Search NASA⌕ Search

SEARCH · Search NASA

Results for “Variational discretization”

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 289 records · Page 16

Variational approach to probabilistic finite elements

Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Belytschko, T.↗

Comet Halley near-nucleus phenomena in 1986

Computer enhanced high resolution groundbased images taken during Halley's most active phases in 1985-86 exhibit all of the coma structures identified in 1910 photographs. The structures result mostly from discrete dust jet activity producing spirals, arcs, and jagged-edged envelopes. Multiple nucleus and antisunward jet phenomena are also observed. The curvature of the jets is consistent with the location of the Earth with respect to the nucleus equatorial plane. The variation in jet activity during the Vega and Giotto flybys is easily seen on the groundbased images. Images of CN jets show that they usually do not correlate with dust jets. Wide field, medium resolution images of faint outer envelopes are required to augment the smaller field, high resolution images of near-nucleus jets in modeling the jets.

Larson, S.↗

Irregular and diurnal variability in asynoptic measurements of stratospheric trace species

The consequences of irregular and diurnal variability on the interpretation of asynoptic measurements of stratospheric trace species are explored. In particular, the fidelity with which the continuous behavior may be recovered from discrete asynoptic measurements is examined. Dynamically created tracer variability in the form of an advected space-time random process is discussed. Diagnostics such as power spectra and time-mean fields are derived asynoptically and compared with the true behavior. Diurnal variations of a photochemically active species are considered, describing variability in terms of a solar waveform which propagates through a latitudinal envelope. Several diagnostics of the behavior are derived asynoptically and compared with the true variability.

Salby, Murry L.↗

Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems

Multigrid methods are very efficient iterative solvers for system of algebraic equations arising from finite element and finite difference discretization of elliptic boundary value problems. The main principle of multigrid methods is to complement the local exchange of information in point-wise iterative methods by a global one utilizing several related systems, called coarse levels, with a smaller number of variables. The coarse levels are often obtained as a hierarchy of discretizations with different characteristic meshsizes, but this requires that the discretization is controlled by the iterative method. To solve linear systems produced by existing finite element software, one needs to create an artificial hierarchy of coarse problems. The principal issue is then to obtain computational complexity and approximation properties similar to those for nested meshes, using only information in the matrix of the system and as little extra information as possible. Such algebraic multigrid method that uses the system matrix only was developed by Ruge. The prolongations were based on the matrix of the system by partial solution from given values at selected coarse points. The coarse grid points were selected so that each point would be interpolated to via so-called strong connections. Our approach is based on smoothed aggregation introduced recently by Vanek. First the set of nodes is decomposed into small mutually disjoint subsets. A tentative piecewise constant interpolation (in the discrete sense) is then defined on those subsets as piecewise constant for second order problems, and piecewise linear for fourth order problems. The prolongation operator is then obtained by smoothing the output of the tentative prolongation and coarse level operators are defined variationally.

Vanek, Petr↗

Wall-Modeled Large Eddy Simulation Method for Unstructured-Grid Navier-Stokes Solvers

This paper reports on the implementation and assessment of a Wall-Modeled Large-Eddy Simulation (WMLES) methodology in an unstructured-grid, node-centered flow solver, FUN3D that is developed and supported at the NASA Langley Research Center. Finite-volume (FV) and finite-element (FE) discretization schemes considered in the study provide formal second-order spatial accuracy. Large-Eddy Simulations (LES) resolve large-scale turbulent-flow features and filter out small-scale effects using the Vreman subgrid-scale model. At solid-wall boundaries, a shear-stress model is employed to provide a proper boundary-flux closure. The nonlinear equations are integrated in time using either an optimized backward difference formula or an implicit multistage Runge-Kutta temporal scheme. The implicit equations at each time step are solved by strong nonlinear iteration schemes. WMLES demonstrations are shown for two high-lift configurations, namely, the McDonnell Douglas 30P30N multielement airfoil and a NASA High-Lift Common Research Model. Results show that the WMLES approaches implemented in the FV and FE discretization methods produce consistent solutions and are capable of capturing key aerodynamic characteristics and flow structures for high-lift configurations at a wide range of angles of attack including maximum-lift conditions. In the 30P30N example, correct trends in the variations of integrated aerodynamic forces and moments, surface pressure distributions, and boundary-layer profiles are captured as the Reynolds number is increased.

