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At least 307 records · Page 17

Bringing "Scientific Expeditions" Into the Schools

Two new technologies, the FASTexpedition and Remote FAST, have been developed that provide remote, 3D, high resolution, dynamic, interactive viewing of scientific data (such as simulations or measurements of fluid dynamics). The FASTexpedition permits one to access scientific data from the World Wide Web, take guided expeditions through the data, and continue with self controlled expeditions through the data. Remote FAST permits collaborators at remote sites to simultaneously view an analysis of scientific data being controlled by one of the collaborators. Control can be transferred between sites. These technologies are now being used for remote collaboration in joint university, industry, and NASA projects in computational fluid dynamics (CFD) and wind tunnel testing. Also, NASA Ames Research Center has initiated a project to make scientific data and guided expeditions through the data available as FASTexpeditions on the World Wide Web for educational purposes. Previously, remote visualiZation of dynamic data was done using video format (transmitting pixel information) such as video conferencing or MPEG movies on the Internet. The concept for this new technology is to send the raw data (e.g., grids, vectors, and scalars) along with viewing scripts over the Internet and have the pixels generated by a visualization tool running on the viewer's local workstation. The visualization tool that is currently used is FAST (Flow Analysis Software Toolkit). The advantages of this new technology over using video format are: 1. The visual is much higher in resolution (1280xl024 pixels with 24 bits of color) than typical video format transmitted over the network. 2. The form of the visualization can be controlled interactively (because the viewer is interactively controlling the visualization tool running on his workstation). 3. A rich variety of guided expeditions through the data can be included easily. 4. A capability is provided for other sites to see a visual analysis of one site as the analysis is interactively performed. Control of the analysis can be passed from site to site. 5. The scenes can be viewed in 3D using stereo vision. 6. The network bandwidth used for the visualization using this new technology is much smaller than when using video format. (The measured peak bandwidth used was 1 Kbit/sec whereas the measured bandwidth for a small video picture was 500 Kbits/sec.)

Watson, Val↗

Wind-US Flow Calculations for the M2129 S-Duct Using Structured and Unstructured Grids

Computational Fluid Dynamics (CFD) flow solutions for the M2129 diffusing S-duct with and without vane effectors were computed by the Wind-US flow solver. Both structured and unstructured 3-D grids were used. Without vane effectors, the duct exhibited massive flow separation in both experiment and CFD. With vane effectors installed, the flow remained attached and aerodynamic losses were reduced. Total pressure recovery and distortion near the duct outlet were computed from the solutions and compared favorably to experimental values. These calculations are part of a validation effort for the Wind-US code. They also provide an example case to aid engineers in learning to use the Wind-US software.

Mohler, Stanley R., Jr.↗

Adjustable Autonomy Testbed

The Adjustable Autonomy Testbed (AAT) is a simulation-based testbed located in the Intelligent Systems Laboratory in the Automation, Robotics and Simulation Division at NASA Johnson Space Center. The purpose of the testbed is to support evaluation and validation of prototypes of adjustable autonomous agent software for control and fault management for complex systems. The AA T project has developed prototype adjustable autonomous agent software and human interfaces for cooperative fault management. This software builds on current autonomous agent technology by altering the architecture, components and interfaces for effective teamwork between autonomous systems and human experts. Autonomous agents include a planner, flexible executive, low level control and deductive model-based fault isolation. Adjustable autonomy is intended to increase the flexibility and effectiveness of fault management with an autonomous system. The test domain for this work is control of advanced life support systems for habitats for planetary exploration. The CONFIG hybrid discrete event simulation environment provides flexible and dynamically reconfigurable models of the behavior of components and fluids in the life support systems. Both discrete event and continuous (discrete time) simulation are supported, and flows and pressures are computed globally. This provides fast dynamic simulations of interacting hardware systems in closed loops that can be reconfigured during operations scenarios, producing complex cascading effects of operations and failures. Current object-oriented model libraries support modeling of fluid systems, and models have been developed of physico-chemical and biological subsystems for processing advanced life support gases. In FY01, water recovery system models will be developed.

