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NASA NTRS1991

User's guide for NETS/PROSSS

Expensive analysis programs are often combined with optimization procedures to solve engineering problems. To obtain an optimal solution requires numerous iterations between the analysis program and the optimizer. This often becomes prohibitive due to the cost and amount of computer time needed to converge to an optimal solution. NETS/PROSSS was developed to address this problem. The purpose of this paper is to serve as a user's guide for NETS/PROSSS. The key features include the neural network, determining the training pairs for the neural network, and the approximated analysis/optimization process. A small problem is given to serve as an example of how to apply the system.

Rogers, James L.↗

NASA NTRS2003

Combining Static Analysis and Model Checking for Software Analysis

We present an iterative technique in which model checking and static analysis are combined to verify large software systems. The role of the static analysis is to compute partial order information which the model checker uses to reduce the state space. During exploration, the model checker also computes aliasing information that it gives to the static analyzer which can then refine its analysis. The result of this refined analysis is then fed back to the model checker which updates its partial order reduction. At each step of this iterative process, the static analysis computes optimistic information which results in an unsafe reduction of the state space. However we show that the process converges to a fired point at which time the partial order information is safe and the whole state space is explored.

Brat, Guillaume↗

NASA NTRS2003

Comparison of Artificial Compressibility Methods

Various artificial compressibility methods for calculating three-dimensional, steady and unsteady, laminar and turbulent, incompressible Navier-Stokes equations are compared in this work. Each method is described in detail along with appropriate physical and numerical boundary conditions. Analysis of well-posedness and numerical solutions to test problems for each method are provided. A comparison based on convergence behavior, accuracy, stability and robustness is used to establish the relative positive and negative characteristics of each method.

Kiris, Cetin↗

NASA NTRS2011

Assessment of Radiative Heating Uncertainty for Hyperbolic Earth Entry

This paper investigates the shock-layer radiative heating uncertainty for hyperbolic Earth entry, with the main focus being a Mars return. In Part I of this work, a baseline simulation approach involving the LAURA Navier-Stokes code with coupled ablation and radiation is presented, with the HARA radiation code being used for the radiation predictions. Flight cases representative of peak-heating Mars or asteroid return are de ned and the strong influence of coupled ablation and radiation on their aerothermodynamic environments are shown. Structural uncertainties inherent in the baseline simulations are identified, with turbulence modeling, precursor absorption, grid convergence, and radiation transport uncertainties combining for a +34% and ..24% structural uncertainty on the radiative heating. A parametric uncertainty analysis, which assumes interval uncertainties, is presented. This analysis accounts for uncertainties in the radiation models as well as heat of formation uncertainties in the flow field model. Discussions and references are provided to support the uncertainty range chosen for each parameter. A parametric uncertainty of +47.3% and -28.3% is computed for the stagnation-point radiative heating for the 15 km/s Mars-return case. A breakdown of the largest individual uncertainty contributors is presented, which includes C3 Swings cross-section, photoionization edge shift, and Opacity Project atomic lines. Combining the structural and parametric uncertainty components results in a total uncertainty of +81.3% and ..52.3% for the Mars-return case. In Part II, the computational technique and uncertainty analysis presented in Part I are applied to 1960s era shock-tube and constricted-arc experimental cases. It is shown that experiments contain shock layer temperatures and radiative ux values relevant to the Mars-return cases of present interest. Comparisons between the predictions and measurements, accounting for the uncertainty in both, are made for a range of experiments. A measure of comparison quality is de ned, which consists of the percent overlap of the predicted uncertainty bar with the corresponding measurement uncertainty bar. For nearly all cases, this percent overlap is greater than zero, and for most of the higher temperature cases (T >13,000 K) it is greater than 50%. These favorable comparisons provide evidence that the baseline computational technique and uncertainty analysis presented in Part I are adequate for Mars-return simulations. In Part III, the computational technique and uncertainty analysis presented in Part I are applied to EAST shock-tube cases. These experimental cases contain wavelength dependent intensity measurements in a wavelength range that covers 60% of the radiative intensity for the 11 km/s, 5 m radius flight case studied in Part I. Comparisons between the predictions and EAST measurements are made for a range of experiments. The uncertainty analysis presented in Part I is applied to each prediction, and comparisons are made using the metrics defined in Part II. The agreement between predictions and measurements is excellent for velocities greater than 10.5 km/s. Both the wavelength dependent and wavelength integrated intensities agree within 30% for nearly all cases considered. This agreement provides confidence in the computational technique and uncertainty analysis presented in Part I, and provides further evidence that this approach is adequate for Mars-return simulations. Part IV of this paper reviews existing experimental data that include the influence of massive ablation on radiative heating. It is concluded that this existing data is not sufficient for the present uncertainty analysis. Experiments to capture the influence of massive ablation on radiation are suggested as future work, along with further studies of the radiative precursor and improvements in the radiation properties of ablation products.

