Results for “Smoothing methods” — Page 35

NASA NTRS1989

Control of the errors of discretization and idealization in finite element analysis

Understanding of the basic principles which control errors of discretization in finite element analysis has increased very substantially since 1980. The main milestones were: (1) development of the theoretical basis of p-extensions (1981); (2) understanding of the proper interplay between mesh design and assignment of polynomial degree to elements. Practical realization of exponential convergence rates, independently of the smoothness of the exact solution (1984); and (3) industrial experience with the new finite element technology known as the p- or hp-version of the finite element method: General Dynamics reported thirty- to forty-fold savings in terms of human time and large savings in computer time (1986). Lockheed reported favorably on their evaluation of error estimation and quality control capabilities of the p-version in industrial settings (1987). The gains in our understanding of how to control the errors of discretization represent only half of the control necessary to ensure that a numerical model is in fact an accurate representation of the corresponding physical system. Control of the errors of idealization is equally important. A brief overview of the main ideas of how to ensure the quality and reliability of mathematical models of structural systems is presented.

Szabo, Barna A.↗

NASA NTRS1989

A highly parallel multigrid-like method for the solution of the Euler equations

We consider a highly parallel multigrid-like method for the solution of the two dimensional steady Euler equations. The new method, introduced as filtering multigrid, is similar to a standard multigrid scheme in that convergence on the finest grid is accelerated by iterations on coarser grids. In the filtering method, however, additional fine grid subproblems are processed concurrently with coarse grid computations to further accelerate convergence. These additional problems are obtained by splitting the residual into a smooth and an oscillatory component. The smooth component is then used to form a coarse grid problem (similar to standard multigrid) while the oscillatory component is used for a fine grid subproblem. The primary advantage in the filtering approach is that fewer iterations are required and that most of the additional work per iteration can be performed in parallel with the standard coarse grid computations. We generalize the filtering algorithm to a version suitable for nonlinear problems. We emphasize that this generalization is conceptually straight-forward and relatively easy to implement. In particular, no explicit linearization (e.g., formation of Jacobians) needs to be performed (similar to the FAS multigrid approach). We illustrate the nonlinear version by applying it to the Euler equations, and presenting numerical results. Finally, a performance evaluation is made based on execution time models and convergence information obtained from numerical experiments.

Tuminaro, Ray S.↗

NASA NTRS1998

Effect of Apex Flap Deflection on Vertical Tail Buffeting

A computational study of the effect of vortex breakdown location on vertical tail buffeting is conducted. The position of the breakdown is modified by employing an apex flap deflected by an experimentally determined optimal angle. The delayed breakdown flow and buffeting response is then compared to the nominal undeflected case. This multidisciplinary problem is solved sequentially for the fluid flow, the elastic tail deformations and the grid displacements. The fluid flow is simulated by time accurately solving the unsteady, compressible, Reynolds-averaged Navier-Stokes equations using an implicit, upwind, flux-difference splitting finite volume scheme. The elastic vibrations of the tails are modeled by uncoupled bending and torsion beam equations. These equations are solved accurately in time using the Galerkin method and a five-stage Runge-Kutta-Verner scheme. The grid for the fluid dynamics calculations is continuously deformed using interpolation functions to disperse the displacements smoothly throughout the computational domain. An angle-of-attack of 35 deg.is chosen such that the wing primary-vortex cores experience vortex breakdown and the resulting turbulent wake flow impinges on tile vertical tails. The dimensions and material properties of the vertical tails are chosen such that the deflections are large enough to insure interaction with the flow, and the natural frequencies are high enough to facilitate a practical computational solution. Results are presented for a baseline uncontrolled buffeting case and a delayed breakdown case in which the apex flap has been deflected 15 deg. The flap was found to be very effective in delaying the breakdown, increasing the location from 50%c to 94%c, which resulted in a 6% increase in lift coefficient and pitching moment. However, the integrated buffet loads and tip responses were roughly equivalent for the two cases.

Massey, Steven J.↗

NASA NTRS2006

Viking Afterbody Heating Computations and Comparisons to Flight Data

Computational fluid dynamics predictions of Viking Lander 1 entry vehicle afterbody heating are compared to flight data. The analysis includes a derivation of heat flux from temperature data at two base cover locations, as well as a discussion of available reconstructed entry trajectories. Based on the raw temperature-time history data, convective heat flux is derived to be 0.63-1.10 W/sq cm for the aluminum base cover at the time of thermocouple failure. Peak heat flux at the fiberglass base cover thermocouple is estimated to be 0.54-0.76 W/sq cm, occurring 16 seconds after peak stagnation point heat flux. Navier-Stokes computational solutions are obtained with two separate codes using an 8-species Mars gas model in chemical and thermal non-equilibrium. Flowfield solutions using local time-stepping did not result in converged heating at either thermocouple location. A global time-stepping approach improved the computational stability, but steady state heat flux was not reached for either base cover location. Both thermocouple locations lie within a separated flow region of the base cover that is likely unsteady. Heat flux computations averaged over the solution history are generally below the flight data and do not vary smoothly over time for both base cover locations. Possible reasons for the mismatch between flight data and flowfield solutions include underestimated conduction effects and limitations of the computational methods.

