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A unified approach based on h-p approximation in space variables and various time discretization schemes for solving both incompressible and compressible flows is presented. Two different techniques for a posteriori error estimation and accompanying h-p adaptive strategies are discussed.
An efficient implicit method for the computation of steady, three-dimensional, compressible Navier-Stokes flowfields is presented. A nonlinear iteration strategy based on planar Gauss-Seidel sweeps is used to drive the solution toward a steady state, with approximate factorization errors within a crossflow plane reduced by the application of a quasi-Newton technique. A hybrid discretization approach is employed, with flux-vector splitting utilized in the streamwise direction and central differences with artificial dissipation used for the transverse fluxes. Convergence histories and comparisons with experimental data are presented for several 3-D shock-boundary layer interactions. Both laminar and turbulent cases are considered, with turbulent closure provided by a modification of the Baldwin-Barth one-equation model. For the problems considered (175,000-325,000 mesh points), the algorithm provides steady-state convergence in 900-2000 CPU seconds on a single processor of a Cray Y-MP.
To better identify the necessary attributes of good stage-value predictors (SVPs), numerous SVPs are designed for an existing: ESDIRK4(3)7L[2]SA [26] and a new: ESDIRK4(3)8L[2]SA scheme.1 Both are stifflyaccurate, stage-order two, explicit, singly-diagonally implicit Runge–Kutta (ESDIRK) schemes. Tradeoffs are studied in the parameter spaces enforcing the constraints on accuracy, linear stability, nonlinear stability and coefficient size to determine which objectives correlate with effective predictors. The SVPs are tested on three challenging external aerodynamics problems [107 − 108 degrees of freedom (DoFs)], each with a different level of stiffness. The problems include two 3D airfoils simulations and one canonical turbulence simulation. All simulations use the compressible Navier-Stokes equations (CNSE). An entropy stable spectral collocation formulation is used for discretizing the spatial terms in the equations. Simulations are performed at a wide variety of temporal error tolerances. Problems that are sufficiently stiff (e.g., lax temporal error tolerances) benefit from SVPs designed with second-order accuracy and stability properties: A-stability, and L-stability, rather than high accuracy constraints. Simulations with modest stiffness (e.g., strict error tolerances) are better suited for SVPs designed using high accuracy constraints. Designing SVPs with enhanced stability properties is tedious but worthwhile. Simulation times are reduced with optimal SVPs by as much as 100% on some stages, with combined stepwise improvements of between 50 − 100% for both methods. A comparative study is performed with the two aforementioned methods as well as four other ESDIRKs. The newly designed ESDIRK4(3)8L[2]SA with γ ≈ 1/10, proves to be the most efficient of the six tested ESDIRK schemes simulating the CNSE.
The synergistic use of active and passive remote sensing (i.e., data fusion) demonstrates the ability of spaceborne light detection and ranging (LiDAR), synthetic aperture radar (SAR) and multispectral imagery for achieving the accuracy requirements of a global forest biomass mapping mission (+/-20 Mg/ha or 20%, the greater of the two, for at least 80% of grid cells). A data fusion approach also provides a means to extend 3D information from discrete spaceborne LiDAR measurements of forest structure across scales much larger than that of the LiDAR footprint. For estimating biomass, these measurements mix a number of errors including those associated with LiDAR footprint sampling over regional-global extents. A general framework for mapping above ground live forest biomass density (AGB) with a data fusion approach is presented and verified using data from NASA field campaigns near Howland, ME, USA, to assess AGB and LiDAR sampling errors across a regionally representative landscape. We combined SAR and Landsat-derived optical (passive optical) image data to identify contiguous areas (>0.5 ha) that are relatively homogenous in remote sensing metrics (forest patches). We used this image-derived data with simulated spaceborne LiDAR derived from orbit and cloud cover simulations and airborne data from NASA's Laser Vegetation Imaging Sensor (LVIS) to compute AGB and estimate LiDAR sampling error for forest patches and 100 m, 250 m, 500 m, and 1 km grid cells. At both the patch and grid scales, we evaluated differences in AGB estimation and sampling error from the combined use of LiDAR with both SAR and passive optical and with either SAR or passive optical alone. First, this data fusion approach demonstrates that incorporating forest patches into the AGB mapping framework can provide sub-grid forest information for coarser grid-level AGB reporting. Second, a data fusion approach for estimating AGB using simulated spaceborne LiDAR with SAR and passive optical image combinations reduced forest AGB sampling errors 12%-38% from those where LiDAR is used with SAR or passive optical alone. In absolute terms, sampling errors were reduced from 14-40 Mg/ha to 11-28 Mg/ha across all grid scales and prediction methods, where minimum sampling errors were 11, 15, 18, and 22 Mg/ha for 1 km, 500 m, 250 m, and 100 m grid scales, respectively. Third, spaceborne global scale accuracy requirements were achieved whereby at least 80% of the grid cells at 100 m, 250 m, 500 m, and 1 km grid levels met AGB accuracy requirements using a combination of passive optical and SAR along with machine learning methods to predict vegetation structure metrics for forested areas without LiDAR samples. Finally, using either passive optical or SAR, accuracy requirements were met at the 500 m and 250 m grid level, respectively..
