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At least 901 records · Page 50

Aerodynamic shape optimization of a HSCT type configuration with improved surface definition

Two distinct parametrization procedures of generating free-form surfaces to represent aerospace vehicles are presented. The first procedure is the representation using spline functions such as nonuniform rational b-splines (NURBS) and the second is a novel (geometrical) parametrization using solutions to a suitably chosen partial differential equation. The main idea is to develop a surface which is more versatile and can be used in an optimization process. Unstructured volume grid is generated by an advancing front algorithm and solutions obtained using an Euler solver. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an automatic differentiator precompiler software tool. Aerodynamic shape optimization of a complete aircraft with twenty four design variables is performed. High speed civil transport aircraft (HSCT) configurations are targeted to demonstrate the process.

Thomas, Almuttil M.↗

Applying integrals of motion to the numerical solution of differential equations

A method is developed for using the integrals of systems of nonlinear, ordinary differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scaler or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Jezewski, D. J.↗

Applying integrals of motion to the numerical solution of differential equations

A method is developed for using the integrals of systems of nonlinear, ordinary, differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scalar or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Vezewski, D. J.↗

Analysis of Alternative Jettison Design Concepts for Deep-space Missions

The management of waste generated onboard spacecraft during future long-duration, deep-space missions will require different solutions from those currently implemented on the International Space Station, which consist exclusively of collecting, storing, and returning the waste to Earth. Alternative options for managing spacecraft waste are to process it for recycling and recovering resources, and to jettison it overboard. The waste generated during a deep-space mission is derived mainly from spacecraft logistics supplies, food and beverage residues, personal or scientific items used by the crew, and unused spare components. Uncontained and unprocessed trash is a health hazard and a habitat volume liability, which makes onboard long-term storage a nonviable option. Jettison of solid, processed waste appear, on the other hand, to be an effective solution for crewed deep-space missions, leading not only to volume reduction and habitat safening, but also to considerable mass savings in the spacecraft’s propulsion system. However, the disposal of trash overboard also creates a navigation hazard for spacecraft and the risk of collisions with planetary bodies. This paper investigates alternative jettison design concepts for L2 libration orbit, Mars conjunction-class, and Mars opposition-class missions.

Jurek Parodi↗

Application of Monte Carlo techniques to optimization of high-energy beam transport in a stochastic environment

An algorithm employing a modified sequential random perturbation, or creeping random search, was applied to the problem of optimizing the parameters of a high-energy beam transport system. The stochastic solution of the mathematical model for first-order magnetic-field expansion allows the inclusion of state-variable constraints, and the inclusion of parameter constraints allowed by the method of algorithm application eliminates the possibility of infeasible solutions. The mathematical model and the algorithm were programmed for a real-time simulation facility; thus, two important features are provided to the beam designer: (1) a strong degree of man-machine communication (even to the extent of bypassing the algorithm and applying analog-matching techniques), and (2) extensive graphics for displaying information concerning both algorithm operation and transport-system behavior. Chromatic aberration was also included in the mathematical model and in the optimization process. Results presented show this method as yielding better solutions (in terms of resolutions) to the particular problem than those of a standard analog program as well as demonstrating flexibility, in terms of elements, constraints, and chromatic aberration, allowed by user interaction with both the algorithm and the stochastic model. Example of slit usage and a limited comparison of predicted results and actual results obtained with a 600 MeV cyclotron are given.

Parrish, R. V.↗

Leading-edge receptivity for blunt-nose bodies

This research program investigates boundary-layer receptivity in the leading-edge region for bodies with blunt leading edges. Receptivity theory provides the link between the unsteady distrubance environment in the free stream and the initial amplitudes of the instability waves in the boundary layer. This is a critical problem which must be addressed in order to develop more accurate prediction methods for boundary-layer transition. The first phase of this project examines the effects of leading-edge bluntness and aerodynamic loading for low Mach number flows. In the second phase of the project, the investigation is extended to supersonic Mach numbers. Singular perturbation techniques are utilized to develop an asymptotic theory for high Reynolds numbers. In the first year, the asymptotic theory was developed for leading-edge receptivity in low Mach number flows. The case of a parabolic nose is considered. Substantial progress was made on the Navier-Sotkes computations. Analytical solutions for the steady and unsteady potential flow fields were incorporated into the code, greatly expanding the types of free-stream disturbances that can be considered while also significantly reducing the the computational requirements. The time-stepping algorithm was modified so that the potential flow perturbations induced by the unsteady pressure field are directly introduced throughout the computational domain, avoiding an artificial 'numerical diffusion' of these from the outer boundary. In addition, the start-up process was modified by introducing the transient Stokes wave solution into the downstream boundary conditions.

