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Comparative Study on High-Order Positivity-preserving WENO Schemes

In gas dynamics and magnetohydrodynamics flows, physically, the density and the pressure p should both be positive. In a standard conservative numerical scheme, however, the computed internal energy is obtained by subtracting the kinetic energy from the total energy, resulting in a computed p that may be negative. Examples are problems in which the dominant energy is kinetic. Negative may often emerge in computing blast waves. In such situations the computed eigenvalues of the Jacobian will become imaginary. Consequently, the initial value problem for the linearized system will be ill posed. This explains why failure of preserving positivity of density or pressure may cause blow-ups of the numerical algorithm. The adhoc methods in numerical strategy which modify the computed negative density and/or the computed negative pressure to be positive are neither a conservative cure nor a stable solution. Conservative positivity-preserving schemes are more appropriate for such flow problems. The ideas of Zhang & Shu (2012) and Hu et al. (2012) precisely address the aforementioned issue. Zhang & Shu constructed a new conservative positivity-preserving procedure to preserve positive density and pressure for high-order WENO schemes by the Lax-Friedrichs flux (WENO/LLF). In general, WENO/LLF is too dissipative for flows such as turbulence with strong shocks computed in direct numerical simulations (DNS) and large eddy simulations (LES). The new conservative positivity-preserving procedure proposed in Hu et al. (2012) can be used with any high-order shock-capturing scheme, including high-order WENO schemes using the Roe's flux (WENO/Roe). The goal of this study is to compare the results obtained by non-positivity-preserving methods with the recently developed positivity-preserving schemes for representative test cases. In particular the more difficult 3D Noh and Sedov problems are considered. These test cases are chosen because of the negative pressure/density most often exhibited by standard high-order shock-capturing schemes. The simulation of a hypersonic nonequilibrium viscous shock tube that is related to the NASA Electric Arc Shock Tube (EAST) is also included. EAST is a high-temperature and high Mach number viscous nonequilibrium flow consisting of 13 species. In addition, as most common shock-capturing schemes have been developed for problems without source terms, when applied to problems with nonlinear and/or sti source terms these methods can result in spurious solutions, even when solving a conservative system of equations with a conservative scheme. This kind of behavior can be observed even for a scalar case (LeVeque & Yee 1990) as well as for the case consisting of two species and one reaction (Wang et al. 2012). For further information concerning this issue see (LeVeque & Yee 1990; Griffiths et al. 1992; Lafon & Yee 1996; Yee et al. 2012). This EAST example indicated that standard high-order shock-capturing methods exhibit instability of density/pressure in addition to grid-dependent discontinuity locations with insufficient grid points. The evaluation of these test cases is based on the stability of the numerical schemes together with the accuracy of the obtained solutions.

WENO

A comparative study and validation of upwind and central-difference Navier-Stokes codes for high-speed flows

A comparative study was made using 4 different computer codes for solving the compressible Navier-Stokes equations. Three different test problems were used, each of which has features typical of high speed internal flow problems of practical importance in the design and analysis of propulsion systems for advanced hypersonic vehicles. These problems are the supersonic flow between two walls, one of which contains a 10 deg compression ramp, the flow through a hypersonic inlet, and the flow in a 3-D corner formed by the intersection of two symmetric wedges. Three of the computer codes use similar recently developed implicit upwind differencing technology, while the fourth uses a well established explicit method. The computed results were compared with experimental data where available.

Rudy, David H.

A comparative study of advanced shock-capturing schemes applied to Burgers' equation

Several variations of the TVD scheme, ENO scheme, FCT scheme, and geometrical schemes, such as MUSCL and PPM, are considered. A comparative study of these schemes as applied to the Burgers' equation is presented. The objective is to assess their performance for problems involving formation and propagation of shocks, shock collisions, and expansion of discontinuities.

Yang, H. Q.