The United States Harmful Algal Bloom and Hypoxia Research Control Act of 2014 identified the need for forecasting and monitoring harmful algal blooms (HAB) in lakes, reservoirs, and estuaries across the nation. Temperature is a driver in HAB forecasting models that affects both HAB growth rates and toxin production. Therefore, temperature data derived from the U.S. Geological Survey Landsat 5 Thematic Mapper and Landsat 7 Enhanced Thematic Mapper Plus thermal band products were validated across 35 lakes and reservoirs, and 24 estuaries. In situ data from the Water Quality Portal (WQP) were used for validation. The WQP serves data collected by state, federal, and tribal groups. Discrete in situ temperature data included measurements at 11,910 U.S. lakes and reservoirs from 1980 through 2015. Landsat temperature measurements could include 170,240 lakes and reservoirs once an operational product is achieved. The Landsat-derived temperature mean absolute error was 1.34 C in lake pixels (is) greater than180 m from land, 4.89 C at the land-water boundary, and 1.11 C in estuaries based on comparison against discrete surface in situ measurements. This is the first study to quantify Landsat resolvable U.S. lakes and reservoirs, and large-scale validation of an operational satellite provisional temperature climate data record algorithm. Due to the high performance of open water pixels, Landsat satellite data may supplement traditional in situ sampling by providing data for most U.S. lakes, reservoirs, and estuaries over consistent seasonal intervals (even with cloud cover) for an extended period of record of more than 35 years.
A significantly improved position for the X-ray source 3U 1921 + 43 has been obtained by ANS and Uhuru. The combined ANS-Uhuru error box is only about 7 by 7 arcmin and is centered on the cD galaxy in the Abell 2319 cluster of galaxies. Radio observations of this cluster indicate that the emission at 610 MHz includes several discrete sources and a weak extended component. This strengthens the general association between extended radio halos and X-ray emission from clusters of galaxies. The radio halo fills the X-ray error box and is consistent with the limits reported for the angular size of the X-ray source
A model has been developed to predict the reflectivity and Doppler performance of a spaceborne weather radar for atmospheric aerosol and cloud monitoring. The goal is to predict radar sensitivity, resolution, uncertainties and other key performance metrics vs. radar design parameters and hardware nonidealities. Analytical formulas are readily available to predict key performance metrics of a space-borne radar system as a function of design parameters such as antenna size, spacecraft velocity, transmit power, and receive noise figure. Effects of some system nonidealities such as antenna pointing errors, power amplifier nonlinearity and phase noise can be estimated using idealized methods. These analytical formulas use idealized forms of the antenna radiation pattern and weather statistics to predict system performance. However, it is desirable to have a more physical model based on discretized weather volumes in which the particle size distribution, Doppler distribution, and other parameters can be varied to study how the radar hardware design parameters and nonidealities affect the measurement of the weather reflectivity and Doppler characteristics. This would allow the radar designers to have more insight into what is being measured and the hardware parameters and errors that need to be carefully controlled to achieve best radar performance, as well as potential methods to calibrate the system or correct errors. This presentation will demonstrate some proof-of-concept Ka-band simulations where the discretized model agrees with the analytical formulas for a simple case where the elements in the discretized weather volume are defined by a constant reflectivity and simple velocity vectors. In particular, the system sensitivity and Doppler uncertainty are evaluated by analytical formulas as well as the discretized model. Future work will expand on this to include more complex weather scenarios and the addition of system nonidealities.
