Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “discretization error”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

An improved error analysis of finite element solutions for postbuckled plates

The accurate calculation of stresses at boundaries and interfaces where FEM analysis may be unreliable is presently undertaken by an error analysis that derives a continuous approximation to discrete finite-element data, which can be differentiated to compute continuous stresses for component-failure predictions. An evaluation is conducted of this approximation in the context of the nonlinear PDEs. A novel interpolation formula which is a simple modification of the double Fourier sine series is used to reduce truncation errors near the rectangular plate boundary by means of an 'extended grid'. Results are presented from a FEM solution, a conventional double-Fourier series' continuous approximation, and a solution applying interpolation on the extended grid, which yields superior convergence properties near the plate boundaries.

Sistla, Rajaram↗
NASA NTRS1998

An Astronomical Test of CCD Photometric Precision

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques. we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Koch, David↗
NASA NTRS1999

A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Larson, Mats G.↗
NASA NTRS2009

Magnetospheric Multiscale (MMS) Mission Commissioning Phase Orbit Determination Error Analysis

The Magnetospheric MultiScale (MMS) mission commissioning phase starts in a 185 km altitude x 12 Earth radii (RE) injection orbit and lasts until the Phase 1 mission orbits and orientation to the Earth-Sun li ne are achieved. During a limited time period in the early part of co mmissioning, five maneuvers are performed to raise the perigee radius to 1.2 R E, with a maneuver every other apogee. The current baseline is for the Goddard Space Flight Center Flight Dynamics Facility to p rovide MMS orbit determination support during the early commissioning phase using all available two-way range and Doppler tracking from bo th the Deep Space Network and Space Network. This paper summarizes th e results from a linear covariance analysis to determine the type and amount of tracking data required to accurately estimate the spacecraf t state, plan each perigee raising maneuver, and support thruster cal ibration during this phase. The primary focus of this study is the na vigation accuracy required to plan the first and the final perigee ra ising maneuvers. Absolute and relative position and velocity error hi stories are generated for all cases and summarized in terms of the ma ximum root-sum-square consider and measurement noise error contributi ons over the definitive and predictive arcs and at discrete times inc luding the maneuver planning and execution times. Details of the meth odology, orbital characteristics, maneuver timeline, error models, and error sensitivities are provided.

Chung, Lauren R.↗
NASA NTRS1996

A Full Multi-Grid Method for the Solution of the Cell Vertex Finite Volume Cauchy-Riemann Equations

The system of inhomogeneous Cauchy-Riemann equations defined on a square domain and subject to Dirichlet boundary conditions is considered. This problem is discretised by using the cell vertex finite volume method on quadrilateral meshes. The resulting algebraic problem is overdetermined and the solution is defined in a least squares sense. By this approach a consistent algebraic problem is obtained which differs from the original one by O(h(exp 2)) perturbations of the right-hand side. A suitable cell-based convergent smoothing iteration is presented which is naturally linked to the least squares formulation. Hence, a standard multi-grid algorithm is reported which combines the given smoother and cell-based transfer operators. Some remarkable reduction properties of these operators are shown. A full multi-grid method is discussed which solves the discrete problem to the level of truncation error by employing one multi-grid cycle at each current level of discretisation. Experiments and applications of the full multi-grid scheme are presented.

Borzi, A.↗
NASA NTRS2005

Pressure-Sensitive Paint Investigation of Double-Delta Wing Vortex Flow Manipulation

A pressure-sensitive paint (PSP) technique was applied in a wind tunnel experiment in the NASA Langley Research Center 8-Foot Transonic Pressure Tunnel to quantify the effect of wing fillets on the global vortex-induced surface static pressure field about a sharp leading-edge 76 deg/40 deg double delta wing, or strake-wing, model at subsonic and transonic speeds. Global calibrations of the PSP were obtained at M = 0.50, 0.70, 0.85, 0.95, and 1.20, a Reynolds number per unit length of 2.0 million, and angles of attack from 10 degrees to 30 degrees using an in-situ method featuring the simultaneous acquisition of electronically-scanned pressures (ESP) at discrete locations on the model. The mean error in the PSP measurements relative to the ESP data was approximately 2 percent or less at M = 0.50 to 0.85 but increased to several percent at M = 0.95 and 1.20. The PSP pressure distributions and pseudo-colored planform view pressure maps clearly revealed the vortex-induced pressure signatures at all Mach numbers and angles of attack. Small fillets having a parabolic or diamond planform situated at the strake-wing intersection were designed to manipulate the vortical flows by, respectively, removing the leading-edge discontinuity or introducing additional discontinuities. The fillets caused global changes in the vortex-dominated surface pressure field that were effectively captured in the PSP measurements. The vortex surface pressure signatures were compared to available off-surface vortex cross-flow structures obtained using a laser vapor screen (LVS) flow visualization technique. The fillet effects on the PSP pressure distributions and the observed leading-edge vortex flow characteristics were consistent with the trends in the measured lift, drag, and pitching moment coefficients.

