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NASA NTRSDate not supplied

Development and Integration of a Thermal Management Simulation for a Quadrotor Parallel Hybrid Propulsion System

This paper details the development of a propulsion system simulation for a six-passenger parallel hybrid quadrotor and utilizes the Numerical Propulsion System Simulation (NPSS) along with the NPSS Power System Library as the development environment. This simulation integrates an engine power plant with an electrical generation and distribution system and includes the required thermal management system. The thermal management system is comprised of liquid cooling loops that reject the heat load through air to coolant heat exchangers and utilizes a map-based performance estimation method. This method is developed within NPSS and detailed in this paper. The full system model is designed to predict system weight, range, and performance through a proposed mission profile. Results of the paper show an all-engine system maintains the best range, while a mostly electric system that utilizes an engine as a backup or a conditional power contributor offers range benefit.

Vertical lift and take off vehicle↗
NASA NTRS2022

Thermal Imaging of Dust Hiding the Black Hole in NGC 1068

In the widely accepted ‘unified model’1 solution of the classification puzzle of active galactic nuclei, the orientation of a dusty accretion torus around the central black hole dominates their appearance. In ‘type-1’ systems, the bright nucleus is visible at the centre of a face-on torus. In ‘type-2’ systems the thick, nearly edge-on torus hides the central engine. Later studies suggested evolutionary effects2 and added dusty clumps and polar winds3 but left the basic picture intact. However, recent high-resolution images4 of the archetypal type-2 galaxy NGC 10685,6, suggested a more radical revision. The images displayed a ring-like emission feature that was proposed to be hot dust surrounding the black hole at the radius where the radiation from the central engine evaporates the dust. That ring is too thin and too far tilted from edge-on to hide the central engine, and ad hoc foreground extinction is needed to explain the type-2 classification. These images quickly generated reinterpretations of the dichotomy between types 1 and 27,8. Here we present new multi-band mid-infrared images of NGC 1068 that detail the dust temperature distribution and reaffirm the original model. Combined with radio data ( J.F.G. and C.M.V.I., manuscript in preparation), our maps locate the central engine that is below the previously reported ring and obscured by a thick, nearly edge-on disk, as predicted by the unified model. We also identify emission from polar flows and absorbing dust that is mineralogically distinct from that towards the Milky Way centre.

Violeta Gamez Rosas↗
NASA NTRS2021

Assessment of M2020 Terrain Relative Landing Accuracy: Flight Performance vs Predicts

Terrain Relative Navigation (TRN) was a critical enabling Entry, Descent, and Landing (EDL) technology that enabled Mars 2020 mission Perseverance rover to land at Jezero crater. TRN pro-vides real-time, autonomous, map-relative position determination and generates a landing target based on a priori knowledge of hazards. The required performance for TRN was to land within 60m of the selected target. The required 60m was sub-allocated to various error sources in three major categories: targeting error, knowledge error, and control error. The targeting error is the error in selecting an appropriate landing target and the knowledge of the target on the surface. It includes the Lander Vision System (LVS) position localization with respect the ground, the synchronization between the Lander Vision System measurement and the main Navigation filter, and errors associated with the LVS Reference Map and Safe Target Selec-tion (STS). The knowledge error is the contribution of knowledge growth from the synchronization with LVS to touchdown. The control error encompasses how accurately the system could stay on the desired reference trajectory. The TRN error budget uses a combination of analysis, simulation, and hardware test-ing results to bound the various error contributions obtained during the verification and validation process. This paper first presents a description the TRN system, focusing on the architecture of LVS and STS. The paper then gives detailed overview of the TRN error budget, with a description of the major error contribu-tions in each of the three categories. Next, the paper gives the results for three versions of the error budget, pre-launch, in-flight pre-landing, and post-landing. The paper compares the pre-flight analysis, the pre-landing analysis using in-flight data during cruise, to the post-landing analysis of the TRN performance. Pre-landing analysis best estimate of the landing performance was 33m, compared to the 60m require-ment. Post-landing analysis estimated a landing accuracy of 8.53m or better, much better than the 33m pre-landing estimate. The actual post-landing imagery calculated the distance of the rover to the targeted location to be 5m. The post-landing analysis closely bounds the image-based assessment of landing accu-racy, indicating the success of the error budget architecture in bounding the landing accuracy, as well as the fidelity of the simulations used to model and predict performance.

