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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Optical attenuation mechanism upgrades, MOBLAS, and TLRS systems

This poster presentation describes the Optical Attenuation Mechanism (OAM) Upgrades to the MOBLAS and TLRS Crustal Dynamics Satellite Laser Ranging (CDSLR) systems. The upgrades were for the purposes of preparing these systems to laser range to the TOPEX/POSEIDON spacecraft when it will be launched in the summer of 1992. The OAM permits the laser receiver to operate over the expected large signal dynamic range from TOPEX/POSEIDON and it reduces the number of pre- and post-calibrations for each satellite during multi-satellite tracking operations. It further simplifies the calibration bias corrections that had been made due to the pass-to-pass variation of the photomultiplier supply voltage and the transmit filter glass thickness. The upgrade incorporated improvements to the optical alignment capability of each CDSLR system through the addition of a CCD camera into the MOBLAS receive telescope and an alignment telescope onto the TLRS optical table. The OAM is stepper motor and microprocessor based; and the system can be controlled either manually by a control switch panel or computer controlled via an EIA RS-232C serial interface. The OAM has a neutral density (ND) range of 0.0 to 4.0 and the positioning is absolute referenced in steps of 0.1 ND. Both the fixed transmit filter and the daylight filter are solenoid actuated with digital inputs and outputs to and from the OAM microprocessor. During automated operation, the operator has the option to overide the remote control and control the OAM system via a local control switch panel.

Eichinger, Richard↗
NASA NTRS1985

Monte Carlo simulations in support of the Shuttle upper atmospheric mass spectrometer experiment

This paper presents the results of calculations obtained with a Direct Simulation Monte Carlo (DSMC) method that describes both the external flow about the nose region of the Shuttle Orbiter and the internal flow in an inlet tube that provides the initial path between the shock-processed gases and a mass spectrometer mounted inside the Orbiter. A dedicated, three-dimensional version of the DSMC was developed during this study for the internal flow simulation along with the procedure for interfacing the external and internal flows. The calculations span the 140 to 95 km altitude range, which includes most of the hypersonic transitional flow encountered during reentry. All calculations were for a multicomponent gas mixture consisting of five chemical species while simulating the effects of transitional, rotational, vibrational, and chemical nonequilibrium. The results of the calculations show that within the entry region of the inlet tube where the gas has equilibrated with the sidewall tube temperature, the pressure is substantially less than the pressure at the external surface. This pressure correction for the entry region is significant for all conditions investigated and increases with altitude. The results highlight the structure of both the external and internal flow. Results of parametric studies show the sensitivity of the equilibrated inlet sidewall pressure to mass flow rates, gas-surface reflection model, tube side-wall temperature variations, and surface recombinations.

Moss, J. N.↗
NASA NTRS1993

Cavitation Modeling in Euler and Navier-Stokes Codes

Many previous researchers have modeled sheet cavitation by means of a constant pressure solution in the cavity region coupled with a velocity potential formulation for the outer flow. The present paper discusses the issues involved in extending these cavitation models to Euler or Navier-Stokes codes. The approach taken is to start from a velocity potential model to ensure our results are compatible with those of previous researchers and available experimental data, and then to implement this model in both Euler and Navier-Stokes codes. The model is then augmented in the Navier-Stokes code by the inclusion of the energy equation which allows the effect of subcooling in the vicinity of the cavity interface to be modeled to take into account the experimentally observed reduction in cavity pressures that occurs in cryogenic fluids such as liquid hydrogen. Although our goal is to assess the practicality of implementing these cavitation models in existing three-dimensional, turbomachinery codes, the emphasis in the present paper will center on two-dimensional computations, most specifically isolated airfoils and cascades. Comparisons between velocity potential, Euler and Navier-Stokes implementations indicate they all produce consistent predictions. Comparisons with experimental results also indicate that the predictions are qualitatively correct and give a reasonable first estimate of sheet cavitation effects in both cryogenic and non-cryogenic fluids. The impact on CPU time and the code modifications required suggests that these models are appropriate for incorporation in current generation turbomachinery codes.