Johnston, Christopher O.↗

NASA NTRS2016

Evaluating ESA CCI Soil Moisture in East Africa

To assess growing season conditions where ground based observations are limited or unavailable, food security and agricultural drought monitoring analysts rely on publicly available remotely sensed rainfall and vegetation greenness. There are also remotely sensed soil moisture observations from missions like the European Space Agency (ESA) Soil Moisture and Ocean Salinity (SMOS) and NASAs Soil Moisture Active Passive (SMAP), however these time series are still too short to conduct studies that demonstrate the utility of these data for operational applications, or to provide historical context for extreme wet or dry events. To promote the use of remotely sensed soil moisture in agricultural drought and food security monitoring, we use East Africa as a case study to evaluate the quality of a 30+ year time series of merged active-passive microwave soil moisture from the ESA Climate Change Initiative (CCI-SM). Compared to the Normalized Difference Vegetation index (NDVI) and modeled soil moisture products, we found substantial spatial and temporal gaps in the early part of the CCI-SM record, with adequate data coverage beginning in 1992. From this point forward, growing season CCI-SM anomalies were well correlated (R greater than 0.5) with modeled, seasonal soil moisture, and in some regions, NDVI. We use correlation analysis and qualitative comparisons at seasonal time scales to show that remotely sensed soil moisture can add information to a convergence of evidence framework that traditionally relies on rainfall and NDVI in moderately vegetated regions.

Amy McNally↗

NASA NTRS1989

Design of optimally smoothing multi-stage schemes for the Euler equations

In this paper, a method is developed for designing multi-stage schemes that give optimal damping of high-frequencies for a given spatial-differencing operator. The objective of the method is to design schemes that combine well with multi-grid acceleration. The schemes are tested on a nonlinear scalar equation, and compared to Runge-Kutta schemes with the maximum stable time-step. The optimally smoothing schemes perform better than the Runge-Kutta schemes, even on a single grid. The analysis is extended to the Euler equations in one space-dimension by use of 'characteristic time-stepping', which preconditions the equations, removing stiffness due to variations among characteristic speeds. Convergence rates independent of the number of cells in the finest grid are achieved for transonic flow with and without a shock. Characteristic time-stepping is shown to be preferable to local time-stepping, although use of the optimally damping schemes appears to enhance the performance of local time-stepping. The extension of the analysis to the two-dimensional Euler equations is hampered by the lack of a model for characteristic time-stepping in two dimensions. Some results for local time-stepping are presented.

Van Leer, Bram↗

NASA NTRS1942

Square plate with clamped edges under normal pressure producing large deflections

A theoretical analysis is given for the stresses and deflections of a square plate with clamped edges under normal pressure producing large deflections. Values of the bending stress and membrane stress at the center of the plate and at the midpoint of the edge are given for center deflections up to 1.9 times the plate thickness. The shape of the deflected surface is given for low pressures and for the highest pressure considered. Convergence of the solution is considered and it is estimated that the possible error is less than 2 percent. The results are compared with the only previous approximate analysis known to the author and agree within 5 percent. They are also shown to compare favorably with the known exact solutions for the long rectangular plate and the circular plate.

PLATES-PRESSURE↗

NASA NTRS1990

Consistency and convergence for numerical radiation conditions

The problem of imposing radiation conditions at artificial boundaries for the numerical simulation of wave propagation is considered. Emphasis is on the behavior and analysis of the error which results from the restriction of the domain. The theory of error estimation is briefly outlined for boundary conditions. Use is made of the asymptotic analysis of propagating wave groups to derive and analyze boundary operators. For dissipative problems this leads to local, accurate conditions, but falls short in the hyperbolic case. A numerical experiment on the solution of the wave equation with cylindrical symmetry is described. A unified presentation of a number of conditions which have been proposed in the literature is given and the time dependence of the error which results from their use is displayed. The results are in qualitative agreement with theoretical considerations. It was found, however, that for this model problem it is particularly difficult to force the error to decay rapidly in time.