Edquist, Karl T.↗

NASA NTRS2006

Viking Afterbody Heating Computations and Comparisons to Flight Data

Computational fluid dynamics predictions of Viking Lander 1 entry vehicle afterbody heating are compared to flight data. The analysis includes a derivation of heat flux from temperature data at two base cover locations, as well as a discussion of available reconstructed entry trajectories. Based on the raw temperature-time history data, convective heat flux is derived to be 0.63-1.10 W/cm2 for the aluminum base cover at the time of thermocouple failure. Peak heat flux at the fiberglass base cover thermocouple is estimated to be 0.54-0.76 W/cm2, occurring 16 seconds after peak stagnation point heat flux. Navier-Stokes computational solutions are obtained with two separate codes using an 8- species Mars gas model in chemical and thermal non-equilibrium. Flowfield solutions using local time-stepping did not result in converged heating at either thermocouple location. A global time-stepping approach improved the computational stability, but steady state heat flux was not reached for either base cover location. Both thermocouple locations lie within a separated flow region of the base cover that is likely unsteady. Heat flux computations averaged over the solution history are generally below the flight data and do not vary smoothly over time for both base cover locations. Possible reasons for the mismatch between flight data and flowfield solutions include underestimated conduction effects and limitations of the computational methods.

Edquist, Karl T.↗

NASA NTRS2005

Kurtosis Approach Nonlinear Blind Source Separation

In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation Keywords: Independent Component Analysis, Kurtosis, Higher order statistics.

Duong, Vu A.↗

NASA NTRS2005

Kurtosis Approach for Nonlinear Blind Source Separation

In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation.

kurtosis↗

NASA NTRS1973

Analysis of internal flow characteristics of a smooth-disk water-brake dynamometer

The principal of absorbing power with an enclosed partially submerged rotating disk through the turbulent viscous shearing of water is discussed. Reference information is used to develop a flow model of the water brake. A method is then presented that uses vector diagrams to relate the effects of rotational flow, through flow, and secondary flow to power absorption. The method is used to describe the operating characteristics of an example 111-cm (43.7-in.) diameter water brake. Correlating performance parameters are developed in a dimensional analysis.

Evans, D. G.↗

NASA NTRS1984

A Method for Measuring the Effective Throughput Time Delay in Simulated Displays Involving Manual Control

The advent and widespread use of the computer-generated image (CGI) device to simulate visual cues has a mixed impact on the realism and fidelity of flight simulators. On the plus side, CGIs provide greater flexibility in scene content than terrain boards and closed circuit television based visual systems, and they have the potential for a greater field of view. However, on the minus side, CGIs introduce into the visual simulation relatively long time delays. In many CGIs, this delay is as much as 200 ms, which is comparable to the inherent delay time of the pilot. Because most GCIs use multiloop processing and smoothing algorithms and are linked to a multiloop host computer, it is seldom possible to identify a unique throughput time delay, and it is therefore difficult to quantify the performance of the closed loop pilot simulator system relative to the real world task. A method to address these issues using the critical task tester is described. Some empirical results from applying the method are presented, and a novel technique for improving the performance of GCIs is discussed.

Jewell, W. F.↗

NASA NTRS1980

Attitude control study for a large flexible spacecraft using a Solar Electric Propulsion System (SEPS)

The attitude control performance of the solar electric propulsion system (SEPS) was evaluated. A thrust vector control system for powered flight control was examined along with a gas jet reaction control system, and a reaction wheel system, both of which have been proposed for nonpowered flight control. Comprehensive computer simulations of each control system were made and evaluated using a 30 mode spacecraft model. Results obtained indicate that thrust vector control and reaction wheel systems offer acceptable smooth proportional control. The gas jet control system is shown to be risky for a flexible structure such as SEPS, and is therefore, not recommended as a primary control method.