Deshpande, Manish↗
NASA NTRS2004

Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method

Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented an effective optimization framework that incorporates a direct-CAD interface. In this work, we enhance the capabilities of this framework with efficient gradient computations using the discrete adjoint method. We present details of the adjoint numerical implementation, which reuses the domain decomposition, multigrid, and time-marching schemes of the flow solver. Furthermore, we explain and demonstrate the use of CAD in conjunction with the Cartesian adjoint approach. The final paper will contain a number of complex geometry, industrially relevant examples with many design variables to demonstrate the effectiveness of the adjoint method on Cartesian meshes.

Nemec, Marian↗
NASA NTRS2017

Quantifying Uncertainties in Navigation and Orbit Propagation Analyses

A tool used to calculate dilution of precision (DOP) was created in order to assist the Space Communications and Navigation (SCaN) program to analyze current and future user missions. The SCaN Center for Engineering, Networks, Integration, and Communication (SCENIC) is developing a new user interface (UI) to augment and replace the capabilities of currently used commercial software, such as Systems Tool Kit (STK). The DOP tool will be integrated in the SCENIC UI and will be used to analyze the accuracy of navigation solutions. This tool was developed using MATLAB and free and open-source tools to save cost and to use already existing orbital software libraries. GPS DOP data was collected and used for validation purposes. The similarities between the DOP tool results and GPS data show that the DOP tool is performing correctly. Additional improvements can be made in the DOP tool to improve its accuracy and performance in analyzing navigation solutions.

dilution of precision↗
NASA NTRS2016

Integrating Satellite and Surface Sensor Networks for Irrigation Management Applications in California

Satellite mapping of evapotranspiration (ET) from irrigated agricultural lands can provide agricultural producers and water managers with information that can be used to optimize agricultural water use, especially in regions with limited water supplies. The timely delivery of information on agricultural crop water requirements has the potential to make irrigation scheduling more practical, convenient, and accurate. We present a system for irrigation scheduling and management support in California and describe lessons learned from the development and implementation of the system. The Satellite Irrigation Management Support (SIMS) framework integrates satellite data with information from agricultural weather networks to map crop canopy development, basal crop coefficients (Kcb), and basal crop evapotranspiration (ETcb) at the scale of individual fields. Information is distributed to agricultural producers and water managers via a web-based irrigation management decision support system and web data services. SIMS also provides an application programming interface (API) that facilitates integration with other irrigation decision support tools, estimation of total crop evapotranspiration (ETc) and calculation of on-farm water use efficiency metrics. Accuracy assessments conducted in commercial fields for more than a dozen crop types to date have shown that SIMS seasonal ETcb estimates are within 10 mean absolute error (MAE) for well-watered crops and within 15 across all crop types studied, and closely track daily ETc and running totals of ETc measured in each field. Use of a soil water balance model to correct for soil evaporation and crop water stress reduces this error to less than 8 MAE across all crop types studied to date relative to field measurements of ETc. Results from irrigation trials conducted by the project for four vegetable crops have also demonstrated the potential for use of ET-based irrigation management strategies to reduce total applied water by 20-40 relative to grower standard practices while maintaining crop yields and quality.

Nemani, Ramakrishna R.↗
NASA NTRS1992

StarView: The object oriented design of the ST DADS user interface

StarView is the user interface being developed for the Hubble Space Telescope Data Archive and Distribution Service (ST DADS). ST DADS is the data archive for HST observations and a relational database catalog describing the archived data. Users will use StarView to query the catalog and select appropriate datasets for study. StarView sends requests for archived datasets to ST DADS which processes the requests and returns the database to the user. StarView is designed to be a powerful and extensible user interface. Unique features include an internal relational database to navigate query results, a form definition language that will work with both CRT and X interfaces, a data definition language that will allow StarView to work with any relational database, and the ability to generate adhoc queries without requiring the user to understand the structure of the ST DADS catalog. Ultimately, StarView will allow the user to refine queries in the local database for improved performance and merge in data from external sources for correlation with other query results. The user will be able to create a query from single or multiple forms, merging the selected attributes into a single query. Arbitrary selection of attributes for querying is supported. The user will be able to select how query results are viewed. A standard form or table-row format may be used. Navigation capabilities are provided to aid the user in viewing query results. Object oriented analysis and design techniques were used in the design of StarView to support the mechanisms and concepts required to implement these features. One such mechanism is the Model-View-Controller (MVC) paradigm. The MVC allows the user to have multiple views of the underlying database, while providing a consistent mechanism for interaction regardless of the view. This approach supports both CRT and X interfaces while providing a common mode of user interaction. Another powerful abstraction is the concept of a Query Model. This concept allows a single query to be built form a single or multiple forms before it is submitted to ST DADS. Supporting this concept is the adhoc query generator which allows the user to select and qualify an indeterminate number attributes from the database. The user does not need any knowledge of how the joins across various tables are to be resolved. The adhoc generator calculates the joins automatically and generates the correct SQL query.