Malin, Jane T.↗

Boundary-Layer Flow Simulations Over Ablating Woven Thermal Protection System Material

Spallation is the mechanical removal of small chunks of material gets removed typically due to high shear conditions of the flow field. This reduces the ability of the thermal protection system (TPS) material to protect the spacecraft as well as cause turbulence in the flow causing higher heating rates. In this work, we focus on the material removal through ablation and high shear flow within the boundary layer region of woven TPS material. Woven TPS (WTPS) material is the latest class of material developed by NASA, to be used within the next generation of space flights. They are complex interlocked weaves designed to create a rigid structure that is highly resistant to heat and can be easily designed and tailored for a wide variety of entry environments. Due to material removal resulting from chemical degradation, the structural integrity of TPS material is affected. Spallation occurs when this structurally compromised material is exposed to the high shear flow conditions within the boundary layer. In order to understand the spallation mechanism within WTPS material, we first perform the material removal simulations which occur primarily through oxidation to obtain the microstructure at various stages of degradation. These simulations are performed using the Porous Microstructure Analysis (PuMA) software developed at NASA Ames. The micro-structure geometry used within these simulations were generated artificially to be similar to the 3D weave architecture of MSR-EEV (Mars Sample Return - Earth Entry Vehicle). The various eroded TPS micro-structures are then subjected to the boundary layer flow conditions to obtain critical surface quantities which contribute to the structural failure mechanism such as heat flux, pressure, and shear stress. The direct simulation Monte Carlo (DSMC) methodology is used to perform these simulations in order to accurately capture the strong gradients within the high-temperature boundary layer flow over the intricate geometry of WTPS material. The boundary layer profile is directly taken from the Computational Fluid Dynamics (CFD) simulation and provided as boundary conditions to the DSMC inlet and outlet. Further, the variation of these properties as the microstructure undergoes changes due to oxidation is also investigated. Finally, these quantities are used as input in PuMA to understand the material expansion/compression and strain within the woven TPS geometry and help in developing a comprehensive spallation and structure failure model.

microstructure↗

Boundary-Layer Flow Simulations Over Ablating Woven Thermal Protection System Material

Spallation is the mechanical removal of small chunks of material gets removed typically due to high shear conditions of the flow field. This reduces the ability of the thermal protection system (TPS) material to protect the spacecraft as well as cause turbulence in the flow causing higher heating rates. In this work, we focus on the material removal through ablation and high shear flow within the boundary layer region of woven TPS material. Woven TPS (WTPS) material is the latest class of material developed by NASA, to be used within the next generation of space flights. They are complex interlocked weaves designed to create a rigid structure that is highly resistant to heat and can be easily designed and tailored for a wide variety of entry environments. Due to material removal resulting from chemical degradation, the structural integrity of TPS material is affected. Spallation occurs when this structurally compromised material is exposed to the high shear flow conditions within the boundary layer. In order to understand the spallation mechanism within WTPS material, we first perform the material removal simulations which occur primarily through oxidation to obtain the microstructure at various stages of degradation. These simulations are performed using the Porous Microstructure Analysis (PuMA) software developed at NASA Ames. The micro-structure geometry used within these simulations were generated artificially to be similar to the 3D weave architecture of MSR-EEV (Mars Sample Return - Earth Entry Vehicle). The various eroded TPS micro-structures are then subjected to the boundary layer flow conditions to obtain critical surface quantities which contribute to the structural failure mechanism such as heat flux, pressure, and shear stress. The direct simulation Monte Carlo (DSMC) methodology is used to perform these simulations in order to accurately capture the strong gradients within the high-temperature boundary layer flow over the intricate geometry of WTPS material. The boundary layer profile is directly taken from the Computational Fluid Dynamics (CFD) simulation and provided as boundary conditions to the DSMC inlet and outlet. Further, the variation of these properties as the microstructure undergoes changes due to oxidation is also investigated. Finally, these quantities are used as input in PuMA to understand the material expansion/compression and strain within the woven TPS geometry and help in developing a comprehensive spallation and structure failure model.

microstructure↗

Computational Analysis of the Transonic Dynamics Tunnel Using FUN3D

This paper presents results from an exploratory two-year effort of applying Computational Fluid Dynamics (CFD) to analyze the empty-tunnel flow in the NASA Langley Research Center Transonic Dynamics Tunnel (TDT). The TDT is a continuous-flow, closed circuit, 16- x 16-foot slotted-test-section wind tunnel, with capabilities to use air or heavy gas as a working fluid. In this study, experimental data acquired in the empty tunnel using the R-134a test medium was used to calibrate the computational data. The experimental calibration data includes wall pressures, boundary-layer profiles, and the tunnel centerline Mach number profiles. Subsonic and supersonic flow regimes were considered, focusing on Mach 0.5, 0.7 and Mach 1.1 in the TDT test section. This study discusses the computational domain, boundary conditions, and initial conditions selected and the resulting steady-state analyses using NASA's FUN3D CFD software.