Hagstrom, Thomas↗

NASA NTRS2003

Applications of Sea-Ice Motion and Deformation Derived from Satellite Data

QuikSCAT backscatter, AMSR and DMSP SSM/I radiance data have been used to derive sea ice motion for both the Arctic and Antarctic region using the wavelet analysis tracking method. All results from QuikSCAT, AMSR and SSM5 are compatible with buoys and can then be merged by data fusion method to generate composite sea ice motion maps for more complete coverage. Furthermore, based on this merged data set daily sea-ice deformation (shear, and convergence) maps have been produced and show consistent spatial and temporal patterns. Temporal correlation maps between ice deformation and SSM/II ice concentration show interesting results in the Arctic, especially the coast area. In this study, principal component analysis for both the merged ice tracking result from satellite data and pressure field from buoy have also been examined for the relationship between the principal components and eigenvectors from these two data sets. While the result shows that principal components of modes 1 and 2 from two data sets are highly correlated which confirms that wind forcing is a major factor driving the ice drift, it also reveals that other high energy modes are not highly correlated which maybe caused by coastal effects. Principal component analysis of Arctic sea-ice motion during fall/winter period in different years shows the reverse of dominant modes or patterns is related to the Arctic Oscillation.

Liu, Antony K.↗

NASA NTRS1976

A scaling law for energy transfer by inelastic electron-molecule collisions in mixtures

The equation governing the electron energy distribution in the presence of a spatially uniform electric field in a weakly ionized gas was reformulated into an integral equation for the logarithmic slope of the distribution function. For gas mixtures in which the dominant electron energy loss mechanism is by vibrational excitation of the molecules, this equation is suitable for approximate analysis and exact numerical solution by iteration. Superelastic collisions are easily included in this formulation, and do not seriously effect the convergence of the numerical scheme. The approximate analytical results are only qualitatively correct, but suggest appropriate parameters which correlate the exact numerical results very well. The distribution function as well as certain gross properties such as net energy transfer into vibration, mean energy, and drift velocity depend primarily on a single nondimensional parameter involving only E/N and the cross sections.

Bienkowski, G. K.↗

NASA NTRS1994

Aspects of unstructured grids and finite-volume solvers for the Euler and Navier-Stokes equations

Basic algorithms for unstructured mesh generation and fluid flow calculation are discussed. In particular the following are addressed: preliminaries of graphs and meshes; duality and data structures; basic graph operations important in CFD (Computational Fluid Dynamics); triangulation methods, including Varonoi diagrams and Delaunay triangulation; maximum principle analysis; finite volume schemes for scalar conservation law equations; finite volume schemes for the Euler and Navier-Stokes equations; and convergence acceleration for steady state calculations.

Barth, T. J.↗

NASA NTRS1996

Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization

Fast methods are proposed for solving the system K(sub N)x = b resulting from the discretization of self-adjoint elliptic equations in three dimensional domains by the spectral element method. The domain is decomposed into hexahedral elements, and in each of these elements the discretization space is formed by polynomials of degree N in each variable. Gauss-Lobatto-Legendre (GLL) quadrature rules replace the integrals in the Galerkin formulation. This system is solved by the preconditioned conjugate gradients method. The conforming finite element space on the GLL mesh consisting of piecewise Q(sub 1) elements produces a stiffness matrix K(sub h) that is spectrally equivalent to the spectral element stiffness matrix K(sub N). The action of the inverse of K(sub h) is expensive for large problems, and is therefore replaced by a Schwarz preconditioner B(sub h) of this finite element stiffness matrix. The preconditioned operator then becomes B(sub h)(exp -l)K(sub N). The technical difficulties stem from the nonregularity of the mesh. Tools to estimate the convergence of a large class of new iterative substructuring and overlapping Schwarz preconditioners are developed. This technique also provides a new analysis for an iterative substructuring method proposed by Pavarino and Widlund for the spectral element discretization.