Comparative study of the phase of diurnal anisotropy on quiet and disturbed days on a long term basis up to recent period

The data from the world wide grid of neutron monitoring stations was analyzed for a comparative study of the phase of diurnal anisotropy on quiet and disturbed days on a long term basis up to recent period. It has been observed that the phase of the diurnal anisotropy on disturbed days where the value of the Ap-index is higher, is found to shift towards earlier hours in comparison to the phase of the diurnal anisotropy on quiet days where the value of Ap-index is lower on all the stations from 1965 to 71. Such a trend is not observable for the later period. This affect is found to be more pronounced on equatorial stations, in particular, in comparison to high latitude stations. It was derived from these observational facts that the relationship between Ap-index and the phase of the diurnal anisotropy is not invariant throughout the period of consideration. Furthermore, the exact cause of such a drastic change is not known, but it demonstrates very clearly that the interplanetary conditions which are responsible for both, diurnal anisotropy of cosmic ray intensity and the geomagnetic Ap-index variation, have drastically changed during the period 1971 and onwards.

Kumar, S.

A comparative study of the nonuniqueness problem of the potential equation

The nonuniqueness problem occurring at transonic speeds with the conservative potential equation is reviewed. Additional evidence supporting the idea that the nonuniqueness problem is inherent to the differential equation is given. An extensive, comparative study between potential and Euler calculations is presented. The results of the study indicate that the nonuniqueness problem is not an inviscid phenomenon, but a result of the conservative potential approximate treatment of shock waves. A new bound on the limit of validity of the potential formulation is discussed.

Salas, M. D.

A comparative study of the influence of buoyancy driven fluid flow on GaAs crystal growth

A systematic investigation of the effect of gravity driven fluid flow on GaAs crystal growth was performed. It includes GaAs crystal growth in the microgravity environment aboard the Space Shuttle. The program involves a controlled comparative study of crystal growth under a variety of earth based conditions with variable orientation and applied magnetic field in addition to the microgravity growth. Earth based growth will be performed under stabilizing as well as destabilizing temperature gradients. The boules grown in space and on earth will be fully characterized to correlate the degree of convection with the distribution of impurities. Both macro- and micro-segregation will be determined. The space growth experiment will be flown in a self-contained payload container through NASA's Get Away Special program.

Kafalas, J. A.

Comparative study of choleretic agents in anesthetized rats as well as in restrained and and unrestrained rats, with or without compensation for biliary loss

Tests were conducted on Wistar rats by using 3 control choleretic agents: 1-phenyl-1-hydroxy n-pentane, dehydrocholic acid, and phenyl-dimethylacetic acid. The effects of these agents were compared in different experimental conditions. The comparative study of choleretic agents in anesthetized rats, in restrained and unrestrained rats, with or without compensation for biliary loss by the biliary secretion of restrained or unrestrained rats does not show, in systematic pharmecodynamic investigations, an obvious superiority over the methods based on the simple technique.

Labrid, C.

A comparative study of infrared radiance measurements by an ER-2 based radiometer and the LANDSAT 5 Thematic Mapper (TM-6)

Infrared radiance measurements were acquired from a radiometer on the NASA ER-2 during a coincident LANDSAT 5 overpass on 28 Oct. 1986 as part of the FIRE Cirrus IFO in the vicinity of Lake Michigan. A comparative study is made to infer microphysical properties of the cirrus cloud field. Radiances are derived from the image by convolving the ER-2 radiometer's effective field of view along the flight path. A multistream radiative transfer model is used to account for the differences in spectral bandwidths, 10.40 to 12.50 microns for the LANDSAT band and 9.90 to 10.87 microns for the radiometer.

Hammer, Philip D.

High Altitude Long Endurance UAV Analysis Model Development and Application Study Comparing Solar Powered Airplane and Airship Station-Keeping Capabilities