Tolivar, A. F.↗

NASA NTRS1980

Calculation of skin-friction coefficients for low Reynolds number turbulent boundary layer flows

An analysis is presented of the reliability of various generally accepted empirical expressions for the prediction of the skin-friction coefficient C/sub f/ of turbulent boundary layers at low Reynolds numbers in zero-pressure-gradient flows on a smooth flat plate. The skin-friction coefficients predicted from these expressions were compared to the skin-friction coefficients of experimental profiles that were determined from a graphical method formulated from the law of the wall. These expressions are found to predict values that are consistently different than those obtained from the graphical method over the range 600 Re/sub theta 2000. A curve-fitted empirical relationship was developed from the present data and yields a better estimated value of C/sub f/ in this range. The data, covering the range 200 Re/sub theta 7000, provide insight into the nature of transitional flows. They show that fully developed turbulent boundary layers occur at Reynolds numbers Re/sub theta/ down to 425. Below this level there appears to be a well-ordered evolutionary process from the laminar to the turbulent profiles. These profiles clearly display the development of the turbulent core region and the shrinking of the laminar sublayer with increasing values of Re/sub theta/.

Barr, P. K.↗

NASA NTRS1982

Cross-validation for densities and regressions

Virtually all nonparametric (infinite dimensional) problems require the choice of a smoothing parameter. It is natural to attempt to use the data to guide the choice of this parameter. The most widely applicable data driven technique is cross validation. The method of cross validation is introduced and results are presented which establish consistency for certain cross validated density estimators and consistency as well as asymptotic normality for rigid regression.

Geman, S.↗

NASA NTRS1988

Creep life prediction based on stochastic model of microstructurally short crack growth

A nondimensional model of microstructurally short crack growth in creep is developed based on a detailed observation of the creep fracture process of 304 stainless steel. In order to deal with the scatter of small crack growth rate data caused by microstructural inhomogeneity, a random variable technique is used in the model. A cumulative probability of the crack length at an arbitary time, G(bar a, bar t), and that of the time when a crack reaches an arbitary length, F(bar t, bar a), are obtained numerically by means of a Monte Carlo method. G(bar a, bar t), and F(bar t, bar a) are the probabilities for a single crack. However, multiple cracks generally initiate on the surface of a smooth specimen from the early stage of creep life to the final stage. TAking into account the multiple crack initiations, the actual crack length distribution observed on the surface of a specimen is predicted by the combination of probabilities for a single crack. The prediction shows a fairly good agreement with the experimental result for creep of 304 stainless steel at 923 K. The probability of creep life is obtained from an assumption that creep fracture takes place when the longest crack reaches a critical length. The observed and predicted scatter of the life is fairly small for the specimens tested.

Kitamura, Takayuki↗

NASA NTRS1989

Creep life prediction based on stochastic model of microstructurally short crack growth

A nondimensional model of microstructurally short crack growth in creep is developed based on a detailed observation of the creep fracture process of 304 stainless steel. In order to deal with the scatter of small crack growth rate data caused by microstructural inhomogeneity, a random variable technique is used in the model. A cumulative probability of the crack length at an arbitrary time, G(bar a, bar t), and that of the time when a crack reaches an arbitrary length, F(bar t, bar a), are obtained numerically by means of a Monte Carlo method. G(bar a, bar t), and F(bar t, bar a) are the probabilities for a single crack. However, multiple cracks generally initiate on the surface of a smooth specimen from the early stage of creep life to the final stage. Taking into account the multiple crack initiations, the actual crack length distribution observed on the surface of a specimen is predicted by the combination of probabilities for a single crack. The prediction shows a fairly good agreement with the experimental result for creep of 304 stainless steel at 923 K. The probability of creep life is obtained from an assumption that creep fracture takes place when the longest crack reaches a critical length. The observed and predicted scatter of the life is fairly small for the specimens tested.

Kitamura, Takayuki↗

NASA NTRS1993

Transition operators in electromagnetic-wave diffraction theory. II - Applications to optics

The theory developed by Hahne (1992) for the diffraction of time-harmonic electromagnetic waves from fixed obstacles is briefly summarized and extended. Applications of the theory are considered which comprise, first, a spherical harmonic expansion of the so-called radiation impedance operator in the theory, for a spherical surface, and second, a reconsideration of familiar short-wavelength approximation from the new standpoint, including a derivation of the so-called physical optics method on the basis of quasi-planar approximation to the radiation impedance operator, augmented by the method of stationary phase. The latter includes a rederivation of the geometrical optics approximation for the complete Green's function for the electromagnetic field in the presence of a smooth- and a convex-surfaced perfectly electrically conductive obstacle.