Chen, Allen↗
NASA NTRS1977

Analytical prediction of the performance and stability of a J85-13 compressor with distorted inlet flow

The parallel compressor concept was studied using a compressor model based on the overall clean-inlet performance map obtained from experimental tests in an altitude chamber using a General Electric J85-13 turbojet engine. The model, which includes a static-pressure balance calculation at compressor discharge, was exercised at conditions corresponding to 10 different screen-induced distortion patterns included in the experimental data base. The spoiled area of these patterns ranged from 30 deg to 180 deg, and the distortion screen density, or the area blocked by the screen wire per unit area of screen, varied from 26 to 69 percent. The study indicates that at the higher corrected speeds, the analytical surge lines obtained are good representations of the corresponding experimental surge lines and are independent of distortion angle or distortion angle or distortion level.

Milner, E. J.↗
NASA NTRS2001

Evidence of Stratosphere-to-Troposphere Transport Within a Mesoscale Model and Total Ozone Mapping Spectrometer Total Ozone

We evaluate evidence for stratospheric mass transport into, and mass remaining in, the troposphere during an intense midlatitude cyclone. Mesoscale forecast model analysis fields from the Mesoscale Analysis and Prediction System were matched with total ozone observations from the Total Ozone Measurement Spectrometer. Combined with parcel back trajectory calculations, the analyses imply that two mechanisms contributed to the mass exchange: (1) An area of dynamically induced exchange was observed on the cyclone's southern edge. Parcels originally in the stratosphere crossed the jet core and were diluted through turbulent mixing with tropospheric air; (2) Diabetic effects reduced parcel potential vorticity (PC) for trajectories traversing precipitation regions, creating a 'PV hole' signature in the center of the cyclone. Air with characteristics of ozone and water vapor found in the lower stratosphere remained in the troposphere. The strength of the latter process may be unusual. Combined with other research, these results suggest that precipitation-induced diabetic effects can significantly modify (either decreasing or increasing) parcel potential vorticity, depending on parcel trajectory configuration with respect to maximum heating regions and jet core. The diabetic heating effect on stratosphere-troposphere exchange (STE) is more important to tropopause erosion than to altering parcel trajectories. In addition, these results underline the importance of using not only PC but also chemical constituents for diagnoses of STE.

Olsen, Mark A.↗
NASA NTRS1997

Design Protocols and Analytical Strategies that Incorporate Structural Reliability Models

Ceramic matrix composites (CMC) and intermetallic materials (e.g., single crystal nickel aluminide) are high performance materials that exhibit attractive mechanical, thermal, and chemical properties. These materials are critically important in advancing certain performance aspects of gas turbine engines. From an aerospace engineers perspective the new generation of ceramic composites and intermetallics offers a significant potential for raising the thrust/weight ratio and reducing NO(sub x) emissions of gas turbine engines. These aspects have increased interest in utilizing these materials in the hot sections of turbine engines. However, as these materials evolve and their performance characteristics improve a persistent need exists for state-of-the-art analytical methods that predict the response of components fabricated from CMC and intermetallic material systems. This need provided the motivation for the technology developed under this research effort. Continuous ceramic fiber composites exhibit an increase in work of fracture, which allows for 'graceful' rather than catastrophic failure. When loaded in the fiber direction these composites retain substantial strength capacity beyond the initiation of transverse matrix cracking despite the fact that neither of its constituents would exhibit such behavior if tested alone. As additional load is applied beyond first matrix cracking, the matrix tends to break in a series of cracks bridged by the ceramic fibers. Any additional load is born increasingly by the fibers until the ultimate strength of the composite is reached. Thus modeling efforts supported under this research effort have focused on predicting this sort of behavior. For single crystal intermetallics the issues that motivated the technology development involved questions relating to material behavior and component design. Thus the research effort supported by this grant had to determine the statistical nature and source of fracture in a high strength, NiAl single crystal turbine blade material; map a simplistic future strength envelope of the material; develop a statistically based reliability computer algorithm; verify the reliability model and computer algorithm-, and model stator vanes for rig tests. Thus establishing design protocols that enable the engineer to analyze and predict the mechanical behavior of ceramic composites and intermetallics would mitigate the prototype (trial and error) approach currently used by the engineering community. The primary objective of the research effort supported by this short term grant is the continued creation of enabling technologies for the macro-analysis of components fabricated from ceramic composites and intermetallic material systems. The creation of enabling technologies aids in shortening the product development cycle of components fabricated from the new high technology materials.