Casarin, Mario↗

NASA NTRS1999

Realistic NLTE Radiative Transfer for Modeling Stellar Winds

This NASA grant supported the development of codes to solve the non-LTE multi-level spherical radiative transfer problem in the presence of velocity fields. Much of this work was done in collaboration with Graham Harper (CASA, University of Colorado). These codes were developed for application to the cool, low-velocity winds of evolved late-type stars. Particular emphasis was placed on modeling the wind of lambda Velorum (K4 lb), the brightest K supergiant in the sky, based on extensive observations of the ultraviolet spectrum with the HST/GHRS from GO program 5307. Several solution techniques were examined, including the Eddington factor Approach described in detail by Bennett & Harper (1997). An Eddington factor variant of Harper's S-MULTI code (Harper 1994) for stationary atmospheres was developed and implemented, although full convergence was not realized. The ratio of wind terminal velocity to turbulent velocity is large (approx. 0.3-0.5) in these cool star winds so this assumption of stationarity provides reasonable starting models. Final models, incorporating specified wind laws, were converged using the comoving CRD S-MULTI code. Details of the solution procedure were published by Bennett & Harper (1997). Our analysis of the wind of lambda Vel, based on wind absorption superimposed on chromospheric emission lines in the ultraviolet, can be found in Carpenter et al. (1999). In this paper, we compare observed wind absorption features to an exact CRD calculation in the comoving frame, and also to a much quicker, but approximate, method using the SEI (Sobolev with Exact Integration) code of Lamers, Cerruti-Sola, & Perinotto (1987). Carpenter et al. (1999) provide detailed comparisons of the exact CRD and approximate SEI results and discuss when SEI is adequate to use for computing wind line profiles. Unfortunately, the observational material is insufficient to unambiguously determine the wind acceleration law for lambda Vel. Relatively few unblended Fe II lines of optical depth sensitive to the wind acceleration region are present in the existing HST/GHRS data set. Most of the Fe II lines are either too optically thick (resulting in a board, black wind absorption profile) or too optically thin (resulting in no wind absorption feature present). Also, most of the ultraviolet spectra obtained from HST GO-5307 was at medium resolution (R approx. 40,000, corresponding to a velocity resolution of 7.5 km/s). This is simply inadequate to resolve the turbulence in the outer wind; a key parameter in theoretical wind models. We can now say that an unambiguous determination of the wind velocity law in lambda Vel will require complete coverage of the ultraviolet spectrum at high dispersion (R approx. 10(exp 5), or 3 km/s). This is now feasible usin, the STIS echelle spectrograph on-board HST.

Bennett, Philip D.↗

NASA NTRS2005

Quantifying Exact Motions Along Lineaments on Europa

Evaluating the precise motions along lineaments on the surface of Jupiter's icy moon, Europa, is a valuable tool for interpreting the development and history of lineaments of various morphologies. Such morphologies include strike-slip faults, dilational bands, ridges, and convergence zones. However, the exact mode of origin and kinematic behavior of these various lineaments are not obvious based on morphology alone. In fact, the apparent motions implied by displaced crosscut features can provide misleading indications of true motions along lineaments. Identifying the precise motions (combinations of sliding and opening/closing) is critical to the accurate characterization and interpretation of each of these lineament types. Lineaments of interest (i.e., those having displaced relatively older features in some manner) are identified on Galileo spacecraft images and measurements are made of the total offset, the separation, and relative orientations of crosscut features with respect to the lineament of interest. Specifically, by using these measured quantities and a series of trigonometric equations, the precise motions (i.e., dilation, convergence, strike-slip, or a combination of strike-slip and dilation or convergence) can be determined. These measurements are, however, limited by the resolution of the available images. This study focuses on motion analysis techniques for Europan lineaments and the precise characterization of fault-orthogonal and/or strike-slip motion along lineaments of varying morphologies. We highlight potential pitfalls of cursory analyses of motion indicators. For example, lineaments with obvious lateral offsets have typically been identified simply as strike-slip faults. This assumption may actually be incorrect, as fault-orthogonal motions may contribute to apparent lateral displacements (offsets or separations). Also, variability in the amount of fault motion along the trace length should theoretically be identifiable using the outlined technique. Strike-slip faults on Europa have conventionally been presumed to have a constant slip magnitude along their lengths; however, we posit that variable distributions of slip may be common, as is typical along terrestrial strike-slip faults.

