Results for “collocation techniques” — Page 9

NASA NTRS1986

A spectral element method for the simulation of unsteady incompressible flows with heat transfer

The spectral element method is a high-order finite element technique for solution of the Navier-Stokes and energy equations. In the isoparametric spectral element discretization, the domain is broken up into general brick elements, and the dependent and independent variables represented as high-order tensor-product Lagrangian interpolants through Chebyshev collocation points. The nonlinear and convective terms in the governing equations are treated with explicit collocation, while the pressure and diffusive contributions are handled implicitly using variational projection operators. The method is applied to flow past a cylinder, flow in grooved channels, and natural convection in an enclosure.

Karniadakis, George E.↗

NASA NTRS2014

Direct Aerosol Radiative Forcing Based on Combined A-Train Observations: Towards All-sky Estimates and Attribution to Aerosol Type

We describe a technique for combining CALIOP aerosol backscatter, MODIS spectral AOD (aerosol optical depth), and OMI AAOD (absorption aerosol optical depth) measurements for the purpose of estimating full spectral sets of aerosol radiative properties, and ultimately for calculating the 3-D distribution of direct aerosol radiative forcing. We present results using one year of data collected in 2007 and show comparisons of the aerosol radiative property estimates to collocated AERONET retrievals. Initial calculations of seasonal clear-sky aerosol radiative forcing based on our multi-sensor aerosol retrievals compare well with over-ocean and top of the atmosphere IPCC-2007 model-based results, and with more recent assessments in the "Climate Change Science Program Report: Atmospheric Aerosol Properties and Climate Impacts" (2009). We discuss some of the challenges that exist in extending our clear-sky results to all-sky conditions. On the basis of comparisons to suborbital measurements, we present some of the limitations of the MODIS and CALIOP retrievals in the presence of adjacent or underlying clouds. Strategies for meeting these challenges are discussed. We also discuss a methodology for using the multi-sensor aerosol retrievals for aerosol type classification based on advanced clustering techniques. The combination of research results permits conclusions regarding the attribution of aerosol radiative forcing to aerosol type.

AOD↗

NASA NTRS1980

Reformulation of Possio's kernel with application to unsteady wind tunnel interference

An efficient method for computing the Possio kernel has remained elusive up to the present time. In this paper the Possio is reformulated so that it can be computed accurately using existing high precision numerical quadrature techniques. Convergence to the correct values is demonstrated and optimization of the integration procedures is discussed. Since more general kernels such as those associated with unsteady flows in ventilated wind tunnels are analytic perturbations of the Possio free air kernel, a more accurate evaluation of their collocation matrices results with an exponential improvement in convergence. An application to predicting frequency response of an airfoil-trailing edge control system in a wind tunnel compared with that in free air is given showing strong interference effects.

Fromme, J. A.↗

NASA NTRS1989

Estimation and filtering techniques for high-accuracy GPS applications

Techniques for determination of very precise orbits for satellites of the Global Positioning System (GPS) are currently being studied and demonstrated. These techniques can be used to make cm-accurate measurements of station locations relative to the geocenter, monitor earth orientation over timescales of hours, and provide tropospheric and clock delay calibrations during observations made with deep space radio antennas at sites where the GPS receivers have been collocated. For high-earth orbiters, meter-level knowledge of position will be available from GPS, while at low altitudes, sub-decimeter accuracy will be possible. Estimation of satellite orbits and other parameters such as ground station positions is carried out with a multi-satellite batch sequential pseudo-epoch state process noise filter. Both square-root information filtering (SRIF) and UD-factorized covariance filtering formulations are implemented in the software.

Lichten, S. M.↗

NASA NTRS1996

First Estimates of the Radiative Forcing of Aerosols Generated from Biomass Burning Using Satellite Data

Collocated measurements from the Advanced Very High Resolution Radiometer (AVHRR) and the Earth Radiation Budget Experiment (ERBE) scanner are used to examine the radiative forcing of atmospheric aerosols generated from biomass burning for 13 images in South America. Using the AVHRR, Local Area Coverage (LAC) data, a new technique based on a combination of spectral and textural measures is developed for detecting these aerosols. Then, the instantaneous shortwave, longwave, and net radiative forcing values are computed from the ERBE instantaneous scanner data. Results for the selected samples from 13 images show that the mean instantaneous net radiative forcing for areas with heavy aerosol loading is about -36 W/sq m and that for the optically thin aerosols are about -16 W/sq m. These results, although preliminary, provide the first estimates of radiative forcing of atmospheric aerosols from biomass burning using satellite data.