Duffy, Stephen F.↗
NASA NTRS1997

Design Protocols and Analytical Strategies that Incorporate Structural Reliability Models

Ceramic matrix composites (CMC) and intermetallic materials (e.g., single crystal nickel aluminide) are high performance materials that exhibit attractive mechanical, thermal and chemical properties. These materials are critically important in advancing certain performance aspects of gas turbine engines. From an aerospace engineer's perspective the new generation of ceramic composites and intermetallics offers a significant potential for raising the thrust/weight ratio and reducing NO(x) emissions of gas turbine engines. These aspects have increased interest in utilizing these materials in the hot sections of turbine engines. However, as these materials evolve and their performance characteristics improve a persistent need exists for state-of-the-art analytical methods that predict the response of components fabricated from CMC and intermetallic material systems. This need provided the motivation for the technology developed under this research effort. Continuous ceramic fiber composites exhibit an increase in work of fracture, which allows for "graceful" rather than catastrophic failure. When loaded in the fiber direction, these composites retain substantial strength capacity beyond the initiation of transverse matrix cracking despite the fact that neither of its constituents would exhibit such behavior if tested alone. As additional load is applied beyond first matrix cracking, the matrix tends to break in a series of cracks bridged by the ceramic fibers. Any additional load is born increasingly by the fibers until the ultimate strength of the composite is reached. Thus modeling efforts supported under this research effort have focused on predicting this sort of behavior. For single crystal intermetallics the issues that motivated the technology development involved questions relating to material behavior and component design. Thus the research effort supported by this grant had to determine the statistical nature and source of fracture in a high strength, NiAl single crystal turbine blade material; map a simplistic failure strength envelope of the material; develop a statistically based reliability computer algorithm, verify the reliability model and computer algorithm, and model stator vanes for rig tests. Thus establishing design protocols that enable the engineer to analyze and predict the mechanical behavior of ceramic composites and intermetallics would mitigate the prototype (trial and error) approach currently used by the engineering community. The primary objective of the research effort supported by this short term grant is the continued creation of enabling technologies for the macroanalysis of components fabricated from ceramic composites and intermetallic material systems. The creation of enabling technologies aids in shortening the product development cycle of components fabricated from the new high technology materials.

Duffy, Stephen F.↗
NASA NTRS2024

A High-Performance Computing Predictive GNSS Performance Monitor for Autonomous Air Vehicles in Urban Environments

This report offers analysis and design insights for leveraging High-Performance Computing (HPC) to predict line-of-sight (LOS) Global Navigation Satellite System (GNSS) availability in a city. This work is motivated by the emerging fields of Advanced and Urban Air Mobility (AAM/UAM), where regulatory authorities are seeking city-scale, meter-resolution risk forecasting in order to safely integrate new flight missions with existing urban life and infrastructure. This work addresses the technical challenge of efficiently computing urban GNSS satellite visibility to predict GNSS performance metrics under these requirements. We present a new HPC-optimized shadow casting algorithm variant as a ray-based approach to forecasting satellite visibility. We apply this algorithm variant in a software-defined prognostic service which generates a GNSS navigation risk-correlated map as a path planning-style potential field. We detail dominant computational burdens, viable simplifying assumptions, and different algorithmic implementations, intending to demonstrate a baseline of computation time needed by each stage in such a service. We conclude by analyzing the prototype service’s prediction accuracy compared to receiver data from Corpus Christi, Texas. This informs design trade-offs along the dimensions of hardware, computation time, and tolerable forecasting error (including proportions of false positives and false negatives).

GNSS↗
NASA NTRS2021

Argentina Food Security & Agriculture: Crop Monitoring and Forecasting for Argentina using NASA Satellite Observations