Kerschen, Edward J.↗

Developing a Logistics Data Process for Support Equipment for NASA Ground Operations

The United States NASA Space Shuttle has long been considered an extremely capable yet relatively expensive rocket. A great part of the roughly US $500 million per launch expense was the support footprint: refurbishment and maintenance of the space shuttle system, together with the long list of resources required to support it, including personnel, tools, facilities, transport and support equipment. NASA determined to make its next rocket system with a smaller logistics footprint, and thereby more cost-effective and quicker turnaround. The logical solution was to adopt a standard Logistics Support Analysis (LSA) process based on GEIA-STD-0007 http://www.logisticsengineers.org/may09pres/GEIASTD0007DEXShortIntro.pdf which is the successor of MIL-STD-1388-2B widely used by U.S., NATO, and other world military services and industries. This approach is unprecedented at NASA: it is the first time a major program of programs, Project Constellation, is factoring logistics and supportability into design at many levels. This paper will focus on one of those levels NASA ground support equipment for the next generation of NASA rockets and on building a Logistics Support Analysis Record (LSAR) for developing and documenting a support solution and inventory of resources for. This LSAR is actually a standards-based database, containing analyses of the time and tools, personnel, facilities and support equipment required to assemble and integrate the stages and umbilicals of a rocket. This paper will cover building this database from scratch: including creating and importing a hierarchical bill of materials (BOM) from legacy data; identifying line-replaceable units (LRUs) of a given piece of equipment; analyzing reliability and maintainability of said LRUs; and therefore making an assessment back to design whether the support solution for a piece of equipment is too much work, i.e., too resource-intensive. If one must replace or inspect an LRU too much, perhaps a modification of the design of the equipment can make such operational effort unnecessary. Finally, this paper addresses processes of tying resources to a timeline of tasks performed in ground operations: this enables various overarching analyses, e.g., a summarization of all resources used for a given piece of equipment. Quality Control of data will also be discussed: importing and exporting data from product teams, including spreadsheets-todatabase or data exchange between databases.

Chakrabarti, Suman↗

Methodology for CFD Design Analysis of National Launch System Nozzle Manifold

The current design environment dictates that high technology CFD (Computational Fluid Dynamics) analysis produce quality results in a timely manner if it is to be integrated into the design process. The design methodology outlined describes the CFD analysis of an NLS (National Launch System) nozzle film cooling manifold. The objective of the analysis was to obtain a qualitative estimate for the flow distribution within the manifold. A complex, 3D, multiple zone, structured grid was generated from a 3D CAD file of the geometry. A Euler solution was computed with a fully implicit compressible flow solver. Post processing consisted of full 3D color graphics and mass averaged performance. The result was a qualitative CFD solution that provided the design team with relevant information concerning the flow distribution in and performance characteristics of the film cooling manifold within an effective time frame. Also, this design methodology was the foundation for a quick turnaround CFD analysis of the next iteration in the manifold design.