Christopher, Sundar A.↗

NASA NTRS1996

First Estimates of the Radiative Forcing of Aerosols Generated from Biomass Burning using Satellite Data

Collocated measurements from the Advanced Very High Resolution Radiometer (AVHRR) and the Earth Radiation Budget Experiment (ERBE) scanner are used to examine the radiative forcing of atmospheric aerosols generated from biomass burning for 13 images in South America. Using the AVHRR, Local Area Coverage (LAC) data, a new technique based on a combination of spectral and textural measures is developed for detecting these aerosols. Then, the instantaneous shortwave, longwave, and net radiative forcing values are computed from the ERBE instantaneous scanner data. Results for the selected samples from 13 images show that the mean instantaneous net radiative forcing for areas with heavy aerosol loading is about -36 W/sq m and that for the optically thin aerosols are about -16 W/sq m. These results, although preliminary, provide the first estimates of radiative forcing of atmospheric aerosols from biomass burning using satellite data.

Chistopher, Sundar A.↗

NASA NTRS1996

First Estimates of the Radiative Forcing of Aerosols Generated from Biomass Burning Using Satellite Data

Collocated measurements from the Advanced Very High Resolution Radiometer (AVHRR) and the Earth Radiation Budget Experiment (ERBE) scanner are used to examine the radiative forcing of atmospheric aerosols generated from biomass burning for 13 images in South America. Using the AVHRR, Local Area Coverage (LAC) data, a new technique based on a combination of spectral and textural measures is developed for detecting these aerosols. Then, the instantaneous shortwave, longwave, and net radiative forcing values arc computed from the ERBE instantaneous scanner data. Results for the selected samples from 13 images show that the mean instantaneous net radiative forcing for areas with heavy aerosol loading is about -36 W/square meter and that for the optically thin aerosols are about -16 W/square meter. These results, although preliminary, provide the first estimates of radiative forcing of atmospheric aerosols from biomass burning using satellite data.

Christopher, Sundar A.↗

NASA NTRSDate not supplied

Geodetic Reference Instrument Transponder for Small Satellites (Gritss)

The accuracy of the Terrestrial Reference Frame is limited by systematic errors in tying the contributions from the different geodetic techniques. Local survey uncertainties are limited due to the inaccessibility of the instrument reference points. NASA is implementing a technology demonstration mission called Geodetic Reference Instrument Transponder for Small Satellites(GRITSS) that uses a small satellite as a space-based ref-refence point for tying together collocated geodetic stations. The technology being demonstrated uses a novel idea of upconverting the Global Positioning System (GPS) signals received at the satellite and transponding them to a VLBI Global Observing System (VGOS) antenna ground station. This approach does not require the satellite to be in view of more than one VLBI station at a time, allowing the use of Low Earth Orbits and an inexpensive CubeSat. The demonstration will initially involve only the NASA VGOS stations in Maryland, Hawaii, and Texas, but may be expanded later in the mission to include other international VGOS stations. This presentation will provide an overview of the GRITSS mission and the measurement concept.

S M Merkowitz↗

NASA NTRSDate not supplied

Geodetic Reference Instrument Transponder for Small Satellites (GRITTS)

The accuracy of the Terrestrial Reference Frame is limited by systematic errors in tying the contributions from the different geodetic techniques. Local survey uncertainties are limited due to the inaccessibility of the instrument reference points. NASA is implementing a technology demonstration mission called Geodetic Reference Instrument Transponder for Small Satellites(GRITSS) that uses a small satellite as a space-based ref-refence point for tying together collocated geodetic stations. The technology being demonstrated uses a novel idea of upconverting the Global Positioning System (GPS) signals received at the satellite and transponding them to a VLBI Global Observing System (VGOS) antenna ground station. This approach does not require the satellite to be in view of more than one VLBI station at a time, allowing the use of Low Earth Orbits and an inexpensive CubeSat. The demonstration will initially involve only the NASA VGOS stations in Maryland, Hawaii, and Texas, but may be expanded later in the mission to include other international VGOS stations. This presentation will provide an overview of the GRITSS mission and the measurement concept.