Williams, J. D.↗
NASA NTRS1994

A second generation 50 Mbps VLSI level zero processing system prototype

Level Zero Processing (LZP) generally refers to telemetry data processing functions performed at ground facilities to remove all communication artifacts from instrument data. These functions typically include frame synchronization, error detection and correction, packet reassembly and sorting, playback reversal, merging, time-ordering, overlap deletion, and production of annotated data sets. The Data Systems Technologies Division (DSTD) at Goddard Space Flight Center (GSFC) has been developing high-performance Very Large Scale Integration Level Zero Processing Systems (VLSI LZPS) since 1989. The first VLSI LZPS prototype demonstrated 20 Megabits per second (Mbp's) capability in 1992. With a new generation of high-density Application-specific Integrated Circuits (ASIC) and a Mass Storage System (MSS) based on the High-performance Parallel Peripheral Interface (HiPPI), a second prototype has been built that achieves full 50 Mbp's performance. This paper describes the second generation LZPS prototype based upon VLSI technologies.

Harris, Jonathan C.↗
NASA NTRS1994

AI and workflow automation: The prototype electronic purchase request system

Automating 'paper' workflow processes with electronic forms and email can dramatically improve the efficiency of those processes. However, applications that involve complex forms that are used for a variety of purposes or that require numerous and varied approvals often require additional software tools to ensure that (1) the electronic form is correctly and completely filled out, and (2) the form is routed to the proper individuals and organizations for approval. The prototype electronic purchase request (PEPR) system, which has been in pilot use at NASA Ames Research Center since December 1993, seamlessly links a commercial electronics forms package and a CLIPS-based knowledge system that first ensures that electronic forms are correct and complete, and then generates an 'electronic routing slip' that is used to route the form to the people who must sign it. The PEPR validation module is context-sensitive, and can apply different validation rules at each step in the approval process. The PEPR system is form-independent, and has been applied to several different types of forms. The system employs a version of CLIPS that has been extended to support AppleScript, a recently-released scripting language for the Macintosh. This 'scriptability' provides both a transparent, flexible interface between the two programs and a means by which a single copy of the knowledge base can be utilized by numerous remote users.

Compton, Michael M.↗
NASA NTRS2012

Optimization of the Multi-Spectral Euclidean Distance Calculation for FPGA-based Spaceborne Systems

Due to the high quantity of operations that spaceborne processing systems must carry out in space, new methodologies and techniques are being presented as good alternatives in order to free the main processor from work and improve the overall performance. These include the development of ancillary dedicated hardware circuits that carry out the more redundant and computationally expensive operations in a faster way, leaving the main processor free to carry out other tasks while waiting for the result. One of these devices is SpaceCube, a FPGA-based system designed by NASA. The opportunity to use FPGA reconfigurable architectures in space allows not only the optimization of the mission operations with hardware-level solutions, but also the ability to create new and improved versions of the circuits, including error corrections, once the satellite is already in orbit. In this work, we propose the optimization of a common operation in remote sensing: the Multi-Spectral Euclidean Distance calculation. For that, two different hardware architectures have been designed and implemented in a Xilinx Virtex-5 FPGA, the same model of FPGAs used by SpaceCube. Previous results have shown that the communications between the embedded processor and the circuit create a bottleneck that affects the overall performance in a negative way. In order to avoid this, advanced methods including memory sharing, Native Port Interface (NPI) connections and Data Burst Transfers have been used.