Haire, Scot L.↗

Chemical Sensors Based on IR Spectroscopy and Surface-Modified Waveguides

Sol-gel processing techniques have been used to apply thin porous films to the surfaces of planar infrared (IR) waveguides to produce widely useful chemical sensors. The thin- film coating serves to diminish the concentration of water and increase the concentration of the analyte in the region probed by the evanescent IR wave. These porous films are composed of silica, and therefore, conventional silica surface modification techniques can be used to give the surface a specific functional character. The sol-gel film was surface-modified to make the film highly hydrophobic. These sensors were shown to be capable of detecting non-polar organic analytes, such as benzonitrile, in aqueous solution with detection limits in the ppb range. Further, these porous sol-gel structures allow the analytes to diffuse into and out of the films rapidly, thus reaching equilibrium in less than ten seconds. These sensors are unique because of the fact that their operation is based on the measurement of an IR absorption spectrum. Thus, these sensors are able to identify the analytes as well as measure concentration with high sensitivity. These developments have been documented in previous reports and publications. Recently, we have also targeted detection of the polar organic molecules acetone and isopropanol in aqueous solution. Polar organics are widely used in industrial and chemical processes, hence it is of interest to monitor their presence in effluents or decontamination process flows. Although large improvements in detection limits were expected with non-polar organic molecules in aqueous solutions using very hydrophobic porous sol-gel films on silicon attenuated total reflectance (Si ATR) waveguides, it was not as clear what the detection enhancements might be for polar organic molecules. This report describes the use of modified sol-gel-coated Si ATR sensors for trace detection and quantitation of small polar organic molecules in aqueous solutions. The detection of both acetone and isopropanol molecules in aqueous solution has been previously reported for chalcogenide fiber optic sensors. The sol-gel film was produced using a mixture of ethyltriethoxysilane and tetraethoxysilane and the surface modification was carried out using trimethylchlorosilane. We have demonstrated that this film concentrates the target polar analytes from aqueous solution in the region probed by the evanescent wave to improve detection limits by as much as a factor of 450.

Lopez, Gabriel P.↗

Transition Modeling Based on the Dual N-factor Method for the CRM-NLF Wind Tunnel Configuration

The dual N-factor method is used to model the boundary-layer transition over the common research model with natural laminar flow (CRM-NLF) aircraft configuration. The flow conditions match selected test conditions from a wind tunnel experiment in the National Transonic Facility at the NASA Langley Research Center. The paper presents a systematic methodology for transition prediction in the presence of a dual shock system and extends the prior capability for iteratively coupled computational fluid dynamics (CFD) predictions to incorporate three-dimensional, transonic wings. The method employs stability computations based on the linear parabolized stability equations (PSE), along with a dual N-factor criterion. The iterative process begins with the fully turbulent Reynolds-averaged-Navier-Stokes (RANS) mean flow solution. For the first iteration, a mean flow solution is calculated with an imposed transition front that aligns with the shock front from the fully turbulent solution. Subsequently, stability computations are performed along a set of streamlines across the wing to calculate the amplification of planar Tollmien-Schlichting (TS) and stationary crossflow (CF) modes. The transition criterion based on the dual N-factor method is used to infer the updated transition front and the process is successively repeated until convergence of the solution. Within three iterations, the predicted fronts for angles of attack of 1.45, 1.98, 2.46 and 2.94 degrees and a mean-aerodynamic-chord Reynolds number equal to 15 million, approach visual convergence in most regions of the studied cases, and the resulting predictions are in good agreement with the transition fronts deduced from measurements of temperature-sensitive paint. Even though surface pressure measurements based on fully-turbulent flow agree well with the measured pressure coefficient distributions, strong viscous-inviscid interaction effects cause significant shifts in the shock locations based on the imposed transition front, underscoring the intrusive nature of static pressure measurements using surface mounted ports on the CRM-NLF configuration.

Boundary Layer Transition↗

Mass Evolution of Mediterranean, Black, Red, and Caspian Seas from GRACE and Altimetry: Accuracy Assessment and Solution Calibration

We present new measurements of mass evolution for the Mediterranean, Black, Red, and Caspian Seas as determined by the NASA Goddard Space Flight Center (GSFC) GRACE time-variable global gravity mascon solutions. These new solutions are compared to sea surface altimetry measurements of sea level anomalies with steric corrections applied. To assess their accuracy, the GRACE and altimetry-derived solutions are applied to the set of forward models used by GSFC for processing the GRACE Level-1B datasets, with the resulting inter-satellite range acceleration residuals providing a useful metric for analyzing solution quality.

Loomis, B. D.↗

An Explicit Linear Filtering Solution for the Optimization of Guidance Systems with Statistical Inputs

The determination of optimum filtering characteristics for guidance system design is generally a tedious process which cannot usually be carried out in general terms. In this report a simple explicit solution is given which is applicable to many different types of problems. It is shown to be applicable to problems which involve optimization of constant-coefficient guidance systems and time-varying homing type systems for several stationary and nonstationary inputs. The solution is also applicable to off-design performance, that is, the evaluation of system performance for inputs for which the system was not specifically optimized. The solution is given in generalized form in terms of the minimum theoretical error, the optimum transfer functions, and the optimum transient response. The effects of input signal, contaminating noise, and limitations on the response are included. From the results given, it is possible in an interception problem, for example, to rapidly assess the effects on minimum theoretical error of such factors as target noise and missile acceleration. It is also possible to answer important questions regarding the effect of type of target maneuver on optimum performance.