Erickson, Gary E.↗
NASA NTRS2004

Pressure-Sensitive Paint Investigation of Double-Delta Wing Vortex Flow Manipulation

A pressure-sensitive paint (PSP) technique was applied in a wind tunnel experiment in the NASA Langley Research Center 8-Foot Transonic Pressure Tunnel to quantify the effect of wing fillets on the global vortex-induced surface static pressure field about a sharp leading-edge 76o/40o double delta wing, or strake-wing, model at subsonic and transonic speeds. Global calibrations of the PSP were obtained at M = 0.50, 0.70, 0.85, 0.95, and 1.20, a Reynolds number per unit length of 2.0 million, and angles of attack from 10 degrees to 20 degrees using an in-situ method featuring the simultaneous acquisition of electronically-scanned pressures (ESP) at discrete locations on the model. The mean error in the PSP measurements relative to the ESP data was approximately 2 percent or less at M = 0.50 to 0.85 but increased to several percent at M =0.95 and 1.20. The PSP pressure distributions and pseudo-colored planform view pressure maps clearly revealed the vortex-induced pressure signatures at all Mach numbers and angles of attack. Small fillets having a parabolic or diamond planform situated at the strake-wing intersection were designed to manipulate the vortical flows by, respectively, removing the leading-edge discontinuity or introducing additional discontinuities. The fillets caused global changes in the vortex-dominated surface pressure field that were effectively captured in the PSP measurements. The vortex surface pressure signatures were compared to available off-surface vortex cross-flow structures obtained using a laser vapor screen (LVS) flow visualization technique. The fillet effects on the PSP pressure distributions and the observed leading-edge vortex flow characteristics were consistent with the trends in the measured lift, drag, and pitching moment coefficients.

Erickson, Gary E.↗
NASA NTRS2006

Wind Tunnel Application of a Pressure-Sensitive Paint Technique to a Double Delta Wing Model at Subsonic and Transonic Speeds

A pressure-sensitive paint (PSP) technique was applied in a wind tunnel experiment in the NASA Langley Research Center 8-Foot Transonic Pressure Tunnel to study the effect of wing fillets on the global vortex induced surface static pressure field about a sharp leading-edge 76 deg./40 deg. double delta wing, or strake-wing, model at subsonic and transonic speeds. Global calibrations of the PSP were obtained at M(sub infinity) = 0.50, 0.70, 0.85, 0.95, and 1.20, a Reynolds number per unit length of 2.0 million, and angles of attack from 10 degrees to 20 degrees using an insitu method featuring the simultaneous acquisition of electronically scanned pressures (ESP) at discrete locations on the model. The mean error in the PSP measurements relative to the ESP data was approximately 2 percent or less at M(sub infinity) = 0.50 to 0.85 but increased to several percent at M(sub infinity) =0.95 and 1.20. The PSP pressure distributions and pseudo-colored, planform-view pressure maps clearly revealed the vortex-induced pressure signatures at all Mach numbers and angles of attack. Small fillets having parabolic or diamond planforms situated at the strake-wing intersection were respectively designed to manipulate the vortical flows by removing the leading-edge discontinuity or introducing additional discontinuities. The fillets caused global changes in the vortex-dominated surface pressure field that were effectively captured in the PSP measurements. The vortex surface pressure signatures were compared to available off-surface vortex cross-flow structures obtained using a laser vapor screen (LVS) flow visualization technique. The fillet effects on the PSP pressure distributions and the observed leading-edge vortex flow characteristics were consistent with the trends in the measured lift, drag, and pitching moment coefficients.

