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All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

HRDI Observations of Inertia-Gravity Waves in the Mesosphere and Lower Thermosphere

Vertical profiles of High-resolution Doppler imager (HRDI) mesospheric winds have small-scale structure (vertical wavelengths between 10 and 20 km) that is virtually always present. Fourier analysis of HRDI zonal and meridional wind profiles have been carried out, and the spectral characteristics are sorted by latitude, month and local time. Power spectral density (PSD) exhibits a universal exp(-km) structure in the 10-20km wavelength regime, with K lying between 2 and 3. The observed PSD for wavelengths between 10 and 20 km is a factor of 3 higher than a null spectrum constructed from HRDI reported error bars multiplied by randomly varying numbers between -1 and +1. Stokes parameters were consolidated by month into Northern and Southern hemisphere middle and high latitudes belts (40-72 degrees), tidal belts (32-16 degrees) and a tropical belt (8S-8N). Vertical waves between 10 and 15 km in wavelength are about 10-15% polarized everywhere. The inferred propagation direction in the middle and high latitude Southern hemisphere is predominantly meridional during solstice, and significantly more zonal during equinoxes. In the tropical belt, the wave orientations are nearly North-South during solstices, with a slightly higher east-west component during equinox. In the tidal belts where the background wind includes a strong meridional tidal wind, the preferred wave orientation has a significant zonal component during equinox. These findings are consistent with the interpretation of wave filtering by the background wind.

Lieberman, Ruth S.↗
NASA NTRS2001

An Implicit Characteristic Based Method for Electromagnetics

An implicit characteristic-based approach for numerical solution of Maxwell's time-dependent curl equations in flux conservative form is introduced. This method combines a characteristic based finite difference spatial approximation with an implicit lower-upper approximate factorization (LU/AF) time integration scheme. This approach is advantageous for three-dimensional applications because the characteristic differencing enables a two-factor approximate factorization that retains its unconditional stability in three space dimensions, and it does not require solution of tridiagonal systems. Results are given both for a Fourier analysis of stability, damping and dispersion properties, and for one-dimensional model problems involving propagation and scattering for free space and dielectric materials using both uniform and nonuniform grids. The explicit Finite Difference Time Domain Method (FDTD) algorithm is used as a convenient reference algorithm for comparison. The one-dimensional results indicate that for low frequency problems on a highly resolved uniform or nonuniform grid, this LU/AF algorithm can produce accurate solutions at Courant numbers significantly greater than one, with a corresponding improvement in efficiency for simulating a given period of time. This approach appears promising for development of dispersion optimized LU/AF schemes for three dimensional applications.

Beggs, John H.↗
NASA NTRS2002

A Two-Dimensional Linear Bicharacteristic Scheme for Electromagnetics

The upwind leapfrog or Linear Bicharacteristic Scheme (LBS) has previously been implemented and demonstrated on one-dimensional electromagnetic wave propagation problems. This memorandum extends the Linear Bicharacteristic Scheme for computational electromagnetics to model lossy dielectric and magnetic materials and perfect electrical conductors in two dimensions. This is accomplished by proper implementation of the LBS for homogeneous lossy dielectric and magnetic media and for perfect electrical conductors. Both the Transverse Electric and Transverse Magnetic polarizations are considered. Computational requirements and a Fourier analysis are also discussed. Heterogeneous media are modeled through implementation of surface boundary conditions and no special extrapolations or interpolations at dielectric material boundaries are required. Results are presented for two-dimensional model problems on uniform grids, and the Finite Difference Time Domain (FDTD) algorithm is chosen as a convenient reference algorithm for comparison. The results demonstrate that the two-dimensional explicit LBS is a dissipation-free, second-order accurate algorithm which uses a smaller stencil than the FDTD algorithm, yet it has less phase velocity error.