Cristo, Alejandro↗
NASA NTRS1973

Multidimensional analysis of fast-spectrum material replacement measurements for systematic estimation of cross section uncertainties

A series of central core and core-reflector interface sample replacement experiments for 16 materials performed in the NASA heavy-metal-reflected, fast spectrum critical assembly (NCA) were analyzed in four and 13 groups using the GAM 2 cross-section set. The individual worths obtained by TDSN and DOT multidimensional transport theory calculations showed significant differences from the experimental results. These were attributed to cross-section uncertainties in the GAM 2 cross sections. Simultaneous analysis of the measured and calculated sample worths permitted separation of the worths into capture and scattering components which systematically provided fast spectrum averaged correction factors to the magnitudes of the GAM 2 absorption and scattering cross sections. Several Los Alamos clean critical assemblies containing Oy, Ta, and Mo as well as one of the NCA compositions were reanalyzed using the corrected cross sections. In all cases the eigenvalues were significantly improved and were recomputed to within 1 percent of the experimental eigenvalue. A comparable procedure may be used for ENDF cross sections when these are available.

Klann, P. G.↗
NASA NTRS2011

JWST Wavefront Control Toolbox

A Matlab-based toolbox has been developed for the wavefront control and optimization of segmented optical surfaces to correct for possible misalignments of James Webb Space Telescope (JWST) using influence functions. The toolbox employs both iterative and non-iterative methods to converge to an optimal solution by minimizing the cost function. The toolbox could be used in either of constrained and unconstrained optimizations. The control process involves 1 to 7 degrees-of-freedom perturbations per segment of primary mirror in addition to the 5 degrees of freedom of secondary mirror. The toolbox consists of a series of Matlab/Simulink functions and modules, developed based on a "wrapper" approach, that handles the interface and data flow between existing commercial optical modeling software packages such as Zemax and Code V. The limitations of the algorithm are dictated by the constraints of the moving parts in the mirrors.

Shin, Shahram Ron↗
NASA NTRS2001

Upgrades to the TPSX Material Properties Database

The TPSX Material Properties Database is a web-based tool that serves as a database for properties of advanced thermal protection materials. TPSX provides an easy user interface for retrieving material property information in a variety of forms, both graphical and text. The primary purpose and advantage of TPSX is to maintain a high quality source of often used thermal protection material properties in a convenient, easily accessible form, for distribution to government and aerospace industry communities. Last year a major upgrade to the TPSX web site was completed. This year, through the efforts of researchers at several NASA centers, the Office of the Chief Engineer awarded funds to update and expand the databases in TPSX. The FY01 effort focuses on updating correcting the Ames and Johnson thermal protection materials databases. In this session we will summarize the improvements made to the web site last year, report on the status of the on-going database updates, describe the planned upgrades for FY02 and FY03, and provide a demonstration of TPSX.

Squire, T. H.↗
NASA NTRS2011

NASA Tech Briefs, December 2011

Topics covered include: 1) SNE Industrial Fieldbus Interface; 2) Composite Thermal Switch; 3) XMOS XC-2 Development Board for Mechanical Control and Data Collection; 4) Receiver Gain Modulation Circuit; 5) NEXUS Scalable and Distributed Next-Generation Avionics Bus for Space Missions; 6) Digital Interface Board to Control Phase and Amplitude of Four Channels; 7) CoNNeCT Baseband Processor Module; 8) Cryogenic 160-GHz MMIC Heterodyne Receiver Module; 9) Ka-Band, Multi-Gigabit-Per-Second Transceiver; 10) All-Solid-State 2.45-to-2.78-THz Source; 11) Onboard Interferometric SAR Processor for the Ka-Band Radar Interferometer (KaRIn); 12) Space Environments Testbed; 13) High-Performance 3D Articulated Robot Display; 14) Athena; 15) In Situ Surface Characterization; 16) Ndarts; 17) Cryo-Etched Black Silicon for Use as Optical Black; 18) Advanced CO2 Removal and Reduction System; 19) Correcting Thermal Deformations in an Active Composite Reflector; 20) Umbilical Deployment Device; 21) Space Mirror Alignment System; 22) Thermionic Power Cell To Harness Heat Energies for Geothermal Applications; 23) Graph Theory Roots of Spatial Operators for Kinematics and Dynamics; 24) Spacesuit Soft Upper Torso Sizing Systems; 25) Radiation Protection Using Single-Wall Carbon Nanotube Derivatives; 26) PMA-PhyloChip DNA Microarray to Elucidate Viable Microbial Community Structure; 27) Lidar Luminance Quantizer; 28) Distributed Capacitive Sensor for Sample Mass Measurement; 29) Base Flow Model Validation; 30) Minimum Landing Error Powered-Descent Guidance for Planetary Missions; 31) Framework for Integrating Science Data Processing Algorithms Into Process Control Systems; 32) Time Synchronization and Distribution Mechanisms for Space Networks; 33) Local Estimators for Spacecraft Formation Flying; 34) Software-Defined Radio for Space-to-Space Communications; 35) Reflective Occultation Mask for Evaluation of Occulter Designs for Planet Finding; and 36) Molecular Adsorber Coating