A laser Doppler velocimeter (LDV) was used to determine the flow conditions downstream of an annular cascade of stator blades operating at an exit critical velocity ratio of 0.87. Two modes of LDV operation (continuous scan and discrete point) were investigated. Conventional pressure probe measurements were also made for comparison with the LDV results. Biasing errors that occur in the LDV measurement of velocity components were also studied. In addition, the effect of pressure probe blockage on the flow conditions was determined with the LDV. Photographs and descriptions of the test equipment used are given.
Recent development using compact difference schemes to solve the Navier-Stokes equations show spectral-like accuracy. A study was made of the numerical characteristics of various combinations of the Runge-Kutta (RK) methods and compact difference schemes to calculate the unsteady Euler equations. The accuracy of finite difference schemes is assessed based on the evaluations of dissipative error. The objectives are reducing the numerical damping and, at the same time, preserving numerical stability. While this approach has tremendous success solving steady flows, numerical characteristics of unsteady calculations remain largely unclear. For unsteady flows, in addition to the dissipative errors, phase velocity and harmonic content of the numerical results are of concern. As a result of the discretization procedure, the simulated unsteady flow motions actually propagate in a dispersive numerical medium. Consequently, the dispersion characteristics of the numerical schemes which relate the phase velocity and wave number may greatly impact the numerical accuracy. The aim is to assess the numerical accuracy of the simulated results. To this end, the Fourier analysis is to provide the dispersive correlations of various numerical schemes. First, a detailed investigation of the existing RK methods is carried out. A generalized form of an N-step RK method is derived. With this generalized form, the criteria are derived for the three and four-step RK methods to be third and fourth-order time accurate for the non-linear equations, e.g., flow equations. These criteria are then applied to commonly used RK methods such as Jameson's 3-step and 4-step schemes and Wray's algorithm to identify the accuracy of the methods. For the spatial discretization, compact difference schemes are presented. The schemes are formulated in the operator-type to render themselves suitable for the Fourier analyses. The performance of the numerical methods is shown by numerical examples. These examples are detailed. described. The third case is a two-dimensional simulation of a Lamb vortex in an uniform flow. This calculation provides a realistic assessment of various finite difference schemes in terms of the conservation of the vortex strength and the harmonic content after travelling a substantial distance. The numerical implementation of Giles' non-refelctive equations coupled with the characteristic equations as the boundary condition is discussed in detail. Finally, the single vortex calculation is extended to simulate vortex pairing. For the distance between two vortices less than a threshold value, numerical results show crisp resolution of the vortex merging.
This paper is concerned with the continued development of a new numerical method, the space-time solution element (STS) method, for solving conservation laws. The present work focuses on the two-dimensional, steady, incompressible Navier-Stokes equations. Using first an integral approach, and then a differential approach, the discrete flux conservation equations presented in a recent paper are rederived. Here a simpler method for determining the flux expressions at cell interfaces is given; a systematic and rigorous derivation of the conditions used to simulate the differential form of the governing conservation law(s) is provided; necessary and sufficient conditions for a discrete approximation to satisfy a conservation law in E2 are derived; and an estimate of the local truncation error is given. A specific scheme is then constructed for the solution of the thin airfoil boundary layer problem. Numerical results are presented which demonstrate the ability of the scheme to accurately resolve the developing boundary layer and wake regions using grids which are much coarser than those employed by other numerical methods. It is shown that ten cells in the cross-stream direction are sufficient to accurately resolve the developing airfoil boundary layer.
Atmospheric methane trends over the last few years have been increasing at a rate of 7-12 parts per billion (ppb) per year after brief a pause in the first decade of this century. The reasons for the pause and subsequent increase remains unclear. Thus, there is a critical need for additional, precise and accurate methane observations to understand the natural and anthropogenic processes that drive the trends in atmospheric methane and to constrain its sources, and sinks. At NASA Goddard Space Flight Center (GSFC), in collaboration with Freedom Photonics Inc., we have been developing a lidar to measure atmospheric methane using Integrated Path Differential Absorption (IPDA) from an airborne platform as a precursor to a future space mission. In this paper we present the design of a laser transmitter operating at ~1651 nmbased on a newly developed Distributed Bragg Grating (DBR) seed laser and an Optical parametric oscillator (OPO). The DBR is rapidly step-tuned over the methane absorption at several discrete wavelengths. This multi-wavelength approach enables us to sample the entire methane lineshape and reduce systematic errors.