There have been ongoing efforts in the Aeronautics Systems Analysis Branch at NASA Langley Research Center to develop a suite of integrated physics-based computational utilities suitable for modeling and analyzing extended-duration missions carried out using solar powered aircraft. From these efforts, SolFlyte has emerged as a state-of-the-art vehicle analysis and mission simulation tool capable of modeling both heavier-than-air (HTA) and lighter-than-air (LTA) vehicle concepts. This study compares solar powered airplane and airship station-keeping capability during a variety of high altitude missions, using SolFlyte as the primary analysis component. Three Unmanned Aerial Vehicle (UAV) concepts were designed for this study: an airplane (Operating Empty Weight (OEW) = 3285 kilograms, span = 127 meters, array area = 450 square meters), a small airship (OEW = 3790 kilograms, length = 115 meters, array area = 570 square meters), and a large airship (OEW = 6250 kilograms, length = 135 meters, array area = 1080 square meters). All the vehicles were sized for payload weight and power requirements of 454 kilograms and 5 kilowatts, respectively. Seven mission sites distributed throughout the United States were selected to provide a basis for assessing the vehicle energy budgets and site-persistent operational availability. Seasonal, 30-day duration missions were simulated at each of the sites during March, June, September, and December; one-year duration missions were simulated at three of the sites. Atmospheric conditions during the simulated missions were correlated to National Climatic Data Center (NCDC) historical data measurements at each mission site, at four flight levels. Unique features of the SolFlyte model are described, including methods for calculating recoverable and energy-optimal flight trajectories and the effects of shadows on solar energy collection. Results of this study indicate that: 1) the airplane concept attained longer periods of on-site capability than either airship concept, and 2) the airship concepts can attain higher levels of energy collection and storage than the airplane concept; however, attaining these energy benefits requires adverse design trades of reduced performance (small airship) or excessive solar array area (large airship).

Ozoroski, Thomas A.

Comparative Study of Lettuce and Radish Grown Under Red and Blue Light-Emitting Diodes (LEDs) and White Fluorescent Lamps

Growing vegetable crops in space will be an essential part of sustaining astronauts during long-term missions. To drive photosynthesis, red and blue light-emitting diodes (LEDs) have attracted attention because of their efficiency, longevity, small size, and safety. In efforts to optimize crop production, there have also been recent interests in analyzing the subtle effects of green light on plant growth, and to determine if it serves as a source of growth enhancement or suppression. A comparative study was performed on two short cycle crops of lettuce (Outredgeous) and radish (Cherry Bomb) grown under two light treatments. The first treatment being red and blue LEDs, and the second treatment consisting of white fluorescent lamps which contain a portion of green light. In addition to comparing biomass production, physiological characterizations were conducted on how the light treatments influence morphology, water use, chlorophyll content, and the production of A TP within plant tissues.

Mickens, Matthew A.

A comparative study of three techniques for using the spectral matrix in wave analysis

Three techniques - power spectral analysis, coherency analysis, and wave analysis - for studying ULF waves in the magnetosphere are described. These techniques, while mathematically dissimilar, are all based on the assumption that, at any single frequency, a single plane wave, propagating along the normal to the plane, is present. Wave polarization parameters provided by these techniques are important in the development of models of wave generation. A comparative study of the three techniques was carried out using simulated data involving known wave and noise properties and real ULF event data from ATS 1 and 6.

Arthur, C. W.

Efficiency study comparing two helicopter planetary reduction stages

A study was conducted to compare the efficiency of two helicopter transmission planetary reduction stages. Experimental measurements and analytical predictions were made. The analysis predicted and experiments verified that one planetary stage was a more efficient design due to the type of planet bearing used in the stage. The effects of torque, speed, lubricant type, and lubricant temperature on planetary efficiency are discussed.

Krantz, Timothy L.

Efficiency study comparing two helicopter planetary reduction stages

A study was conducted to compare the efficiency of two helicopter transmission planetary reduction stages. Experimental measurements and analytical predictions were made. The analysis predicted and experiments verified that one planetary stage was a more efficient design due to the type of planet bearing used in the stage. The effects of torque, speed, lubricant type, and lubricant temperature on planetary efficiency are discussed.

Krantz, Timothy L.