Chwalowski, Pawel↗

NASA Tech Briefs, March 2010

Topics covered include: Software Tool Integrating Data Flow Diagrams and Petri Nets; Adaptive Nulling for Interferometric Detection of Planets; Reducing the Volume of NASA Earth-Science Data; Reception of Multiple Telemetry Signals via One Dish Antenna; Space-Qualified Traveling-Wave Tube; Smart Power Supply for Battery-Powered Systems; Parallel Processing of Broad-Band PPM Signals; Inexpensive Implementation of Many Strain Gauges; Constant-Differential-Pressure Two-Fluid Accumulator; Inflatable Tubular Structures Rigidized with Foams; Power Generator with Thermo-Differential Modules; Mechanical Extraction of Power From Ocean Currents and Tides; Nitrous Oxide/Paraffin Hybrid Rocket Engines; Optimized Li-Ion Electrolytes Containing Fluorinated Ester Co-Solvents; Probabilistic Multi-Factor Interaction Model for Complex Material Behavior; Foldable Instrumented Bits for Ultrasonic/Sonic Penetrators; Compact Rare Earth Emitter Hollow Cathode; High-Precision Shape Control of In-Space Deployable Large Membrane/Thin-Shell Reflectors; Rapid Active Sampling Package; Miniature Lightweight Ion Pump; Cryogenic Transport of High-Pressure-System Recharge Gas; Water-Vapor Raman Lidar System Reaches Higher Altitude; Compact Ku-Band T/R Module for High-Resolution Radar Imaging of Cold Land Processes; Wide-Field-of-View, High-Resolution, Stereoscopic Imager; Electrical Capacitance Volume Tomography with High-Contrast Dielectrics; Wavefront Control and Image Restoration with Less Computing; Polarization Imaging Apparatus; Stereoscopic Machine-Vision System Using Projected Circles; Metal Vapor Arcing Risk Assessment Tool; Performance Bounds on Two Concatenated, Interleaved Codes; Parameterizing Coefficients of a POD-Based Dynamical System; Confidence-Based Feature Acquisition; Algorithm for Lossless Compression of Calibrated Hyperspectral Imagery; Universal Decoder for PPM of any Order; Algorithm for Stabilizing a POD-Based Dynamical System; Mission Reliability Estimation for Repairable Robot Teams; Processing AIRS Scientific Data Through Level 3; Web-Based Requesting and Scheduling Use of Facilities; AutoGen Version 5.0; Time-Tag Generation Script; PPM Receiver Implemented in Software; Tropospheric Emission Spectrometer Product File Readers; Reporting Differences Between Spacecraft Sequence Files; Coordinating "Execute" Data for ISS and Space Shuttle; Database for Safety-Oriented Tracking of Chemicals; Apparatus for Cold, Pressurized Biogeochemical Experiments; Growing B Lymphocytes in a Three-Dimensional Culture System; Tissue-like 3D Assemblies of Human Broncho-Epithelial Cells; Isolation of Resistance-Bearing Microorganisms; Oscillating Cell Culture Bioreactor; and Liquid Cooling/Warming Garment.