S. M. Merkowitz↗

NASA NTRSDate not supplied

Geodetic Reference Instrument Transponder for Small Satellites (GRITTS)

The accuracy of the Terrestrial Reference Frame is limited by systematic errors in tying the contributions from the different geodetic techniques. Local survey uncertainties are limited due to the inaccessibility of the instrument reference points. NASA is implementing a technology demonstration mission called Geodetic Reference Instrument Transponder for Small Satellites(GRITSS) that uses a small satellite as a space-based ref-refence point for tying together collocated geodetic stations. The technology being demonstrated uses a novel idea of upconverting the Global Positioning System (GPS) signals received at the satellite and transponding them to a VLBI Global Observing System (VGOS) antenna ground station. This approach does not require the satellite to be in view of more than one VLBI station at a time, allowing the use of Low Earth Orbits and an inexpensive CubeSat. The demonstration will initially involve only the NASA VGOS stations in Maryland, Hawaii, and Texas, but may be expanded later in the mission to include other international VGOS stations. This presentation will provide an overview of the GRITSS mission and the measurement concept.

S M Merkowitz↗

NASA NTRS2013

High-Order Space-Time Methods for Conservation Laws

Current high-order methods such as discontinuous Galerkin and/or flux reconstruction can provide effective discretization for the spatial derivatives. Together with a time discretization, such methods result in either too small a time step size in the case of an explicit scheme or a very large system in the case of an implicit one. To tackle these problems, two new high-order space-time schemes for conservation laws are introduced: the first is explicit and the second, implicit. The explicit method here, also called the moment scheme, achieves a Courant-Friedrichs-Lewy (CFL) condition of 1 for the case of one-spatial dimension regardless of the degree of the polynomial approximation. (For standard explicit methods, if the spatial approximation is of degree p, then the time step sizes are typically proportional to 1/p(exp 2)). Fourier analyses for the one and two-dimensional cases are carried out. The property of super accuracy (or super convergence) is discussed. The implicit method is a simplified but optimal version of the discontinuous Galerkin scheme applied to time. It reduces to a collocation implicit Runge-Kutta (RK) method for ordinary differential equations (ODE) called Radau IIA. The explicit and implicit schemes are closely related since they employ the same intermediate time levels, and the former can serve as a key building block in an iterative procedure for the latter. A limiting technique for the piecewise linear scheme is also discussed. The technique can suppress oscillations near a discontinuity while preserving accuracy near extrema. Preliminary numerical results are shown

Huynh, H. T.↗

NASA NTRS2006

Detection of Ice Polar Stratospheric Clouds from Assimilation of Atmospheric Infrared Sounder Data

A novel technique is presented for detection of ice polar stratospheric clouds (PSCs) that form at extremely low temperatures in the lower polar stratosphere during winter. Temperature is a major factor in determining abundance of PSCs, which in turn provide surfaces for heterogeneous chemical reactions leading to ozone loss and radiative cooling. The technique infers the presence of ice PSCs using radiances from the Atmospheric Infrared Sounder (AIRS) in the Goddard Earth Observing System version 5 (GEOS-5) data assimilation system. Brightness temperatures are computed from short-term GEOS-5 forecasts for several hundred AIRS channels, using a radiation transfer module. The differences between collocated AIRS observations and these computed values are the observed-minus-forecast (O-F) residuals in the assimilation system. Because the radiation model assumes clear-sky conditions, we hypothesize that these O-F residuals contain quantitative information about PSCs. This is confirmed using sparse data from the Polar Ozone and Aerosol Measurement (POAM) III occultation instrument. The analysis focuses on 0-F residuals for the 6.79pm AIRS moisture channel. At coincident locations, when POAM III detects ice clouds, the AIRS O-F residuals for this channel are lower than -2K. When no ice PSCs are evident in POAM III data, the AIRS 0-F residuals are larger. Given this relationship, the high spatial density of AIRS data is used to construct maps of regions where 0-F residuals are lower than -2K, as a proxy for ice PSCs. The spatial scales and spatio-temporal variations of these PSCs in the Antarctic and Arctic are discussed on the basis of these maps.