Beggs, John H.↗
NASA NTRS2001

An Implicit LU/AF FDTD Method

There has been some recent work to develop two and three-dimensional alternating direction implicit (ADI) FDTD schemes. These ADI schemes are based upon the original ADI concept developed by Peaceman and Rachford and Douglas and Gunn, which is a popular solution method in Computational Fluid Dynamics (CFD). These ADI schemes work well and they require solution of a tridiagonal system of equations. A new approach proposed in this paper applies a LU/AF approximate factorization technique from CFD to Maxwell s equations in flux conservative form for one space dimension. The result is a scheme that will retain its unconditional stability in three space dimensions, but does not require the solution of tridiagonal systems. The theory for this new algorithm is outlined in a one-dimensional context for clarity. An extension to two and threedimensional cases is discussed. Results of Fourier analysis are discussed for both stability and dispersion/damping properties of the algorithm. Results are presented for a one-dimensional model problem, and the explicit FDTD algorithm is chosen as a convenient reference for comparison.

Beggs, John H.↗
NASA NTRS1993

Effect of upright tilt on ventricular/vascular coupling in chronically instrumented primates

Studies of the hydraulic loading conditions on the heart in humans, especially pulsatile load, have primarily been limited to the supine state. Therefore, we have chosen a nonhuman primate model, the baboon, to assess left ventricular/vascular coupling in both supine and upright positions. Primate subjects were studied by catheterization under sedation and then after surgical implantation of transducers. This allowed the evaluation of postural stress in the chronically instrumented conscious baboon and then after light dissociative doses of ketamine. Basic hemodynamic variables were evaluated for baboons in supine and upright positions. Fourier analysis was applied to aortic pressure and flow to obtain input and characteristic impedance and the ratio of pulsatile (Wp) to total (Wt) left ventricular power (Wp/Wt). The aortic reflected, or backward, pressure was also calculated. Peripheral resistance increased (P = 0.01) and reflected pressure decreased (17.74 +/- 1.50 vs. 15.21 +/- 2 mmHg; P < 0.01) in upright subjects. Characteristic impedance and Wp/Wt were unchanged. Postoperatively, peripheral resistance increased (2,651 +/- 311 vs. 3,667 +/- 276; P < 0.05) and mean power and Wt decreased (P < 0.01) without changes in reflected pressure. All variables were unchanged after light dissociative doses of ketamine. Thus there is no significant change in efficiency of left ventricular/vascular coupling formulated in terms of Wp/Wt or input impedance with postural stress.

NASA Program Space Physiology and Countermeasures↗
NASA NTRS1943

Periodic Heat Transfer at Small Pressure Fluctuations

The effect of cyclic gas pressure variations on the periodic heat transfer at a flat wall is theoretically analyzed and the differential equation describing the process and its solution for relatively. Small pressure fluctuations developed, thus explaining the periodic heat cycle between gas and wall surface. The processes for pure harmonic pressure and temperature oscillations, respectively, in the gas space are described by means of a constant heat transfer coefficient and the equally constant phase angle between the appearance of the maximum values of the pressure and heat flow most conveniently expressed mathematically in the form of a complex heat transfer coefficient. Any cyclic pressure oscillations, can be reduced by Fourier analysis to harmonic oscillations, which result in specific, mutual relationships of heat-transfer coefficients and phase angles for the different harmonics.

Pfriem, H.↗
NASA NTRS1997

Wavelet Methods Developed to Detect and Control Compressor Stall

A "wavelet" is, by definition, an amplitude-varying, short waveform with a finite bandwidth (e.g., that shown in the first two graphs). Naturally, wavelets are more effective than the sinusoids of Fourier analysis for matching and reconstructing signal features. In wavelet transformation and inversion, all transient or periodic data features (as in compressor-inlet pressures) can be detected and reconstructed by stretching or contracting a single wavelet to generate the matching building blocks. Consequently, wavelet analysis provides many flexible and effective ways to reduce noise and extract signals which surpass classical techniques - making it very attractive for data analysis, modeling, and active control of stall and surge in high-speed turbojet compressors. Therefore, fast and practical wavelet methods are being developed in-house at the NASA Lewis Research Center to assist in these tasks. This includes establishing user-friendly links between some fundamental wavelet analysis ideas and the classical theories (or practices) of system identification, data analysis, and processing.