Early harvest information helps guide agricultural commodity assessments in Argentina, providing valuable planning information to identify potentially food-insecure regions, anticipate transportation and storage demands, predict price fluctuations, and project commodity trends. However, crop yield estimates are currently subjective, based on interviews with qualified informants (i.e., farmers, agribusiness actors). In partnership with the Buenos Aires Grain Exchange, we leveraged Terra Moderate Resolution Imaging Spectroradiometer (MODIS), Soil Moisture Active Passive (SMAP), and Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (GPM IMERG) NASA Earth observations to develop a Google Earth Engine (GEE) toolset to monitor vegetation growth. The first component of the toolset produces spatial and temporal maps of temperature, precipitation, soil moisture, and the Normalized Difference Vegetation Index (NDVI), allowing users to visualize the influence of the region’s climate and weather. Next, we developed an autoregressive model to predict NDVI several months in advance. Lastly, we created a linear regression model of crop yield and NDVI for soybeans, corn, and wheat, and input the forecasted NDVI to generate a predicted crop yield output. The NDVI forecasting model produced accurate predictions at two, four, and six months when examining the most recent growing season. In the crop yield model, soybeans exhibited moderately strong correlation, wheat had consistent weak correlation, and corn varied from weak to strong correlation depending on zone. This information is vital for vegetation growth monitoring by identifying areas of high growth and allocating resources to areas of lower growth to efficiently maximize crop yields.

DEVELOP Tech Paper↗
NASA NTRS2005

Analysis of Multiple Precipitation Products and Preliminary Assessment of Their Impact on Global Land Data Assimilation System (GLDAS) Land Surface States

Land surface models (LSMs) are computer programs, similar to weather and climate prediction models, which simulate the stocks and fluxes of water (including soil moisture, snow, evaporation, and runoff) and energy (including the temperature of and sensible heat released from the soil) after they arrive on the land surface as precipitation and sunlight. It is not currently possible to measure all of the variables of interest everywhere on Earth with sufficient accuracy and space-time resolution. Hence LSMs have been developed to integrate the available observations with our understanding of the physical processes involved, using powerful computers, in order to map these stocks and fluxes as they change in time. The maps are used to improve weather forecasts, support water resources and agricultural applications, and study the Earth's water cycle and climate variability. NASA's Global Land Data Assimilation System (GLDAS) project facilitates testing of several different LSMs with a variety of input datasets (e.g., precipitation, plant type). Precipitation is arguably the most important input to LSMs. Many precipitation datasets have been produced using satellite and rain gauge observations and weather forecast models. In this study, seven different global precipitation datasets were evaluated over the United States, where dense rain gauge networks contribute to reliable precipitation maps. We then used the seven datasets as inputs to GLDAS simulations, so that we could diagnose their impacts on output stocks and fluxes of water. In terms of totals, the Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP) had the closest agreement with the US rain gauge dataset for all seasons except winter. The CMAP precipitation was also the most closely correlated in time with the rain gauge data during spring, fall, and winter, while the satellitebased estimates performed best in summer. The GLDAS simulations revealed that modeled soil moisture is highly sensitive to precipitation, with differences in spring and summer as large as 45% depending on the choice of precipitation input.

Gottschalck, Jon↗
NASA NTRS2004

On Nonlinear Combustion Instability in Liquid Propellant Rocket Motors

All liquid propellant rocket instability calculations in current use have limited value in the predictive sense and serve mainly as a correlating framework for the available data sets. The well-known n-t model first introduced by Crocco and Cheng in 1956 is still used as the primary analytical tool of this type. A multitude of attempts to establish practical analytical methods have achieved only limited success. These methods usually produce only stability boundary maps that are of little use in making critical design decisions in new motor development programs. Recent progress in understanding the mechanisms of combustion instability in solid propellant rockets"' provides a firm foundation for a new approach to prediction, diagnosis, and correction of the closely related problems in liquid motor instability. For predictive tools to be useful in the motor design process, they must have the capability to accurately determine: 1) time evolution of the pressure oscillations and limit amplitude, 2) critical triggering pulse amplitude, and 3) unsteady heat transfer rates at injector surfaces and chamber walls. The method described in this paper relates these critical motor characteristics directly to system design parameters. Inclusion of mechanisms such as wave steepening, vorticity production and transport, and unsteady detonation wave phenomena greatly enhance the representation of key features of motor chamber oscillatory behavior. The basic theoretical model is described and preliminary computations are compared to experimental data. A plan to develop the new predictive method into a comprehensive analysis tool is also described.