Hahne, G. E.↗

NASA NTRSDate not supplied

Parallelized Quadrupole Simulations of Thermographic Responses of Composites

Thermography has been shown to be a viable technique for inspection of composites. Model inversion of the thermography data requires a fast method for performing the forward problem. Viable numerical methods for the thermal response forward problem are finite element, finite difference and the quadrupole method. Normally both the finite element and finite difference methods solve for the thermal response in the time domain which limits one’s ability to increase the speed of the simulation by parallelization. In contrast, the quadrupole method solves for the Laplace transform of the thermal response. One of the features of the Laplace transform methodology is the solution at any discrete time is independent of the solution at all other times. Therefore, it is easy to separate into a set of independent calculations with each of the times of interest being performed in parallel. Additionally, the numeric inversion of the Laplace transform typically involves numerically solving for the Laplace transform at multiple Laplace frequencies. Each of those solutions are also independent of solutions at other frequencies and can be calculated in parallel. By parallelization of this method, it is possible to perform the simulations of three-dimensional configurations in seconds. When the input stimulus for thermal response is a delta function heat flux (a reasonable approximation for flash heating), the thermal response is smooth. For this case, it is possible to accurately estimate the thermal response at any time within a given time interval from a set of simulations separated by exponentially increasing time steps. From these simulations, it is possible to accurately interpolate to find the response at intermediate times by a spline interpolation of the logarithm of time versus logarithm of temperature. The thermal response with exponential time stepping is shown to produce values for the thermal response which are within 1% of values within the time interval. The simulations are compared to finite element simulations of the same inspection configurations. The simulations are also compared to the thermographic measurements on composites where shape and depth of the delaminations are obtained from other inspection methods.

Thermography↗

NASA NTRSDate not supplied

Parallelized Quadrupole Simulations of Thermographic Responses of Composites

Thermography has been shown to be a viable technique for inspection of composites. Model inversion of the thermography data requires a fast method for performing the forward problem. Viable numerical methods for the thermal response forward problem are finite element, finite difference and the quadrupole method. Normally both the finite element and finite difference methods solve for the thermal response in the time domain which limits one’s ability to increase the speed of the simulation by parallelization. In contrast, the quadrupole method solves for the Laplace transform of the thermal response. One of the features of the Laplace transform methodology is the solution at any discrete time is independent of the solution at all other times. Therefore, it is easy to separate into a set of independent calculations with each of the times of interest being performed in parallel. Additionally, the numeric inversion of the Laplace transform typically involves numerically solving for the Laplace transform at multiple Laplace frequencies. Each of those solutions are also independent of solutions at other frequencies and can be calculated in parallel. By parallelization of this method, it is possible to perform the simulations of three-dimensional configurations in seconds. When the input stimulus for thermal response is a delta function heat flux (a reasonable approximation for flash heating), the thermal response is smooth. For this case, it is possible to accurately estimate the thermal response at any time within a given time interval from a set of simulations separated by exponentially increasing time steps. From these simulations, it is possible to accurately interpolate to find the response at intermediate times by a spline interpolation of the logarithm of time versus logarithm of temperature. The thermal response with exponential time stepping is shown to produce values for the thermal response which are within 1% of values within the time interval. The simulations are compared to finite element simulations of the same inspection configurations. The simulations are also compared to the thermographic measurements on composites where shape and depth of the delaminations are obtained from other inspection methods.

Thermography↗

NASA NTRS2001

Inexpensive Method for Growing Unidirectional Oriented Materials Using Friction-Transferred Poly(tetrafluoroethylene) Substrates

In recent years, there has been an increasing interest in properties of unidirectional materials grown on highly oriented polymer surfaces such as the poly(tetrafluoroethylene) (PTFE) films coated onto smooth glass surfaces. In this technique, a thin PTFE film is deposited by sliding or rubbing a Teflon bar over a heated glass surface at a specific temperature. Depending on the pressure, temperature and sliding rate the thickness of deposited layers can be varied from 30 A to 150 A. The PTFE-coated substrate is simple yet surprising versatile for oriented growth of many organic, inorganic and polymer. The significant aspect of PTFE films is their unusual ability to molecularly align a wide variety of materials grown onto them from solution, melt or vapor phase deposition, at temperature below the melting point of PTFE (approx. 340 C). The PTFE structure may be derived, in part, from the multitude of ridges forming in the film and these ridges can presumably provide effective nucleation sites to induce the unidirectional growth of variety of materials. Electron diffraction studies of these films revealed that the PTFE macromolecules are oriented parallel to each other along the sliding direction. Direct observation of the film thickness, molecular structure and individual fluorine atoms from these highly oriented films were achieved using atomic force microscopy (AFM). In this paper, we also report the first direct observation of individual fluorine atoms, and the measurement of the fluorine-helix and carbon-helix radii to be 1.70 A and 0.54 A, respectively.

Lee, Jonathan A.↗