CFD; turbulence modeling; High-Lift flow simulatio↗

Space Shuttle Redesigned Solid Rocket Motor nozzle natural frequency variations with burn time

The effects of erosion and thermal degradation on the Space Shuttle Redesigned Solid Rocket Motor (RSRM) nozzle's structural dynamic characteristics were analytically evaluated. Also considered was stiffening of the structure due to internal pressurization. A detailed NASTRAN finite element model of the nozzle was developed and used to evaluate the influence of these effects at several discrete times during motor burn. Methods were developed for treating erosion and thermal degradation, and a procedure was developed to account for internal pressure stiffening using differential stiffness matrix techniques. Results were verified using static firing test accelerometer data. Fast Fourier Transform and Maximum Entropy Method techniques were applied to the data to generate waterfall plots which track modal frequencies with burn time. Results indicate that the lower frequency nozzle 'vectoring' modes are only slightly affected by erosion, thermal effects and internal pressurization. The higher frequency shell modes of the nozzle are, however, significantly reduced.

Lui, C. Y.↗

Albedo and color contrasts on asteroid surfaces

Asteroids in general display only small or negligible variations in spectrum or albedo during a rotational cycle. Color variations with rotation are described in the literature but are usually comparable to the noise in the measurements. Twenty-four asteroids have been systematically monitored for such color changes. Only 3 Juno, 4 Vesta, 6 Hebe, 71 Niobe, 349 Dembowska, and 944 Hidalgo display color variations larger than 0.03 mag. In each of these cases the asteroid appears redder near maximum brightness. Of seven asteroids monitored polarimetrically, only 4 Vesta shows a convincing variation, attributed to an albedo change with rotation. The lightcurve can be explained by albedo differences alone; Vesta apparently has a nearly spheroidal shape. Nothwithstanding the above results, the degree of uniformity of most asteroid surfaces is remarkable. If asteroids exist with large discrete domains of ferrosilicate, metallic, and/or carbonaceous material together on their surfaces, they have not yet been identified.

Degewij, J.↗

A sampling procedure to guide the collection of narrow-band, high-resolution spatially and spectrally representative reflectance data

A multistage sampling procedure using image processing, geographical information systems, and analytical photogrammetry is presented which can be used to guide the collection of representative, high-resolution spectra and discrete reflectance targets for future satellite sensors. The procedure is general and can be adapted to characterize areas as small as minor watersheds and as large as multistate regions. Beginning with a user-determined study area, successive reductions in size and spectral variation are performed using image analysis techniques on data from the Multispectral Scanner, orbital and simulated Thematic Mapper, low altitude photography synchronized with the simulator, and associated digital data. An integrated image-based geographical information system supports processing requirements.

Brand, R. R.↗

Time-accurate Navier-Stokes calculations with multigrid acceleration

A numerical scheme to solve the unsteady Navier-Stokes equations is described. The scheme is implemented by modifying the multigrid-multiblock version of the steady Navier-Stokes equations solver, TLNS3D. The scheme is fully implicit in time and uses TLNS3D to iteratively invert the equations at each physical time step. The design objective of the scheme is unconditional stability (at least for first- and second-order discretizations of the physical time derivatives). With unconditional stability, the choice of the time step is based on the physical phenomena to be resolved rather than limited by numerical stability which is especially important for high Reynolds number viscous flows, where the spatial variation of grid cell size can be as much as six orders of magnitude. An analysis of the iterative procedure and the implementation of this procedure in TLNS3D are discussed. Numerical results are presented to show both the capabilities of the scheme and its speed up relative to the use of global minimum time stepping. Reductions in computational times of an order of magnitude are demonstrated.