Stewart, Elwood C.↗

Shared direct memory access on the Explorer 2-LX

Advances in Expert System technology and Artificial Intelligence have provided a framework for applying automated Intelligence to the solution of problems which were generally perceived as intractable using more classical approaches. As a result, hybrid architectures and parallel processing capability have become more common in computing environments. The Texas Instruments Explorer II-LX is an example of a machine which combines a symbolic processing environment, and a computationally oriented environment in a single chassis for integrated problem solutions. This user's manual is an attempt to make these capabilities more accessible to a wider range of engineers and programmers with problems well suited to solution in such an environment.

Musgrave, Jeffrey L.↗

Piezoelectric impedance-based high-accuracy damage identification using sparsity conscious multi-objective optimization inverse analysis

Two elements are essential in structural health monitoring utilizing dynamic responses: response measurement with high-frequency contents, i.e., small characteristic wavelengths, that can adequately reflect damage features, and effective inverse identification analysis that is however oftentimes under-determined. The advancement of smart structure integration has led to active interrogation through frequency-sweeping piezoelectric impedance measurement at high frequency range. In this research we develop a multi-objective optimization formulation for the identification of damage location and severity utilizing piezoelectric impedance. While one optimization objective is to match the response measurement with finite element model prediction in the damage parametric space, the other is the number of locations of damage, i.e., the sparsity of damage index as the solution vector, since damage usually occurs within a small number of locations. This multi-objective formulation fits well the under-determined nature of damage identification, as it naturally provides multiple solutions as basis for further elucidation. The challenge remaining is how to find a small solution set that can include the actual damage scenario. Here we develop a novel inverse identification framework utilizing the intelligent swarm optimizer which possesses flexibility for enhancement. We first embed a sparsity enforcement process into the population generation of the optimizer, which yields a solution repository intrinsically possessing sparsity. We then apply reinforcement learning so the agents can adaptively opt for local strategies with the aim of enriching the searching patterns to diversify the solutions. Through the incorporation of a Q-table, searching toward more promising directions will be rewarded. Our case analyses employing experimental data indicate that this sparsity-conscious multi-objective particle swarm optimization technique can lead to a small solution set which generally encompasses the true damage scenario. This effectively solves the structural damage identification problem with piezoelectric impedance measurement.

Yang Zhang↗

NASA’s Satellite Needs Working Group Management Office: Developing Solutions in an Agile, Open Science Environment

Every two years, the National Aeronautics and Space Administration (NASA) leads an assessment of U.S. Federal civilian agency Earth observation needs submitted through the Satellite Needs Working Group (SNWG) survey. In four survey cycles beginning in 2016, nearly 400 high-priority satellite needs have been identified, spanning Earth Science and representing a wide variety of potential applications for Earth observation data. During each assessment cycle, new data products and services (i.e., solutions) that meet the needs of multiple agencies are identified and proposed for funding. The majority of solutions being developed or currently operational are global in scope, including harmonized land surface reflectance data from Landsat and Sentinel-2; composites of cloud properties derived from MODIS, VIIRS, and five geostationary satellites; dynamic surface water extent and land surface disturbance products derived from multiple optical and radar missions; a suite of low-latency products from the ICESat-2 mission; and a soil moisture product derived from the upcoming NISAR mission. The SNWG Management Office, within the Earth Action element of NASA’s Earth Science Division, manages both the biennial SNWG survey assessment and the development of solutions starting at full capacity with the 2020 cycle. Each solution project is required to align with NASA’s open science policy, including developing source code in an open code repository, having an open-source software license, and making all data freely available via NASA’s Earthdata website. The presentation will include an overview of the SNWG process, its emphasis on open science, and highlight several operational solutions freely available to the global research and applications communities.