Le, Dzu K.↗
NASA NTRS2007

Convergence Acceleration of Runge-Kutta Schemes for Solving the Navier-Stokes Equations

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 can be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. This RK/implicit scheme is used as a smoother for multigrid. Fourier analysis is applied to determine damping properties. Numerical dissipation operators based on the Roe scheme, a matrix dissipation, and the CUSP scheme are considered in evaluating the RK/implicit scheme. In addition, the effect of the number of RK stages is examined. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. Turbulent flows over an airfoil and wing at subsonic and transonic conditions are computed. The effects of the cell aspect ratio on convergence are investigated for Reynolds numbers between 5:7 x 10(exp 6) and 100 x 10(exp 6). It is demonstrated that the implicit preconditioner can reduce the computational time of a well-tuned standard RK scheme by a factor between four and ten.

Swanson, Roy C., Jr.↗
NASA NTRS1997

Ellipsometer

In an ellipsometer, a phase-modulated, polarized light beam is applied to a sample, electrical signals are obtained representing the orthogonal planes of polarization of the light after it has interacted with the sample and the constants of the sample are calculated from the two resulting electrical signals. The phase modulation is sufficiently small so that the calibration errors are negligible. For this purpose, the phase modulator, phase modulates the light within a range of no more than ten degrees peak to peak. The two electrical signals are expanded by Fourier analysis and the coefficients thereof utilized to calculate psi and delta.

Ducharme, Stephen Paul↗
NASA NTRS1995

Small modulation ellipsometry

In an ellipsometer, a phase-modulated, polarized light beam is applied to a sample, electrical signals are obtained representing the orthogonal planes of polarization of the light after it has interacted with the sample and the constants of the sample are calculated from the two resulting electrical signals. The phase modulation is sufficiently small so that the calibration errors are negligible. For this purpose, the phase modulator phase modulates the light within a range of no more than ten degrees modulations peak to peak. The two electrical signals are expanded by Fourier analysis and the coefficients thereof utilized to calculate psi and delta.

Ducharme, Stephen P.↗
NASA NTRS2006

Application of p-Multigrid to Discontinuous Galerkin Formulations of the Poisson Equation

We investigate p-multigrid as a solution method for several different discontinuous Galerkin (DG) formulations of the Poisson equation. Different combinations of relaxation schemes and basis sets have been combined with the DG formulations to find the best performing combination. The damping factors of the schemes have been determined using Fourier analysis for both one and two-dimensional problems. One important finding is that when using DG formulations, the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable. To ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques. Of the relaxation schemes, we find that the combination of Jacobi relaxation with the spectral element basis is fairly effective. The results using this combination are p sensitive in both one and two dimensions, but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes. A competitive alternative is a block Gauss-Seidel relaxation. This actually out performs a more expensive line relaxation when the mesh is isotropic. When the mesh becomes highly anisotropic, the implicit line method and the Gauss-Seidel implicit line method are the only effective schemes. Adding the Gauss-Seidel terms to the implicit line method gives a significant improvement over the line relaxation method.

Helenbrook, B. T.↗
NASA NTRS2006

SABER (TIMED) and MLS (UARS) Temperature Observations of Mesospheric and Stratospheric QBO and Related Tidal Variations

More than three years of temperature observations from the SABER (TIMED) and MLS WARS) instruments are analyzed to study the annual and inter-annual variations extending from the stratosphere into the upper mesosphere. The SABER measurements provide data from a wide altitude range (15 to 95 km) for the years 2002 to 2004, while the MLS data were taken in the 16 to 55 km altitude range a decade earlier. Because of the sampling properties of SABER and MLS, the variations with local solar time must be accounted for when estimating the zonal mean variations. An algorithm is thus applied that delineates with Fourier analysis the year-long variations of the migrating tides and zonal mean component. The amplitude of the diurnal tide near the equator shows a strong semiannual periodicity with maxima near equinox, which vary from year to year to indicate the influence from the Quasi-biennial Oscillation (QBO) in the zonal circulation. The zonal mean QBO temperature variations are analyzed over a range of latitudes and altitudes, and the results are presented for latitudes from 48"s to 48"N. New results are obtained for the QBO, especially in the upper stratosphere and mesosphere, and at mid-latitudes. At Equatorial latitudes, the QBO amplitudes show local peaks, albeit small, that occur at different altitudes. From about 20 to 40 km, and within about 15" of the Equator, the amplitudes can approach 3S K for the stratospheric QBO or SQBO. For the mesospheric QBO or MQBO, we find peaks near 70 km, with temperature amplitudes reaching 3.5"K, and near 85 km, the amplitudes approach 2.5OK. Morphologically, the amplitude and phase variations derived from the SABER and MLS measurements are in qualitative agreement. The QBO amplitudes tend to peak at the Equator but then increase again pole-ward of about 15" to 20'. The phase progression with altitude varies more gradually at the Equator than at mid-latitudes. A comparison of the observations with results from the Numerical Spectral Model (NSM) reveals that there is qualitative agreement. The NSM generates the QBO extending from the stratosphere into the upper mesosphere, with temperature variations extending to mid latitudes, but the predicted amplitudes are smaller than those observed.