Source record↗

Infinite possibilities: Computational structures technology

Computational Fluid Dynamics (or CFD) methods are very familiar to the research community. Even the general public has had some exposure to CFD images, primarily through the news media. However, very little attention has been paid to CST--Computational Structures Technology. Yet, no important design can be completed without it. During the first half of this century, researchers only dreamed of designing and building structures on a computer. Today their dreams have become practical realities as computational methods are used in all phases of design, fabrication and testing of engineering systems. Increasingly complex structures can now be built in even shorter periods of time. Over the past four decades, computer technology has been developing, and early finite element methods have grown from small in-house programs to numerous commercial software programs. When coupled with advanced computing systems, they help engineers make dramatic leaps in designing and testing concepts. The goals of CST include: predicting how a structure will behave under actual operating conditions; designing and complementing other experiments conducted on a structure; investigating microstructural damage or chaotic, unpredictable behavior; helping material developers in improving material systems; and being a useful tool in design systems optimization and sensitivity techniques. Applying CST to a structure problem requires five steps: (1) observe the specific problem; (2) develop a computational model for numerical simulation; (3) develop and assemble software and hardware for running the codes; (4) post-process and interpret the results; and (5) use the model to analyze and design the actual structure. Researchers in both industry and academia continue to make significant contributions to advance this technology with improvements in software, collaborative computing environments and supercomputing systems. As these environments and systems evolve, computational structures technology will evolve. By using CST in the design and operation of future structures systems, engineers will have a better understanding of how a system responds and lasts, more cost-effective methods of designing and testing models, and improved productivity. For informational and educational purposes, a videotape is being produced using both static and dynamic images from research institutions, software and hardware companies, private individuals, and historical photographs and drawings. The extensive number of CST resources indicates its widespread use. Applications run the gamut from simpler university-simulated problems to those requiring solutions on supercomputers. In some cases, an image or an animation will be mapped onto the actual structure to show the relevance of the computer model to the structure. Transferring the digital files to videotape presents a number of problems related to maintaining the quality of the original image, while still producing a broadcast quality videotape. Since researchers normally do not create a computer image using traditional composition theories or video production requirements, often the image loses some of its original digital quality and impact when transferred to videotape. Although many CST images are currently available, those that are edited into the final project must meet two important criteria: they must complement the narration, and they must be broadcast quality when recorded on videotape.

Beam, Sherilee F.↗

Tools for 3D scientific visualization in computational aerodynamics

The purpose is to describe the tools and techniques in use at the NASA Ames Research Center for performing visualization of computational aerodynamics, for example visualization of flow fields from computer simulations of fluid dynamics about vehicles such as the Space Shuttle. The hardware used for visualization is a high-performance graphics workstation connected to a super computer with a high speed channel. At present, the workstation is a Silicon Graphics IRIS 3130, the supercomputer is a CRAY2, and the high speed channel is a hyperchannel. The three techniques used for visualization are post-processing, tracking, and steering. Post-processing analysis is done after the simulation. Tracking analysis is done during a simulation but is not interactive, whereas steering analysis involves modifying the simulation interactively during the simulation. Using post-processing methods, a flow simulation is executed on a supercomputer and, after the simulation is complete, the results of the simulation are processed for viewing. The software in use and under development at NASA Ames Research Center for performing these types of tasks in computational aerodynamics is described. Workstation performance issues, benchmarking, and high-performance networks for this purpose are also discussed as well as descriptions of other hardware for digital video and film recording.

Bancroft, Gordon↗

Visual analysis of fluid dynamics at NASA's numerical aerodynamic simulation facility

A study aimed at describing and illustrating visualization tools used in Computational Fluid Dynamics (CFD) and indicating how these tools are likely to change by showing a projected resolution of the human computer interface is presented. The following are outlined using a graphically based test format: the revolution of human computer environments for CFD research; comparison of current environments; current environments with the ideal; predictions for the future CFD environments; what can be done to accelerate the improvements. The following comments are given: when acquiring visualization tools, potential rapid changes must be considered; environmental changes over the next ten years due to human computer interface cannot be fathomed; data flow packages such as AVS, apE, Explorer and Data Explorer are easy to learn and use for small problems, excellent for prototyping, but not so efficient for large problems; the approximation techniques used in visualization software must be appropriate for the data; it has become more cost effective to move jobs that fit on workstations and run only memory intensive jobs on the supercomputer; use of three dimensional skills will be maximized when the three dimensional environment is built in from the start.

Watson, Velvin R.↗

Computational Methods for HSCT-Inlet Controls/CFD Interdisciplinary Research

A program aimed at facilitating the use of computational fluid dynamics (CFD) simulations by the controls discipline is presented. The objective is to reduce the development time and cost for propulsion system controls by using CFD simulations to obtain high-fidelity system models for control design and as numerical test beds for control system testing and validation. An interdisciplinary team has been formed to develop analytical and computational tools in three discipline areas: controls, CFD, and computational technology. The controls effort has focused on specifying requirements for an interface between the controls specialist and CFD simulations and a new method for extracting linear, reduced-order control models from CFD simulations. Existing CFD codes are being modified to permit time accurate execution and provide realistic boundary conditions for controls studies. Parallel processing and distributed computing techniques, along with existing system integration software, are being used to reduce CFD execution times and to support the development of an integrated analysis/design system. This paper describes: the initial application for the technology being developed, the high speed civil transport (HSCT) inlet control problem; activities being pursued in each discipline area; and a prototype analysis/design system in place for interactive operation and visualization of a time-accurate HSCT-inlet simulation.

