomena span several orders of magnitude in both time and length scales, resulting in high computational costs and memory demands. Here, this work highlights the computational and memory challenges associated with analyzing molecular trajectories in reciprocal space and demonstrates a method to address them. We introduce FLAMESFast, Low-storage, Accurate, and Memory-Efficient adaptive Sampling, which is a direct method for calculation of structure factors, allowing us to select only the required number of wavevectors for binning. We also use wavenumber-dependent time steps to extract dynamics. Our FLAMES approach effectively mitigates computational and memory/storage bottlenecks. We demonstrate the method using simulations of a model system, liquid octane, at various temperatures. Comparisons with experimental data and real space computation show that the FLAMES technique achieves high accuracy in resolving temperature- and spatially dependent dynamics while being significantly more computationally efficient and requiring less memory and storage than methods based on a uniform wavevector grid and fixed temporal spacing.

Chen, Guang [Argonne National Laboratory (ANL), Ar↗

DOE OSTI2024

Spatiotemporally Registered In-Situ and Ex-Situ Datasets for Laser-based Blown Powder Directed Energy Deposition

This dataset is comprised of in situ sensing data collected during laser-based, blown powder directed energy deposition (DED) of Inconel 718 representing eight different printing conditions: (1) nominal, (2) +15% scan speed, (3) +12% laser power, (4) +42% powder feed rate, (5) +100% jerk limit, (6) +10% layer height, (7) +20% hatch spacing, (8) +20% carrier gas flow. All eight DED builds constructed an identical test coupon geometry consisting of geometric features representative of industrial print requirements (e.g., bulk deposition, thin walls, overhangs). In situ data consists of xyz-coordinates (100 Hz) and on-axis melt pool camera video (60 Hz), both of which have been temporally synchronized to spatially map the melt pool camera data. In addition, post-build X-ray computed tomography (XCT) data for each of the eight test geometries have been spatially registered to the recorded xyz-coordinates, allowing for comparisons between melt pool camera data and flaws identified in the XCT data.

additive manufacturing↗

DOE OSTI2025

Modeling detonation with CartaBlanca simulations

The accurate modeling of high explosive (HE) detonation and the con- sequent large solid deformation, failure, plastic flow, porosity growth, and shock wave propagation is important because simulations can capture spatial and temporal features that experimental diagnostics cannot capture. However, the simulation of the explosive event poses challenges to a computational scientist. These include the accurate modeling of ductile damage, crack formation, plastic deformation, as well as physical and nu- merical instabilities. The material response can be history-dependent and subject to large material deformation. Our research simulates the impact of a high explosive (Detasheet) onto a tantulum metal plate. We performed the simulations using CartaBlanca at different mesh resolutions. We decided the study would be impactful if we perform the simulations with the Material Point Method. Differences were observed at the different mesh resolutions in velocity and nodal stress magnitude, so increased mesh resolutions may be required. In addition, the Discontinuous Galerkin method would be needed to account for the large gas expansion.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Final report- UFL - RAPIDS2: A SciDAC Institute for Computer Science, Data, and Artificial Intelligence

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1991

Automated multisensor registration - Requirements and techniques

The synergistic utilization of data from a suite of remote sensors requires multi-dimensional analysis of the data. Prior to this analysis, processing is required to correct for the systematic geometric distortions characteristic of each sensor, followed by a registration operation to remove any residual offsets. Furthermore, to handle a large volume of data and high data rates, the registration process must be fully automated. A conceptual approach is presented that integrates a variety of registration techniques and selects the candidate algorithm based on certain performance criteria. The performance requirements for an operational algorithm are formulated given the spatially, temporally, and spectrally varying factors that influence the image characteristics and the science requirements of various applications. Several computational techniques are tested and their performance evaluated using a multisensor test data set assembled from the Landsat TM, Seasat, SIR-B, TIMS, and SPOT sensors. The results are discussed and recommendations for future studies are given.

Rignot, Eric J. M.↗

NASA NTRS1994

Analyses and forecasts with LAWS winds

Horizontal fluxes of atmospheric water vapor are studied for summer months during 1989 and 1992 over North and South America based on analyses from European Center for Medium Range Weather Forecasts, US National Meteorological Center, and United Kingdom Meteorological Office. The calculations are performed over 20 deg by 20 deg box-shaped midlatitude domains located to the east of the Rocky Mountains in North America, and to the east of the Andes Mountains in South America. The fluxes are determined from operational center gridded analyses of wind and moisture. Differences in the monthly mean moisture flux divergence determined from these analyses are as large as 7 cm/month precipitable water equivalent over South America, and 3 cm/month over North America. Gridded analyses at higher spatial and temporal resolution exhibit better agreement in the moisture budget study. However, significant discrepancies of the moisture flux divergence computed from different gridded analyses still exist. The conclusion is more pessimistic than Rasmusson's estimate based on station data. Further analysis reveals that the most significant sources of error result from model surface elevation fields, gaps in the data archive, and uncertainties in the wind and specific humidity analyses. Uncertainties in the wind analyses are the most important problem. The low-level jets, in particular, are substantially different in the different data archives. Part of the reason for this may be due to the way the different analysis models parameterized physical processes affecting low-level jets. The results support the inference that the noise/signal ratio of the moisture budget may be improved more rapidly by providing better wind observations and analyses than by providing better moisture data.

Wang, Muyin↗

NASA NTRS2000

Numerical Solutions to the Third CAA Workshop Benchmark Problems

This paper presents numerical solutions to the problems of propagation of sound waves through a transonic nozzle, shock-sound interactions, and automobile noise involving feedback of the third NASA Computational Aeroacoustics (CAA) Workshop on benchmark problems. The numerical algorithm is based on a dual time scheme for temporal discretization and a third-order finite volume scheme for spatial discretization. The aims of this study are to apply a dual time stepping scheme to treat aeroacoustic problems of sound propagation and to validate our CAA solver with the benchmark problems for developing a numerical tool for noise analysis and control.

Loh, Roy H.↗