Erickson, Gary E.↗
NASA NTRS2013

Cursor Control Device Test Battery

The test battery was developed to provide a standard procedure for cursor control device evaluation. The software was built in Visual Basic and consists of nine tasks and a main menu that integrates the set-up of the tasks. The tasks can be used individually, or in a series defined in the main menu. Task 1, the Unidirectional Pointing Task, tests the speed and accuracy of clicking on targets. Two rectangles with an adjustable width and adjustable center- to-center distance are presented. The task is to click back and forth between the two rectangles. Clicks outside of the rectangles are recorded as errors. Task 2, Multidirectional Pointing Task, measures speed and accuracy of clicking on targets approached from different angles. Twenty-five numbered squares of adjustable width are arranged around an adjustable diameter circle. The task is to point and click on the numbered squares (placed on opposite sides of the circle) in consecutive order. Clicks outside of the squares are recorded as errors. Task 3, Unidirectional (horizontal) Dragging Task, is similar to dragging a file into a folder on a computer desktop. Task 3 requires dragging a square of adjustable width from one rectangle and dropping it into another. The width of each rectangle is adjustable, as well as the distance between the two rectangles. Dropping the square outside of the rectangles is recorded as an error. Task 4, Unidirectional Path Following, is similar to Task 3. The task is to drag a square through a tunnel consisting of two lines. The size of the square and the width of the tunnel are adjustable. If the square touches any of the lines, it is counted as an error and the task is restarted. Task 5, Text Selection, involves clicking on a Start button, and then moving directly to the underlined portion of the displayed text and highlighting it. The pointing distance to the text is adjustable, as well as the to-be-selected font size and the underlined character length. If the selection does not include all of the underlined characters, or includes non-underlined characters, it is recorded as an error. Task 6, Multi-size and Multi-distance Pointing, presents the participant with 24 consecutively numbered buttons of different sizes (63 to 163 pixels), and at different distances (60 to 80 pixels) from the Start button. The task is to click on the Start button, and then move directly to, and click on, each numbered target button in consecutive order. Clicks outside of the target area are errors. Task 7, Standard Interface Elements Task, involves interacting with standard interface elements as instructed in written procedures, including: drop-down menus, sliders, text boxes, radio buttons, and check boxes. Task completion time is recorded. In Task 8, a circular track is presented with a disc in it at the top. Track width and disc size are adjustable. The task is to move the disc with circular motion within the path without touching the boundaries of the track. Time and errors are recorded. Task 9 is a discrete task that allows evaluation of discrete cursor control devices that tab from target to target, such as a castle switch. The task is to follow a predefined path and to click on the yellow targets along the path.

Kritina Holden↗
NASA NTRS2015

A Fast Visible-Infrared Imaging Radiometer Suite Simulator for Cloudy Atmopheres

A fast instrument simulator is developed to simulate the observations made in cloudy atmospheres by the Visible Infrared Imaging Radiometer Suite (VIIRS). The correlated k-distribution (CKD) technique is used to compute the transmissivity of absorbing atmospheric gases. The bulk scattering properties of ice clouds used in this study are based on the ice model used for the MODIS Collection 6 ice cloud products. Two fast radiative transfer models based on pre-computed ice cloud look-up-tables are used for the VIIRS solar and infrared channels. The accuracy and efficiency of the fast simulator are quantify in comparison with a combination of the rigorous line-by-line (LBLRTM) and discrete ordinate radiative transfer (DISORT) models. Relative errors are less than 2 for simulated TOA reflectances for the solar channels and the brightness temperature differences for the infrared channels are less than 0.2 K. The simulator is over three orders of magnitude faster than the benchmark LBLRTM+DISORT model. Furthermore, the cloudy atmosphere reflectances and brightness temperatures from the fast VIIRS simulator compare favorably with those from VIIRS observations.

VIIRS Instrument Simulator↗
NASA NTRS2021

Solving Two-Equation Turbulence Models With a Perspective on Solving Transport Equations

There are three principal objectives of this report. The first objective is to investigate frequently used two-equation models when solving the RANS equations. In this study, we consider the 2006Wilcox and the 2003 Menter Shear Stress Transport (SST) models. Also, a simple change of the Wilcox model is introduced to improve computational predictions for transonic flows. Computations for flows over two different airfoils are examined to compare these turbulence models. Effects on modeling the physics of each flow due to variations in the models, such as using either strainrate or vorticity in the turbulence production term, are considered and discussed. The second objective of this report is to not only explore but also evaluate the performance of the solution algorithm for the mean flow and the transport equations. The RANS and turbulence modeling equations aresolved in a weakly coupled manner with a diagonal implicit Runge-Kutta (DIRK) solution algorithm. Throughout this report, emphasis is given to reducing the residuals to machine zero in all flow calculations, so as to eliminate the error due to numerical integration of the discrete governing equations. The final objective is to provide a perspective on solving transport equations for turbulence modeling. Aspects of solving such stiff systems of equations, as well as various numerical difficulties and possible techniques to overcome them, are considered. Discussion is also provided concerning what is called ’numerical compatibility’, which is an essential requirement when designing a solution algorithm for solving transport equations.