Katrina Virts↗

GC/MS Method Development for Separating Lunar Volatile Ice Simulant Headspace Gases

Various investigators propose the lunar surface contains widely distributed volatiles, especially water- like species, i.e. OH and H2O. Surface volatiles are theorized to exist as a hydrated regolith layer, concentrated in extremely cold polar permanently shadowed regions (PSR), and/or solar wind implantation reservoirs in lunar glasses. The proposed sources of lunar surface volatiles range from cometary impacts, solar wind, or a supply present during moon formation. Future Artemis missions aim to collect and return the samples containing volatiles collected near lunar polar craters or PSRs. We, as advanced curation scientists, are responsible for developing techniques and methodologies for preserving returned sample integrity as much as possible. Pristine volatile-bearing samples are invaluable to the scientific community seeking to unravel the history of the solar system. Realistically, a sample will experience alteration during collection, transportation back to earth, and storage. The Planetary Exploration and Astromaterials Research Lab (PEARL) seeks to understand temperature and pressure effects on high-fidelity volatile-containing regolith simulants, the foundation for the future of cold curation. This abstract outlines the separation, identification, and quantification of headspace gases over volatile ice feed stock material using gas chromatography/mass spectrometry (GC/MS). Preliminary objectives concentrated on sample handling, reproducibility, and understanding the elution characteristics for each analyte. Initial GC/MS method development experiments utilized diluted static headspace sample preparation. Diluted samples were used because sampling headspace gases directly from a vial containing liquid analyte resulted in overloading of the column and detector. Overloading is evident based on chromatogram peak shapes and instrument contamination, or carry over, between experiments. A mixture of three alcohols were used for a majority of the sample handling and reproducibility studies. Reproducibility was tested via multiple users, calibration curves, and check standards. Stock solutions of condensed lunar volatile analytes included methanol, ammonia in methanol, hydrogen sulfide in water, and an equal volume mixture of methanol, ethanol, and isopropanol. Current samples use room air as the headspace sample matrix, however future experiments will incorporate an inert purge gas, such as argon or nitrogen. Three mL of each analyte solution were capped in separate 20 mL crimp top GC vials. Dilutions were carried out by removing an aliquot of headspace gases with a calibrated 1 mL gastight syringe and immediately transferring to a 20 mL capped crimp top vial. The GC/MS is a Thermo Fisher Trace 1310/ISQ 7000 with a TriPlus RSH autosampler and split/splitless injector module. The experiments outlined in this abstract use the following hardware: a 2.5 mL gastight headspace syringe tool, 1 mm ID x 78.5 mm length ultra-inert straight injection liner, and a TG-BondQ 30 m × 0.32 mm × 10 μm column. Various parameters, such as hardware selection and the temperature, pressure, and split ratio set points, continue to evolve as the overall experiment is refined. Diluted headspace chromatograms were collected for the individual stock solutions. Retention times, peak shapes, and mass spectra were evaluated and added to the data processing method for each molecule of interest. Figure 1 shows the total ion chromatograms for the three major lunar volatile simulant stock solutions: methanol, 7 N ammonia in methanol, and 0.4% hydrogen sulfide in water. Tailing peak shapes for ammonia (2.98 min rt) and water (4.06 min rt) indicate the molecules are not properly eluting from the selected column with the current separation method. Additionally, hydrogen sulfide and ammonia have overlapping peak windows, which could impact quantification. Ongoing experiments aim to address the peak shape and overlapping via the separation method and hardware selection. Sample preparation reproducibility experiments used stock solution containing equal volumes of a non- interactive mixture of methanol, ethanol, and isopropanol. Mass spectrum ion traces were used to identify and quantify all three alcohols. Peaks were automatically detected, identified, and integrated through the mass spectra detection and processing parameters. Calibration response curves and check standards were used to evaluate the validity of the sample preparation procedure. Figure 2 shows the methanol chromatogram peak area versus total headspace dilution volume transferred from the alcohol mixture vial. The calibration response curves and check standards validate sample preparation procedure. Continuing data analysis efforts are working towards correlating the peak area and instrument response factor to the headspace analyte concentration and condensed phase composition. Static headspace gas chromatography theory relies on Dalton’s law, Raoult’s law, Henry’s Law, and the Kolb and Ettre equation to associate peak area to the analyte composition in a non-ideal solution. Equation 1 is a simplified expression derived from the aforementioned theories. Future experiments involve liquid injections of the individual stock solutions, liquid and headspace analysis of various stock solution combinations, and the addition of regolith simulants to the mixtures. Temperature is another variable expected to affect reaction rates and will be explored.