Stajner, Ivanka↗

NASA NTRS1977

Geodetic linear estimation technique and the norm choice problem

In this work the mathematical and probabilistic background of standard linear estimation techniques used in geodesy is clarified, and their interrelationship is revealed with the help of best approximation theory and the normal equations. Emphasis is given to the separation of the deterministic solution to the approximation problem from the probabilistic justification of the metric of the approximation. Least squares prediction has been related to deterministic (exact) collocation, and minimum error bound has been identified as a prediction optimality criterion in the latter. Criteria for the optimal choice of norm in Hilbert space collocation are proposed for gravimetric geodesy problems.

Dermanis, A.↗

NASA NTRS1992

Validation of three-dimensional incompressible spatial direct numerical simulation code: A comparison with linear stability and parabolic stability equation theories for boundary-layer transition on a flat plate

Spatially evolving instabilities in a boundary layer on a flat plate are computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. In a truncated physical domain, a nonstaggered mesh is used for the grid. A Chebyshev-collocation method is used normal to the wall; finite difference and compact difference methods are used in the streamwise direction; and a Fourier series is used in the spanwise direction. For time stepping, implicit Crank-Nicolson and explicit Runge-Kutta schemes are used to the time-splitting method. The influence-matrix technique is used to solve the pressure equation. At the outflow boundary, the buffer-domain technique is used to prevent convective wave reflection or upstream propagation of information from the boundary. Results of the DNS are compared with those from both linear stability theory (LST) and parabolized stability equation (PSE) theory. Computed disturbance amplitudes and phases are in very good agreement with those of LST (for small inflow disturbance amplitudes). A measure of the sensitivity of the inflow condition is demonstrated with both LST and PSE theory used to approximate inflows. Although the DNS numerics are very different than those of PSE theory, the results are in good agreement. A small discrepancy in the results that does occur is likely a result of the variation in PSE boundary condition treatment in the far field. Finally, a small-amplitude wave triad is forced at the inflow, and simulation results are compared with those of LST. Again, very good agreement is found between DNS and LST results for the 3-D simulations, the implication being that the disturbance amplitudes are sufficiently small that nonlinear interactions are negligible.

Joslin, Ronald D.↗

NASA NTRS1995

Efficient modeling of interconnects and capacitive discontinuities in high-speed digital circuits

Modeling of interconnects and associated discontinuities with the recent advances high-speed digital circuits has gained a considerable interest over the last decade although the theoretical bases for analyzing these structures were well-established as early as the 1960s. Ongoing research at the present time is focused on devising methods which can be applied to more general geometries than the ones considered in earlier days and, at the same time, improving the computational efficiency and accuracy of these methods. In this thesis, numerically efficient methods to compute the transmission line parameters of a multiconductor system and the equivalent capacitances of various strip discontinuities are presented based on the quasi-static approximation. The presented techniques are applicable to conductors embedded in an arbitrary number of dielectric layers with two possible locations of ground planes at the top and bottom of the dielectric layers. The cross-sections of conductors can be arbitrary as long as they can be described with polygons. An integral equation approach in conjunction with the collocation method is used in the presented methods. A closed-form Green's function is derived based on weighted real images thus avoiding nested infinite summations in the exact Green's function; therefore, this closed-form Green's function is numerically more efficient than the exact Green's function. All elements associated with the moment matrix are computed using the closed-form formulas. Various numerical examples are considered to verify the presented methods, and a comparison of the computed results with other published results showed good agreement.