Vetter, J. C.↗

NASA NTRS2016

Closing the Contrast Gap Between Testbed and Model Prediction with WFIRST-CGI Shaped Pupil Coronagraph

JPL has recently passed an important milestone in its technology development for a proposed NASA WFIRST mission: demonstration of a better than 1x10-8 contrast over broad bandwidth (10%) on both shaped pupil coronagraph (SPC) and hybrid Lyot coronagraph (HLC) testbeds with WFIRST telescope optics. Challenges remain, however, in the technology readiness for the proposed mission. One such is the discrepancy between the achieved contrast on testbeds and their corresponding model predictions. A series of testbed diagnosis and modeling activity were planned and (some) carried out on SPC testbed in order to close the gap. A very useful tool we developed was to analyze the measured testbed Jacobian and compare with its model version that was used to control image plane speckle pattern. The difference between these two is the error in the control Jacobian. When the error, which includes both amplitude and phase, was inserted into a separate prediction model with nominal Jacobian, the model prediction became closely matching the SPC testbed behavior in both contrast floor and contrast convergence speed. This offers a new perspective and is a step closer toward model validation for high contrast coronagraph. Further Jacobian analysis and modeling provided clues to the possible sources for the mismatch: the DM misregistration and the underrepresented testbed optics wavefront error (WFE) and the deformable mirror (DM) setting for correcting this WFE. These analyses suggested that high contrast coronagraph has a tight tolerance in the accuracy of its control Jacobian. Modifications to both testbed control model as well as prediction model are being implemented and future works discussed.

diffraction modeling↗

NASA NTRS2020

Passive Roll Stabilization of the Near Earth Asteroid Scout Solar Sail Mission

The Near Earth Asteroid (NEA) Scout is a small satellite, solar sail mission set to launch on Artemis I. Analysis of the NEA Scout solar radiation pressure model determined that, for certain solar incidence angles, there exists at least one locally stable equilibrium point about the “roll” axis, or the axis normal to the solar sail plane. This analysis is extended to three other geometrically similar solar sail models, and a Lyapunov stability analysis is conducted demonstrating that the stable equilibria are locally stable for the majority of roll angles in a wide range of solar incidence angles. Under certain assumptions, it is possible that only two axis control is required for non-spinning solar sails. If the roll axis is controlled, an active rate damping controller can be designed to asymptotically stabilize the system. Simulation results are presented that follow the stability analysis, where in the homogenous case, the system enters a limit cycle and, in the actively damped case, the system asymptotically converges to the equilibrium point.

Ivan Rodrigues Bertaska↗

NASA NTRS2018

Analyzing the Relationship between Tracking and Covariance for Satellite Collision Avoidance

This presentation will display statistical analysis performed with over 150,000 Conjunction Data Messages (CDMs) received for the Earth Observing System (EOS) Aqua, Aura and Terra satellites within the three year period of March 2015 through February 2018. The analysis performed demonstrates the relationship between the covariance of a secondary object and the amount of tracks it receives, as a function of Time to Closest Approach (TCA). The examination indicates that higher tracking frequencies result in lower uncertainties inclusively from the time the data is screened up until TCA. Further investigation displays the impacts of how additional observations of secondary objects lower their position uncertainties and what period of time prior to TCA convergence of the covariance can be expected depending on how well the objects are tracked. Data points from several recent EOS High Interest Events (HIEs) are used to exemplify this analysis.

Collision Avoidance↗

NASA NTRS1994

Multiblock analysis for Shuttle Orbiter reentry heating from Mach 24 to Mach 12

A multiblock, laminar heating analysis for the shuttle orbiter at three trajectory points ranging from Mach 24.3 to Mach 12.86 on reentry is described. The analysis is performed using the Langley Aerothermodynamic Upwind Relaxation Algorithm with a seven species chemical nonequilibrium model. A finite-catalytic-wall model appropriate for shuttle tiles at a radiative equilibrium wall temperature is applied. Computed heating levels are generally in good agreement with the flight data, although a few rather large discrepancies remain unexplained. The multiblock relaxation strategy partitions the flowfield into manageable blocks requiring a fraction of the computational resources (time and memory) required by a full domain approach. In fact, the computational cost for a solution at even a single trajectory point would be prohibitively expensive at the given resolution without the multiblock approach. Converged blocks are reassembled to enable a fully coupled converged solution over the entire vehicle, starting from a nearly converged initial condition.

LANGLEY AEROTHERMODYNAMIC UPWI↗