Huang, Frank T.↗
NASA NTRS2006

Discerning Trends in Performance Across Multiple Events

Mass Data is a computer program that enables rapid, easy discernment of trends in performance data across multiple flights and ground tests. The program can perform Fourier analysis and other functions for the purposes of frequency analysis and trending of all variables. These functions facilitate identification of past use of diagnosed systems and of anomalies in such systems, and enable rapid assessment of related current problems. Many variables, for computation of which it is usually necessary to perform extensive manual manipulation of raw downlist data, are automatically computed and made available to all users, regularly eliminating the need for what would otherwise be an extensive amount of engineering analysis. Data from flight, ground test, and simulation are preprocessed and stored in one central location for instantaneous access and comparison for diagnostic and trending purposes. Rules are created so that an event log is created for every flight, making it easy to locate information on similar maneuvers across many flights. The same rules can be created for test sets and simulations, and are searchable, so that information on like events is easily accessible.

Slater, Simon↗
NASA NTRS2011

Convergence of Defect-Correction and Multigrid Iterations for Inviscid Flows

Convergence of multigrid and defect-correction iterations is comprehensively studied within different incompressible and compressible inviscid regimes on high-density grids. Good smoothing properties of the defect-correction relaxation have been shown using both a modified Fourier analysis and a more general idealized-coarse-grid analysis. Single-grid defect correction alone has some slowly converging iterations on grids of medium density. The convergence is especially slow for near-sonic flows and for very low compressible Mach numbers. Additionally, the fast asymptotic convergence seen on medium density grids deteriorates on high-density grids. Certain downstream-boundary modes are very slowly damped on high-density grids. Multigrid scheme accelerates convergence of the slow defect-correction iterations to the extent determined by the coarse-grid correction. The two-level asymptotic convergence rates are stable and significantly below one in most of the regions but slow convergence is noted for near-sonic and very low-Mach compressible flows. Multigrid solver has been applied to the NACA 0012 airfoil and to different flow regimes, such as near-tangency and stagnation. Certain convergence difficulties have been encountered within stagnation regions. Nonetheless, for the airfoil flow, with a sharp trailing-edge, residuals were fast converging for a subcritical flow on a sequence of grids. For supercritical flow, residuals converged slower on some intermediate grids than on the finest grid or the two coarsest grids.