Oh, K. S.↗

NASA NTRS1976

Higher-order numerical methods derived from three-point polynomial interpolation

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and Hermitian finite-difference discretization. The equations generally apply for both uniform and variable meshes. Hybrid schemes resulting from different polynomial approximations for first and second derivatives lead to the nonuniform mesh extension of the so-called compact or Pade difference techniques. A variety of fourth-order methods are described and this concept is extended to sixth-order. Solutions with these procedures are presented for the similar and non-similar boundary layer equations with and without mass transfer, the Burgers equation, and the incompressible viscous flow in a driven cavity. Finally, the interpolation procedure is used to derive higher-order temporal integration schemes and results are shown for the diffusion equation.

Rubin, S. G.↗

NASA NTRS1991

On the wall-normal velocity of the compressible boundary-layer equations

Numerical methods for the compressible boundary-layer equations are facilitated by transformation from the physical (x,y) plane to a computational (xi,eta) plane in which the evolution of the flow is 'slow' in the time-like xi direction. The commonly used Levy-Lees transformation results in a computationally well-behaved problem for a wide class of non-similar boundary-layer flows, but it complicates interpretation of the solution in physical space. Specifically, the transformation is inherently nonlinear, and the physical wall-normal velocity is transformed out of the problem and is not readily recovered. In light of recent research which shows mean-flow non-parallelism to significantly influence the stability of high-speed compressible flows, the contribution of the wall-normal velocity in the analysis of stability should not be routinely neglected. Conventional methods extract the wall-normal velocity in physical space from the continuity equation, using finite-difference techniques and interpolation procedures. The present spectrally-accurate method extracts the wall-normal velocity directly from the transformation itself, without interpolation, leaving the continuity equation free as a check on the quality of the solution. The present method for recovering wall-normal velocity, when used in conjunction with a highly-accurate spectral collocation method for solving the compressible boundary-layer equations, results in a discrete solution which is extraordinarily smooth and accurate, and which satisfies the continuity equation nearly to machine precision. These qualities make the method well suited to the computation of the non-parallel mean flows needed by spatial direct numerical simulations (DNS) and parabolized stability equation (PSE) approaches to the analysis of stability.

Pruett, C. David↗

NASA NTRSDate not supplied

Enhancing Radiative Transfer Models for Optimized Assimilation of Microwave and Radar Observations

Radiative transfer models are extensively used for the assimilation of satellite observations into NWP models as well as retrieving geophysical products from satellite measurements. The Community Radiative Transfer Model (CRTM) is a community model developed by NOAA JCSDA and widely used for different purposes requiring RT calculations. CRTM requires bulk optical properties of hydrometeors in the form of lookup tables in order to perform all-sky RT calculations. However, the current cloud scattering lookup tables in CRTM assume spherical shapes for all frozen hydrometeors, whereas actual clouds contain frozen particles with diverse shapes. The first part of this talk presents the implementation and validation of a comprehensive Discrete Dipole Approximation (DDA) cloud scattering database into CRTM, specifically targeting microwave frequencies. The DDA technique proves effective in simulating the optical properties of non-spherical hydrometeors in the microwave region. The original DDA database assumes total random orientation in calculating single scattering properties. To generate the required mass scattering parameters for CRTM, the single scattering properties and water content dependent particle size distributions are used. The evaluation of results involved a collocated dataset comprising short-term forecasts from the Integrated Forecast System of the European Center for Medium-Range Weather Forecasts and satellite microwave data. The findings demonstrate that the DDA lookup tables significantly reduce discrepancies between simulated and observed values when compared to the Mie tables. Passive instruments lack the ability to provide vertically resolved measurements of clouds and precipitation, which can be obtained by active radar instruments. However, incorporating these active measurements into data assimilation systems presents challenges due to the absence of fast forward radiative transfer models and difficulties in error modeling. The second part of the talk focuses on the development, evaluation, and sensitivity analysis of a forward radar model integrated into CRTM. The forward radar model utilizes scattering properties obtained from hydrometeor lookup tables generated using the discrete dipole approximation. By utilizing CRTM instrument-specific coefficients, the model can calculate both reflectivity and attenuated reflectivity for any given radar instrument and zenith angles. Evaluation using CloudSat measurements demonstrates a strong agreement between simulations and observations when the input profiles of hydrometeors align with the measured reflectivity profiles.

Isaac Moradi↗