Comparative Study of Lettuce and Radish Grown Under Red and Blue LEDs and White Fluorescent Lamps

Growing vegetable crops in space will be an essential part of sustaining astronauts during long-range missions. To drive photosynthesis, red and blue light-emitting diodes (LEDs) have attracted attention because of their efficiency, longevity, small size, and safety. In efforts to optimize crop yield, there is also recent interest in analyzing the subtle effects of additional wavelengths on plant growth. For instance, since plants often look purplish gray under red and blue LEDs, the addition of green light allows easy recognition of disease and the assessment of plant health status. However, it is important to know if wavelengths outside the traditional red and blue wavebands have a direct effect on enhancing or hindering the mechanisms involved in plant growth. In this experiment, a comparative study was performed on two short cycle crops of red romaine lettuce (Lactuca sativa cv. "Outredgeous") and radish (Raphanus sativa cv. 'Cherry Bomb'), which were grown under two light treatments. The first treatment being red (630 nm) and blue (450 nm) LEDs alone, while the second treatment consisted of daylight tri-phosphor fluorescent lamps (CCT approximately 5000 K) at equal photosynthetic photon flux (PPF). The treatment effects were evaluated by measuring the fresh biomass produced, plant morphology and leaf dimensions, leaf chlorophyll content, and adenosine triphosphate (ATP) within plant leaf/storage root tissues.

Food Production

A comparative study of diversification events: the early Paleozoic versus the Mesozoic

We compare two major long-term diversifications of marine animal families that began during periods of low diversity but produced strikingly different numbers of phyla, classes, and orders. The first is the early-Paleozoic diversification (late Vendian-Ordovician; 182 MY duration) and the other the Mesozoic phase of the post-Paleozoic diversification (183 MY duration). The earlier diversification was associated with a great burst of morphological invention producing many phyla, classes, and orders and displaying high per taxon rates of family origination. The later diversification lacked novel morphologies recognized as phyla and classes, produced fewer orders, and displayed lower per taxon rates of family appearances. The chief difference between the diversifications appears to be that the earlier one proceeded from relatively narrow portions of adaptive space, whereas the latter proceeded from species widely scattered among adaptive zones and representing a variety of body plans. This difference is believed to explain the major differences in the products of these great radiations. Our data support those models that hold that evolutionary opportunity is a major factor in the outcome of evolutionary processes.

NASA Discipline Exobiology

A comparative study of prebiotic and present day translational models

It is generally recognized that the understanding of the molecular basis of primitive translation is a fundamental step in developing a theory of the origin of life. However, even in modern molecular biology, the mechanism for the decoding of messenger RNA triplet codons into an amino acid sequence of a protein on the ribosome is understood incompletely. Most of the proposed models for prebiotic translation lack, not only experimental support, but also a careful theoretical scrutiny of their compatibility with well understood stereochemical and energetic principles of nucleic acid structure, molecular recognition principles, and the chemistry of peptide bond formation. Present studies are concerned with comparative structural modelling and mechanistic simulation of the decoding apparatus ranging from those proposed for prebiotic conditions to the ones involved in modern biology. Any primitive decoding machinery based on nucleic acids and proteins, and most likely the modern day system, has to satisfy certain geometrical constraints. The charged amino acyl and the peptidyl termini of successive adaptors have to be adjacent in space in order to satisfy the stereochemical requirements for amide bond formation. Simultaneously, the same adaptors have to recognize successive codons on the messenger. This translational complex has to be realized by components that obey nucleic acid conformational principles, stabilities, and specificities. This generalized condition greatly restricts the number of acceptable adaptor structures.

Rein, R.

Evaluating the Trustworthiness of Deep Neural Networks in Deployment – A Comparative Study (Replicability Study)

As deep neural networks (DNNs) are increasingly used in safety critical applications, there is a growing concern for their trustworthiness. Even highly trained, high-performant networks are not 100% accurate. However, it is very difficult to predict their behaviour during deployment without ground truth. In this paper, we provide a comparative and replicability study on recent approaches that have been proposed to evaluate the trustworthiness of DNNs. We find that it is very difficult to run and reproduce the results for these approaches on their replication packages, and it is even more difficult to run the tools on artifacts other than their own. Further, it is difficult to compare the effectiveness of the tools, due to lack of clearly defined evaluation metrics. Our results indicate that more effort is needed in our research community to obtain sound techniques for evaluating the trustworthiness of neural networks in safety-critical domains. To this end, we contribute an evaluation framework that incorporates the considered approaches and enables evaluation on common benchmarks, using common metrics. Using this framework, we run a comparative study of the three approaches.

Trustworthy AI