Source record↗
NASA NTRS2013

The GLAS Standard Data Products Specification-Level 1, Version 9

The Geoscience Laser Altimeter System (GLAS) is the primary instrument for the ICESat (Ice, Cloud and Land Elevation Satellite) laser altimetry mission. ICESat was the benchmark Earth Observing System (EOS) mission for measuring ice sheet mass balance, cloud and aerosol heights, as well as land topography and vegetation characteristics. From 2003 to 2009, the ICESat mission provided multi-year elevation data needed to determine ice sheet mass balance as well as cloud property information, especially for stratospheric clouds common over polar areas. It also provided topography and vegetation data around the globe, in addition to the polar-specific coverage over the Greenland and Antarctic ice sheets.This document defines the Level-1 GLAS standard data products. This document addresses the data flow, interfaces, record and data formats associated with the GLAS Level 1 standard data products. GLAS Level 1 standard data products are composed of Level 1A and Level 1B data products. The term standard data products refers to those EOS instrument data that are routinely generated for public distribution. The National Snow and Ice Data Center (NSDIC) distribute these products. Each data product has a unique Product Identification code assigned by the Senior Project Scientist. GLAS Level 1A and Level 1B Data Products are composed from those Level 0 data that have been reformatted or transformed to corrected and calibrated data in physical units at the full instrument rate and resolution.

Lee, Jeffrey E.↗
NASA NTRS2024

X-57 Cruise Motor GVT Using Fixed-Base Correction Technique

The National Aeronautics and Space Administration (NASA) Armstrong Flight Research Center (AFRC) completed a modal survey of the X-57 Maxwell aircraft cruise motor system to help inform cruise motor redesign efforts. X-57 Maxwell was an electric propulsion demonstrator aircraft developed by NASA to inform airworthiness standards for electrified-aircraft. The cruise motor system modal survey was completed in spring of 2023 utilizing the fixed-base correction (FBC) ground vibration test (GVT) technique developed by ATA Engineering, to decouple the motor modes from the aircraft modes. Previously during the full aircraft GVT, a detailed modal assessment of the cruise motors was not performed. Owing to the X-57 project’s phase in the aircraft development cycle when the motor redesign effort occurred, the cruise motor GVT could only be performed with the cruise motor system installed on the aircraft, with most of its installation hardware (wiring, baffling, sensors, etc.) attached. An impact hammer was used to provide excitation input at various locations within the tight confines of the cruise motor installation. To better support motor redesign efforts, the FBC methodology was utilized to fix, separate and de-couple the cruise motor modes from aircraft modal response. During the GVT, this required additional impact tap tests on candidate fixed-boundary points for each degree of freedom (DOF) to be fixed. Additional triaxial accelerometers installed at the candidate points were used to compute frequency response functions (FRFs) in X, Y, and Z directions to enable those DOFs to be numerically fixed. Test data was acquired using Hottinger Brüel & Kjær’s LAN-XI data acquisition hardware and BK Connect software. FBC post-test processing was performed using the Structural Modification Using Frequency Response Functions (SMURF) technique with ATA Engineering’s Interface between MATLAB, Analysis, Test (IMAT) software. Utilizing the FBC technique relieved test engineers from having to instrument the entire aircraft to identify and separate aircraft response from cruise motor modes of interest. The FBC technique also permitted structural analysis engineers to omit secondary components from their finite element model (FEM) of the cruise motor system. This FBC modal survey was successful, and the first time NASA AFRC utilized the FBC method on an aircraft rather than a test fixture, and also using an impact hammer rather than multiple shakers allowing significant project schedule and cost savings