Diskin, Boris↗
NASA NTRS2010

Electrostatic Evaluation of the ARES I FTS Antenna Materials

Surface resistivity and volume resistivity data show all the tested non-metallic materials of the Ares I FTS antenna assembly to be insulative. The external materials (White foam, phenolic) should be able to develop a large surface charge density upon tribocharging with ice crystal impingement. Dielectric breakdown tests on the FTS antenna housing materials show that each of the insulative materials are very resistive to electrical breakdown. The thicknesses of these materials in a nominal housing should protect the antenna from direct breakdown from external triboelectric charging potentials. Per data from the Air Force study, a maximum external electric potential in the range of 100kV can be developed on surfaces tribocharged by ice crystal impingement. Testing showed that under operational pressure ranges, this level of exterior voltage can result in a potential of about 6 kV induced on the electrically floating interior antenna vanes. Testing the vanes up to this voltage level showed that electrostatic discharges can occur between the electrically floating vanes and the center, grounded screw heads. Repeated tests with multiple invisible and visible discharges caused only superficial physical damage to the vanes. Fourier analysis of the discharge signals showed that the frequency range of credible discharges would not interfere with the nominal operation of the FTS antenna. However, due to the limited scope, short timetable, and limited funding of this study, a direct measurement of the triboelectric charge that could be generated on the Ares I antenna housing when the rocket traverses an ice cloud at supersonic speeds was not performed. Instead, data for the limited Air Force study [3] was used as input for our experiments. The Air Force data used was not collected with a sensor located to provide us with the best approximation at the geometry of the Ares I rocket, namely that of the windshield electrometer, because brush discharges to the metal frame of the windshield periodically depleted any charge accumulated. The configuration of the Ares I antenna assembly does not include any exposed metals in the vicinity and the windshield data could not be used. Since the windshield sensor data was unusable, we decided that the Patch 2 location would provide us with a rough approximation to the Ares I antenna configuration and would give us an indication of the possible charging levels that would develop. This was the data that we used in this study. Whether these charging levels would be of the same order of magnitude as the actual charges developed by the Ares I traversing a cloud with ice particles is at this point unknown. An actual experimental test, requiring the acquisition of additional instrumentation, is strongly advised before a final recommendation can be formulated regarding the safe levels of electrostatic charging on the antenna housing. Thus the results of this study should be considered to be preliminary.

Hogue, Michael D.↗
NASA NTRS2015

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.

Mazaheri, Alireza↗
NASA NTRS2017

On High-Order Upwind Methods for Advection

In the fourth installment of the celebrated series of five papers entitled "Towards the ultimate conservative difference scheme", Van Leer (1977) introduced five schemes for advection, the first three are piecewise linear, and the last two, piecewise parabolic. Among the five, scheme I, which is the least accurate, extends with relative ease to systems of equations in multiple dimensions. As a result, it became the most popular and is widely known as the MUSCL scheme (monotone upstream-centered schemes for conservation laws). Schemes III and V have the same accuracy, are the most accurate, and are closely related to current high-order methods. Scheme III uses a piecewise linear approximation that is discontinuous across cells, and can be considered as a precursor of the discontinuous Galerkin methods. Scheme V employs a piecewise quadratic approximation that is, as opposed to the case of scheme III, continuous across cells. This method is the basis for the on-going "active flux scheme" developed by Roe and collaborators. Here, schemes III and V are shown to be equivalent in the sense that they yield identical (reconstructed) solutions, provided the initial condition for scheme III is defined from that of scheme V in a manner dependent on the CFL number. This equivalence is counter intuitive since it is generally believed that piecewise linear and piecewise parabolic methods cannot produce the same solutions due to their different degrees of approximation. The finding also shows a key connection between the approaches of discontinuous and continuous polynomial approximations. In addition to the discussed equivalence, a framework using both projection and interpolation that extends schemes III and V into a single family of high-order schemes is introduced. For these high-order extensions, it is demonstrated via Fourier analysis that schemes with the same number of degrees of freedom 𝐾 per cell, in spite of the different piecewise polynomial degrees, share the same sets of eigenvalues and thus, have the same stability and accuracy. Moreover, these schemes are accurate to order 2𝐾−1, which is higher than the expected order of 𝐾.

high-order methods↗
NASA NTRS2020

Large-Scale Assessment of Polygon-Edge Boulder Clustering in the Martian Northern Lowlands

Two features evident in many images of the martian northern low-lands are polygonal fractures (especially northwards of 60°N) and meter-scale surface boulders. Since their first observation, several attempts have been made to classify and study these polygons as well as how the forces that form these polygons may modify the surface. Surface boulders have been used as a potential indicator of such modification, though current studies find evidence both for and against their association with the underlying polygons. Both these investigations are limited by the same fundamental challenge: map-ping the location of surface boulders manually is not practical at large scales. Here, we use the Martian Boulder Automatic Recognition System (MBARS) to provide image-wide assessments of boulder location and size, enabling large-scale assessment of boulder populations. To compare these boulder locations with the underlying polygons, we modified the 2-D Fourier analysis described by Orloff in 2013 to analyze boulder locations. When compared with Orloff’s observations of polygon scales, this provides an avenue for large-scale comparison of boulder-cluster scale and polygon scale.

Hood, Don R.↗