Cole, Gary L.↗

Computation of Sensitivity Derivatives of Navier-Stokes Equations using Complex Variables

Accurate computation of sensitivity derivatives is becoming an important item in Computational Fluid Dynamics (CFD) because of recent emphasis on using nonlinear CFD methods in aerodynamic design, optimization, stability and control related problems. Several techniques are available to compute gradients or sensitivity derivatives of desired flow quantities or cost functions with respect to selected independent (design) variables. Perhaps the most common and oldest method is to use straightforward finite-differences for the evaluation of sensitivity derivatives. Although very simple, this method is prone to errors associated with choice of step sizes and can be cumbersome for geometric variables. The cost per design variable for computing sensitivity derivatives with central differencing is at least equal to the cost of three full analyses, but is usually much larger in practice due to difficulty in choosing step sizes. Another approach gaining popularity is the use of Automatic Differentiation software (such as ADIFOR) to process the source code, which in turn can be used to evaluate the sensitivity derivatives of preselected functions with respect to chosen design variables. In principle, this approach is also very straightforward and quite promising. The main drawback is the large memory requirement because memory use increases linearly with the number of design variables. ADIFOR software can also be cumber-some for large CFD codes and has not yet reached a full maturity level for production codes, especially in parallel computing environments.

Vatsa, Veer N.↗

Simulation of Fluid Flow and Collection Efficiency for a SEA Inc. Multi-Element Probe and Ice Crystal Detector Using GlennICE

Numerical simulation results of fluid flow and collection efficiency of the Science Engineering Associates Inc. Multi-Element Probe (Multiwire) and Ice Crystal Detector (ICD) are presented. Fluid flow simulations were conducted using NASA's FUN3D while collection efficiency simulations were conducted using NASA's LEWICE3D software and GlennICE software. For both probes, 3D unsteady flow results were time averaged. Simulations were computed for freestream velocities ranging from 85 to 185 m/s and freestream total pressures of 44.8 and 93.1 kPa. Collection efficiency results were computed for four spherical particle diameter sizes of 5, 20, 50, and 100 µm. GlennICE collection efficiency results for the multiwire were compared with previously published collection efficiency values calculated using LEWICE3D. Numerical collection efficiency results for the Ice Crystal Detector are presented for the first time.

aircraft, icing, Computational Fluid Dynamics↗

Simulation of Fluid Flow and Collection Efficiency for a SEA Inc. Multi-Element Probe and Ice Crystal Detector Using GlennICE

Numerical simulation results of fluid flow and collection efficiency of the Science Engineering Associates Inc. Multi-Element Probe (Multiwire) and Ice Crystal Detector (ICD) are presented. Fluid flow simulations were conducted using NASA's FUN3D while collection efficiency simulations were conducted using NASA's LEWICE3D software and GlennICE software. For both probes, 3D unsteady flow results were time-averaged. Simulations were computed for free steam velocities ranging from 85 to 185 m/s and freestream total pressures of 44.8 and 93.1 kPa. Collection efficiency results were computed for four spherical particle diameter sizes of 5, 20, 50, and 100 µm. GlennICE collection efficiency results for the multiwire were compared with previously published collection efficiency values calculated using LEWICE3D. Numerical collection efficiency results for the Ice Crystal Detector are presented for the first time.