Modal Survey↗
NASA NTRS2019

2018 NISAR Applications Workshop: Forest and Disturbance; Workshop Report

Forest lands cover the globe and are important sources for providing ecosystem services including: carbon sequestration, biodiversity, timber, air and water quality. As such, counties around the world have dedicated programs for managing them. Accurate and timely information concerning the status of these forests (moisture, biomass, disturbance type, etc.) is essential to those Nations’ human and ecological health as well as economy. The joint NASA/US Forest Service workshop focused on arming forest land managers with observations and remote sensing information from the upcoming NASA-ISRO (Indian Space Research Organization) SAR (Synthetic Aperture Radar) (NISAR) satellite mission (expected to launch early 2022). Participants included representatives from different US Federal Agencies, private sector, and non-governmental organizations (NGO) that are key players in facilitating integration of Earth Observations (EO) into forest management and decision support workflows. They included scientists, technicians, and program managers with a responsibility for data acquisition and exploitation such as product development, delivery, and use, and capacity building. Discussions were held over two days to convey the broader forest and disturbance community information needs for various representative participants and programs and to facilitate the delivery of NISAR mission geospatial products and observational capabilities. Case studies were presented to demonstrate the current state of practice in the use of SAR remote sensing for applications of direct importance to forest and disturbance land management community. Eleven organizations presented their information requirements in response to a set of questions provided by the NASA team, then the NASA team responded by describing the degree to which NISAR could meet these requirements. Discussion ensued about needed data product specifications to increase utility (e.g., projection, latency, etc.), tools and capacity building. The general findings of this workshop were that (a) NISAR observations will be particularly useful to the global forest carbon and disturbance monitoring applications, but that certain data product design decisions (projections and radiometric and terrain corrections) need to be considered to increase utility; b) the biomass and disturbance detection algorithms meet many of the community needs, however there are other information products of value (e.g., soil moisture or disturbance classification, not just detection) and all products should be compliant with existing community standards for reporting uncertainty; c) providing SAR education to the community will be key specifically thinking about putting the information first and the SAR theory second, providing a simple guide of standard data processing steps (e.g., dB (decibel) to power conversion and speckle filtering); d) the community needs a user-friendly interface for finding free, archived data over their geographic regions of interest; e) user-friendly tools that connect to open-sources GIS (Global Information System) software (e.g., QGIS (Quantum GIS)) that include a graphical user interface (GUI) for SAR processing that enables both download and cloud processing. To integrate these findings and prepare the community before NISAR launches, it was suggested that there be a dedicated NISAR Forest and Disturbance Applications Working Group (as per the specifications in the NISAR Utilization Plan). After launch, it was decided that the community continue capacity building activities.

Stavros, Natasha↗
NASA NTRS2005

Full Multigrid Flow Solver

FMG3D (full multigrid 3 dimensions) is a pilot computer program that solves equations of fluid flow using a finite difference representation on a structured grid. Infrastructure exists for three dimensions but the current implementation treats only two dimensions. Written in Fortran 90, FMG3D takes advantage of the recursive subroutine feature, dynamic memory allocation, and structured-programming constructs of that language. FMG3D supports multi-block grids with three types of block-to-block interfaces: periodic, C-zero, and C-infinity. For all three types, grid points must match at interfaces. For periodic and C-infinity types, derivatives of grid metrics must be continuous at interfaces. The available equation sets are as follows: scalar elliptic equations, scalar convection equations, and the pressure-Poisson formulation of the Navier-Stokes equations for an incompressible fluid. All the equation sets are implemented with nonzero forcing functions to enable the use of user-specified solutions to assist in verification and validation. The equations are solved with a full multigrid scheme using a full approximation scheme to converge the solution on each succeeding grid level. Restriction to the next coarser mesh uses direct injection for variables and full weighting for residual quantities; prolongation of the coarse grid correction from the coarse mesh to the fine mesh uses bilinear interpolation; and prolongation of the coarse grid solution uses bicubic interpolation.

Mineck, Raymond E.↗