Sims, J. D.↗
NASA NTRS2001

AVIRIS Land-Surface Mapping in Support of the Boreal Ecosystem-Atmosphere Study (BOREAS)

A key scientific objective of the original Boreal Ecosystem-Atmospheric Study (BOREAS) field campaign (1993-1996) was to obtain the baseline data required for modeling and predicting fluxes of energy, mass, and trace gases in the boreal forest biome. These data sets are necessary to determine the sensitivity of the boreal forest biome to potential climatic changes and potential biophysical feedbacks on climate. A considerable volume of remotely-sensed and supporting field data were acquired by numerous researchers to meet this objective. By design, remote sensing and modeling were considered critical components for scaling efforts, extending point measurements from flux towers and field sites over larger spatial and longer temporal scales. A major focus of the BOREAS follow-on program is concerned with integrating the diverse remotely sensed and ground-based data sets to address specific questions such as carbon dynamics at local to regional scales. The Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) has the potential of contributing to BOREAS through: (1) accurate retrieved apparent surface reflectance; (2) improved landcover classification; and (3) direct assessment of biochemical/biophysical information such as canopy liquid water and chlorophyll concentration through pigment fits. In this paper, we present initial products for major flux tower sites including: (1) surface reflectance of dominant cover types; (2) a land-cover classification developed using spectral mixture analysis (SMA) and Multiple Endmember Spectral Mixture Analysis (MESMA); and (3) liquid water maps. Our goal is to compare these land-cover maps to existing maps and to incorporate AVIRIS image products into models of photosynthetic flux.

Roberts, Dar A.↗
NASA NTRS2001

Investigating Uncertainty in Predicting Carbon Dynamics in North American Biomes: Putting Support-Effect Bias in Perspective

A fundamental strategy in NASA's Earth Observing System's (EOS) monitoring of vegetation and its contribution to the global carbon cycle is to rely on deterministic, process-based ecosystem models to make predictions of carbon flux over large regions. These models are parameterized (that is, the input variables are derived) using remotely sensed images such as those from the Moderate Resolution Imaging Spectroradiometer (MODIS), ground measurements and interpolated maps. Since early applications of these models, investigators have noted that results depend partly on the spatial support of the input variables. In general, the larger the support of the input data, the greater the chance that the effects of important components of the ecosystem will be averaged out. A review of previous work shows that using large supports can cause either positive or negative bias in carbon flux predictions. To put the magnitude and direction of these biases in perspective, we must quantify the range of uncertainty on our best measurements of carbon-related variables made on equivalent areas. In other words, support-effect bias should be placed in the context of prediction uncertainty from other sources. If the range of uncertainty at the smallest support is less than the support-effect bias, more research emphasis should probably be placed on support sizes that are intermediate between those of field measurements and MODIS. If the uncertainty range at the smallest support is larger than the support-effect bias, the accuracy of MODIS-based predictions will be difficult to quantify and more emphasis should be placed on field-scale characterization and sampling. This talk will describe methods to address these issues using a field measurement campaign in North America and "upscaling" using geostatistical estimation and simulation.

Dungan, Jennifer L.↗
NASA NTRS2011

Project Management Using Modern Guidance, Navigation and Control Theory

Implementing guidance, navigation, and control (GN&C) theory principles and applying them to the human element of project management and control is not a new concept. As both the literature on the subject and the real-world applications are neither readily available nor comprehensive with regard to how such principles might be applied, this paper has been written to educate the project manager on the "laws of physics" of his or her project (not to teach a GN&C engineer how to become a project manager) and to provide an intuitive, mathematical explanation as to the control and behavior of projects. This paper will also address how the fundamental principles of modern GN&C were applied to the National Aeronautics and Space Administration's (NASA) Constellation Program (CxP) space suit project, ensuring the project was managed within cost, schedule, and budget. A project that is akin to a physical system can be modeled and managed using the same over arching principles of GN&C that would be used if that project were a complex vehicle, a complex system(s), or complex software with time-varying processes (at times nonlinear) containing multiple data inputs of varying accuracy and a range of operating points. The classic GN&C theory approach could thus be applied to small, well-defined projects; yet when working with larger, multiyear projects necessitating multiple organizational structures, numerous external influences, and a multitude of diverse resources, modern GN&C principles are required to model and manage the project. The fundamental principles of a GN&C system incorporate these basic concepts: State, Behavior, Feedback Control, Navigation, Guidance and Planning Logic systems. The State of a system defines the aspects of the system that can change over time; e.g., position, velocity, acceleration, coordinate-based attitude, and temperature, etc. The Behavior of the system focuses more on what changes are possible within the system; this is denoted in the state of the system. The behavior of a system, as captured in the system modeling, when properly done will aid in accurately predicting future system performance. The Feedback Control system understands the state and behavior of the system and uses feedback to adjust control inputs into the system. The feedback, which is the right arm of the Control system, allows change to be affected in the overall system; it therefore is important to not only correctly identify the system feedback inputs, but also the system response to the feedback inputs. The Navigation system takes multiple data inputs and based on a priori knowledge of the inputs, develops a statistically based weighting of the inputs and measurements to determine the system's state. Guidance and Planning Logic of the system, complete with an understanding of where the system is (provided by the Navigation system), will in turn determine where the system needs to be and how to get it there. With any system/project, it is critical that the objective of the system/project be clearly defined -- not only to plan but to measure performance and to aid in guiding the system or the project. The system principles discussed above, which can be and have been applied to the current CxP space suit development project, can also be mapped to real-world constituents, thus allowing project managers to apply systems theories that are well defined in engineering and mathematics to a discipline (i.e., Project Management) that historically has been based in personal experience and intuition. This mapping of GN&C theory to Project Management will, in turn, permit a direct, methodical approach to Project Management, planning and control providing a tool to help predict (and guide) performance and an understanding of the project constraints, how the project can be controlled, and the impacts to external influences and inputs. This approach, to a project manager, flows down to the three bottom-line variables of cost, schedule, and scope ando the needed control of these three variables to successfully perform and complete a project.