Cecilia L. Amick↗

Preparation Process and Dielectric Properties of Ba(0.5)Sr(0.5)TiO3-P(VDF-CTFE) Nanocomposites

Ceramic-polymer 0-3 nanocomposites, in which nanosized Ba(0.5)Sr(0.5)TiO3 (BST) powders were used as ceramic filler and P(VDF-CTFE) 88/12 mol% [poly(vinylidene fluoridechlorotrifluoroethylene)] copolymer was used as matrix, were studied over a concentration range from 0 to 50 vol.% of BST powders. It is found that the solution cast composites are porous and a hot-press process can eliminate the porosity, which results in a dense composite film. Two different configurations used in the hot-press process are studied. Although there is no clear difference in the uniformity and microstructure of the composites prepared using these two configurations, the composite prepared using one configuration exhibit a higher dielectric constant with a lower loss. For the composite with 40 vol. BST, a dielectric constant of 70 with a loss of 0.07 at 1 kHz is obtained at room temperature. The composites exhibit a lower dielectric loss than the polymer matrix at high frequency. However, at low frequency, the composites exhibit a higher loss than the polymer matrix due to a low frequency relaxation process that appears in the composites. It is believed that this relaxation process is related to the interfacial layer formed between BST particle and the polymer matrix. The temperature dependence of the dielectric property of the composites was studied. It is found that the dielectric constant of these composites is almost independent of the temperature over a temperature range from 20 to 120 C. Key words: A. Polymer-matrix composites (PMCs); B. Electrical Properties; E. Casting; E. Heat treatment; Dielectric properties.

Zhang, Lin↗

Adaptive grid methods for RLV environment assessment and nozzle analysis

Rapid access to highly accurate data about complex configurations is needed for multi-disciplinary optimization and design. In order to efficiently meet these requirements a closer coupling between the analysis algorithms and the discretization process is needed. In some cases, such as free surface, temporally varying geometries, and fluid structure interaction, the need is unavoidable. In other cases the need is to rapidly generate and modify high quality grids. Techniques such as unstructured and/or solution-adaptive methods can be used to speed the grid generation process and to automatically cluster mesh points in regions of interest. Global features of the flow can be significantly affected by isolated regions of inadequately resolved flow. These regions may not exhibit high gradients and can be difficult to detect. Thus excessive resolution in certain regions does not necessarily increase the accuracy of the overall solution. Several approaches have been employed for both structured and unstructured grid adaption. The most widely used involve grid point redistribution, local grid point enrichment/derefinement or local modification of the actual flow solver. However, the success of any one of these methods ultimately depends on the feature detection algorithm used to determine solution domain regions which require a fine mesh for their accurate representation. Typically, weight functions are constructed to mimic the local truncation error and may require substantial user input. Most problems of engineering interest involve multi-block grids and widely disparate length scales. Hence, it is desirable that the adaptive grid feature detection algorithm be developed to recognize flow structures of different type as well as differing intensity, and adequately address scaling and normalization across blocks. These weight functions can then be used to construct blending functions for algebraic redistribution, interpolation functions for unstructured grid generation, forcing functions to attract/repel points in an elliptic system, or to trigger local refinement, based upon application of an equidistribution principle. The popularity of solution-adaptive techniques is growing in tandem with unstructured methods. The difficultly of precisely controlling mesh densities and orientations with current unstructured grid generation systems has driven the use of solution-adaptive meshing. Use of derivatives of density or pressure are widely used for construction of such weight functions, and have been proven very successful for inviscid flows with shocks. However, less success has been realized for flowfields with viscous layers, vortices or shocks of disparate strength. It is difficult to maintain the appropriate mesh point spacing in the various regions which require a fine spacing for adequate resolution. Mesh points often migrate from important regions due to refinement of dominant features. An example of this is the well know tendency of adaptive methods to increase the resolution of shocks in the flowfield around airfoils, but in the incorrect location due to inadequate resolution of the stagnation region. This problem has been the motivation for this research.

Thornburg, Hugh J.↗