turbulence modeling↗
NASA NTRS2010

Maximum Likelihood Time-of-Arrival Estimation of Optical Pulses via Photon-Counting Photodetectors

Many optical imaging, ranging, and communications systems rely on the estimation of the arrival time of an optical pulse. Recently, such systems have been increasingly employing photon-counting photodetector technology, which changes the statistics of the observed photocurrent. This requires time-of-arrival estimators to be developed and their performances characterized. The statistics of the output of an ideal photodetector, which are well modeled as a Poisson point process, were considered. An analytical model was developed for the mean-square error of the maximum likelihood (ML) estimator, demonstrating two phenomena that cause deviations from the minimum achievable error at low signal power. An approximation was derived to the threshold at which the ML estimator essentially fails to provide better than a random guess of the pulse arrival time. Comparing the analytic model performance predictions to those obtained via simulations, it was verified that the model accurately predicts the ML performance over all regimes considered. There is little prior art that attempts to understand the fundamental limitations to time-of-arrival estimation from Poisson statistics. This work establishes both a simple mathematical description of the error behavior, and the associated physical processes that yield this behavior. Previous work on mean-square error characterization for ML estimators has predominantly focused on additive Gaussian noise. This work demonstrates that the discrete nature of the Poisson noise process leads to a distinctly different error behavior.

Erkmen, Baris I.↗
NASA NTRS1991

Program Analyzes Errors In STAGS

EAC computer program designed for analysis of errors in results of STAGS computer program (COSMIC Program HQN-10967). Requires input data for geometry of plate, properties of material, and set of boundary conditions. These input data come from STAGS code. (The specific link between input and output data from STAGS and input data for EAC is POSTP, postprocessor program in STAGS processors.) EAC computes continuous solution from discrete results of STAGS in order to estimate error of results of STAGS. Written in FORTRAN 77.

Thurston, Gaylen A.↗
NASA NTRS2000

Stress Recovery and Error Estimation for 3-D Shell Structures

The C1-continuous stress fields obtained from finite element analyses are in general lower- order accurate than are the corresponding displacement fields. Much effort has focussed on increasing their accuracy and/or their continuity, both for improved stress prediction and especially error estimation. A previous project developed a penalized, discrete least squares variational procedure that increases the accuracy and continuity of the stress field. The variational problem is solved by a post-processing, 'finite-element-type' analysis to recover a smooth, more accurate, C1-continuous stress field given the 'raw' finite element stresses. This analysis has been named the SEA/PDLS. The recovered stress field can be used in a posteriori error estimators, such as the Zienkiewicz-Zhu error estimator or equilibrium error estimators. The procedure was well-developed for the two-dimensional (plane) case involving low-order finite elements. It has been demonstrated that, if optimal finite element stresses are used for the post-processing, the recovered stress field is globally superconvergent. Extension of this work to three dimensional solids is straightforward. Attachment: Stress recovery and error estimation for shell structure (abstract only). A 4-node, shear-deformable flat shell element developed via explicit Kirchhoff constraints (abstract only). A novel four-node quadrilateral smoothing element for stress enhancement and error estimation (abstract only).

Riggs, H. R.↗
NASA NTRS1966

The adaptive prediction of time series.

Adaptive technique determination of optimum operations for pure prediction of discrete time series with respect to mean square error cost function

GAUSSIAN DISTRIBUTION↗
NASA NTRS1982

An improved switching converter model

The nonlinear modeling and analysis of dc-dc converters in the continuous mode and discontinuous mode was done by averaging and discrete sampling techniques. A model was developed by combining these two techniques. This model, the discrete average model, accurately predicts the envelope of the output voltage and is easy to implement in circuit and state variable forms. The proposed model is shown to be dependent on the type of duty cycle control. The proper selection of the power stage model, between average and discrete average, is largely a function of the error processor in the feedback loop. The accuracy of the measurement data taken by a conventional technique is affected by the conditions at which the data is collected.

Shortt, D. J.↗