Hill, Terry R.↗
NASA NTRS2014

Development of Web Mapping Service Capabilities to Support NASA Disasters Applications/App Development

During the last year several significant disasters have occurred such as Superstorm Sandy on the East coast of the United States, and Typhoon Bopha in the Phillipines, along with several others. In support of these disasters NASA's Short‐term Prediction Research and Transition (SPoRT) Center delivered various products derived from satellite imagery to help in the assessment of damage and recovery of the affected areas. To better support the decision makers responding to the disasters SPoRT quickly developed several solutions to provide the data using open Geographical Information Service (GIS) formats. Providing the data in open GIS standard formats allowed the end user to easily integrate the data into existing Decision Support Systems (DSS). Both Tile Mapping Service (TMS) and Web Mapping Service (WMS) were leveraged to quickly provide the data to the end‐user. Development of the deliver methodology allowed quick response to rapidly developing disasters and enabled NASA SPoRT to bring science data to decision makers in a successful research to operations transition.

Burks, Jason E.↗
NASA NTRS1973

Thunderstorms and ground-based radio noise as observed by radio astronomy Explorer 1

Radio Astronomy Explorer (RAE) data were analyzed to determine the frequency dependence of HF terrestrial radio noise power. RAE observations of individual thunderstorms, mid-ocean areas, and specific geographic regions for which concommitant ground based measurements are available indicate that noise power is a monotonically decreasing function of frequency which conforms to expectations over the geographic locations and time periods investigated. In all cases investigated, active thunderstorm regions emit slightly higher power as contrasted to RAE observations of the region during meteorologically quiet periods. Noise levels are some 15 db higher than predicted values over mid-ocean, while in locations where ground based measurements are available a maximum deviation of 5 db occurs. Worldwide contour mapping of the noise power at 6000 km for five individual months and four observing frequencies, examples of which are given, indicate high noise levels over continental land masses with corresponding lower levels over ocean regions.

Caruso, J. A.↗
NASA NTRS1975

The use of satellite data for regional planning

The experience of the Ohio-Kentucky-Indiana Regional Council of Governments in its development of a regional land use inventory from computer processing of LANDSAT 1 digital tapes and the use of those data in the OKI water quality planning program are discussed. A major part of the planning program is the prediction of water quality in rivers and lakes resulting from existing and future land uses. A model has been developed that can predict the flow of sediment, total phosphorus, total nitrogen, and organic wastes into major streams. An essential input to this model is an accurate map of land use derived from LANDSAT 1 digital tapes.

Hessling, A. H.↗
NASA NTRS1979

An explicit algorithm for a fluid approach to nonlinear optics propagation using splitting and rezoning techniques

The paper presents a three-dimensional analysis of the nonlinear light matter interaction in a hydrodynamic context. It is reported that the resulting equations are a generalization of the Navier-Stokes equations subjected to an internal potential which depends solely upon the fluid density. In addition, three numerical approaches are presented to solve the governing equations using an extension of McCormack predict-corrector scheme. These are a uniform grid, a dynamic rezoned grid, and a splitting technique. It is concluded that the use of adaptive mapping and splitting techniques with McCormack two-level predictor-corrector scheme results in an efficient and reliable code whose storage requirements are modest compared with other second order methods of equal accuracy.

Mattar, F. P.↗