aircraft, icing, Computational Fluid Dynamics↗

Domain decomposition: A bridge between nature and parallel computers

Domain decomposition is an intuitive organizing principle for a partial differential equation (PDE) computation, both physically and architecturally. However, its significance extends beyond the readily apparent issues of geometry and discretization, on one hand, and of modular software and distributed hardware, on the other. Engineering and computer science aspects are bridged by an old but recently enriched mathematical theory that offers the subject not only unity, but also tools for analysis and generalization. Domain decomposition induces function-space and operator decompositions with valuable properties. Function-space bases and operator splittings that are not derived from domain decompositions generally lack one or more of these properties. The evolution of domain decomposition methods for elliptically dominated problems has linked two major algorithmic developments of the last 15 years: multilevel and Krylov methods. Domain decomposition methods may be considered descendants of both classes with an inheritance from each: they are nearly optimal and at the same time efficiently parallelizable. Many computationally driven application areas are ripe for these developments. A progression is made from a mathematically informal motivation for domain decomposition methods to a specific focus on fluid dynamics applications. To be introductory rather than comprehensive, simple examples are provided while convergence proofs and algorithmic details are left to the original references; however, an attempt is made to convey their most salient features, especially where this leads to algorithmic insight.

Keyes, David E.↗

Cross-Validation of Computational and Experimental Distributed Surface Pressures on the Space Launch System

This paper presents a new workflow for comparing experimental pressure-sensitive paint (PSP) data to computational fluid dynamic (CFD) simulations by way of mapping data from corresponding grids utilizing interpolation methods. In addition to generating quantitative and qualitative point-to-point comparisons between PSP and CFD data, this workflow extracts sectional loading data from both grids and generates lineload comparison charts for corresponding PSP and CFD runs. Experimental PSP data presented in this paper were taken from a 2016 NASA Ames Research Center Unitary Plan Wind Tunnel 11- by 11-Foot Transonic WindTunnel Facility test of the NASA Space Launch System. CFD simulation data for comparison purposes were generated using the FUN3D code. Overall, interpolation onto PSP grids versus CFD grids yields comparable surface pressure fields. However, lineload comparisons are easier to make on the CFD grid-mapped data due to the grid topology and the current capabilities of the lineload analysis tools at NASA Langley Research Center. This workflow is written using contemporary software (Python, Tecplot, PyTecplot), is compatible with existing tools at NASA Langley, and is developed to be adaptable depending on the situation.

SLS↗

NASA Langley FUN3D Analyses in Support of the 1st AIAA Stability and Control Prediction Workshop

This work summarizes the results of FUN3D analyses conducted for the 1st AIAA Stability and Control Workshop on behalf of participants from the NASA Langley Research Center. The workshop was created to establish best practices for the prediction of stability and control derivatives using computational fluid dynamics and assess the limitations of these methods when those best practices are applied. The inaugural workshop considered the ONERA version of the NASA/Boeing Common Research Model, which includes the wing, body, horizontal tail, and a vertical tail designed by ONERA. Wind tunnel data at small sideslip angles remain unpublished and served as ‘blind’ data for computational comparisons. The present research generated workshop test case data using the NASA FUN3D code, which is a parallelized, unstructured, node-based, finite-volume discretization, Reynolds-averaged Navier-Stokes flow solver. Steady- state numerical simulations were conducted for workshop test cases investigating the following: grid convergence, Mach number effect on static stability, wind tunnel sting increments, static stability-derivative calculations, and a sideslip angle sweep. Results were generated for two series of unstructured, mixed-element grids, one set provided by the workshop and another set created using the HeldenMesh grid generation software. The results provided include total- and component-level breakdowns of the force and moment coefficients, in addition to sectional pressure distributions for the wing and tail components for comparisons to wind tunnel data.

CFD↗

Surface modeling and grid generation for aeropropulsion CFD

The efforts in geometry modeling and grid generation at the NASA Lewis Research Center, as applied to the computational fluid dynamic (CFD) analysis of aeropropulsion systems, are presented. The efforts are mainly characterized by a focus on the analysis of components of an aeropropulsion system, which involve turbulent viscous flow with heat transfer and chemistry. Thus, this discussion will follow that characterization and will sequence through the components of typical propulsion systems consisting of inlets, compressors, combustors, turbines, and nozzles. For each component, some applications of CFD analysis will be presented to show how CFD is used to compute the desired performance information, how geometry modeling and grid generation are performed, and what issues have developed related to geometry modeling and grid generation. The discussion will illustrate the following needs related to geometry modeling and grid generation as observed in aeropropulsion analysis: (1) accurate and efficient resolution of turbulent viscous and chemically-reacting flowfields; (2) easy-to-use interfaces with CAD data for automated grid generation about complex geometries; and (3) automated batch grid generation software for use with design and optimization software.

Choo, Yung K.↗