This paper presents the general relative orbit dynamics equations and GPS (Global Positioning System) orbit observational equations that have been developed for on-board control of spacecraft flying in formation. The approach to the implementation of the autonomous control for orbit acquisition and maintenance of spacecraft formation using GPS code pseudoranges are presented. As a practical application of the models and method provided in this paper, the orbit control of the Earth-Orbiter 1(EO-1) / Landsat 7 system has been designed, using the discrete-time linear optimal output feedback control. For the actuator of the on/off type reaction jets, the implementation problem of the pulse-amplitude modulation is also studied. Simulation results of autonomous orbit control and maintenance, for 3-dimensional initial orbit error, using optimal output feedback control are shown. These simulation results certified the feasibility of the implementation of the autonomous maintenance control for EO-1/Landsat 7 formation flying by means of the discrete-time linear optimal output feedback control.
Rate distortion functions for two-dimensional homogeneous isotropic images are compared with the performance of 5 source encoders designed for such images. Both unweighted and frequency weighted mean square error distortion measures are considered. The coders considered are differential PCM (DPCM) using six previous samples in the prediction, herein called 6 pel (picutre element) DPCM; simple DPCM using single sample prediction; 6 pel DPCM followed by entropy coding; 8 x 8 discrete cosine transform coder, and 4 x 4 Hadamard transform coder. Other transform coders were studied and found to have about the same performance as the two transform coders above. With the mean square error distortion measure DPCM with entropy coding performed best. The relative performance of the coders changes slightly when the distortion measure is frequency weighted mean square error. The performance of all the coders was separated by only about 4 dB.
This paper considers defect-correction solvers for a second order upwind-biased discretization of the 2D convection equation. The following important features are reported: (1) The asymptotic convergence rate is about 0.5 per defect-correction iteration. (2) If the operators involved in defect-correction iterations have different approximation order, then the initial convergence rates may be very slow. The number of iterations required to get into the asymptotic convergence regime might grow on fine grids as a negative power of h. In the case of a second order target operator and a first order driver operator, this number of iterations is roughly proportional to h-1/3. (3) If both the operators have the second approximation order, the defect-correction solver demonstrates the asymptotic convergence rate after three iterations at most. The same three iterations are required to converge algebraic error below the truncation error level. A novel comprehensive half-space Fourier mode analysis (which, by the way, can take into account the influence of discretized outflow boundary conditions as well) for the defect-correction method is developed. This analysis explains many phenomena observed in solving non-elliptic equations and provides a close prediction of the actual solution behavior. It predicts the convergence rate for each iteration and the asymptotic convergence rate. As a result of this analysis, a new very efficient adaptive multigrid algorithm solving the discrete problem to within a given accuracy is proposed. Numerical simulations confirm the accuracy of the analysis and the efficiency of the proposed algorithm. The results of the numerical tests are reported.
Guiding one state of linear dynamical system to prescribed rms terminal accuracy in presence of injection, measurement and engine-mechanization error
A model for on-line diagnosis was investigated for discrete-time systems, and resettable sequential systems. Generalized notions of a realization are discussed along with fault tolerance and errors. Further investigation into the theory of on-line diagnosis is recommended for three levels: binary state-assigned level, logical circuit level, and the subsystem-network level.
A suboptimal dynamic compensator to be used in conjunction with the ordinary discrete time Kalman filter was derived. The resultant compensated Kalman Filter has the property that steady state bias estimation errors, resulting from modelling errors, were eliminated.
An in-flight wing wake section drag investigation was conducted using traversing pitot and static probes. The primary objective was to develop measurement techniques and improve the accuracy of in-flight wing profile drag measurements for low values of dynamic pressure and Reynolds number. Data were obtained on a sailplane for speeds from about 40 knots to 125 knots at chord Reynolds numbers between 1,000,000 and 3,000,000. Tests were conducted with zero flap deflection, deflected flaps, and various degrees of surface roughness, and for smooth and rough atmospheric conditions. Several techniques were used to increase data reliability and to minimize certain bias errors. A discussion of the effects of a total pressure probe in a pressure gradient, and the effects of discrete turbulence levels, on the data presented and other experimental results is also included.