Melson, N. Duane↗

Multigrid Acceleration of Time-Accurate Navier-Stokes Calculations

A numerical scheme to solve the unsteady Navier-Stokes equations is described. The scheme is fully implicit in time and is unconditionally stable (at least for first- and second-order discretizations of the physical time derivatives). With unconditional stability, the choice of the time step is based on the physical phenomena to be resolved rather than limited by numerical stability. This is especially important for high Reynolds number viscous flows, where the spatial variation of grid cell size can be as much as six orders of magnitude. A multigrid-multiblock, steady-state, three-dimensional Navier-Stokes solver, TLNS3D, was modified to iteratively invert the equations at each physical time step. The implementation of this procedure in TLNS3D is discussed. The implications of applying several popular turbulence models to unsteady flow are also considered. Numerical results are presented to show the application of the scheme to various two-dimensional turbulent flows. The results of a three-dimensional laminar flow calculation are also given.

Melson, N. Duane↗

Results of Aerothermodynamic and Boundary-Layer Transition Testing of 0.0362-Scale X-38 (Rev. 3.1) Vehicle in NASA Langley 20-Inch Mach 6 Tunnel

The aeroheating characteristics of the X-38 Revision 3.1 lifting-body configuration have been experimentally examined in the Langley 20-inch Mach 6 Tunnel. Global surface heat transfer distributions, surface streamline patterns, and shock shapes were measured on a 0.0362-scale model of a proposed Space Station Crew Return Vehicle at Mach 6 in air. Parametric variations include angles-of-attack of 20 deg, 30 deg, and 40 deg; Reynolds numbers based on model length of 0.9 to 3.7 million; and body-flap deflections of O deg, 20 deg, 25 deg, and 30 deg. The effects of discrete roughness elements, which included trip height, location, size, and orientation, as well as multiple-trip parametrics, were investigated. This document is intended to serve as a quick release of preliminary data to the X-38 program; analysis is limited to observations of the experimental trends in order to expedite dissemination.

Berry, Scott A.↗

Survey of recent work on the analysis of discretely attached corrugated shear webs.

Summary and progress report of more recent work by the author and his students on the theoretical analysis of stiffness, stresses, and deformations of corrugated shear webs with discrete, rather than continuous, attachment between the ends of the corrugations and the surrounding members. Various kinds of discrete attachment are considered, and two kinds of corrugation cross section: the trapezoidal and the curvilinear, the latter having crests and valleys made up of identical circular arcs. The more recent analyses employ the method of minimum total potential energy and the calculus of variations to obtain differential equations and boundary conditions governing the longitudinal variation of various component modes used to describe the deformations of a cross section. They are believed to be more accurate than earlier analyses in that they generally permit more degrees of freedom in the assumed deformations. In particular, they abandon the assumption, characteristic of the earlier analyses, that the straight-line generators of the corrugation remain straight during the shearing of the web.

Libove, C.↗

An extreme ultraviolet spectrometer experiment for the Shuttle Get Away Special Program

An extreme ultraviolet (EUV) spectrometer experiment operated successfully during the STS-7 mission in an experiment to measure the global and diurnal variation of the EUV airglow. The spectrometer is an F 3.5 Wadsworth mount with mechanical collimator, a 75 x 75 mm grating, and a bare microchannel plate detector providing a spectral resolution of 7 X FWHM. Read-out of the signal is through discrete channels or resistive anode techniques. The experiment includes a microcomputer, 20 Mbit tape recorder, and a 28V, 40 Ahr silver-zinc battery. It is the first GAS payload to use an opening door. The spectrometer's 0.1 x 4.2 deg field of view is pointed vertically out of the shuttle bay. During the STS-7 flight data were acquired continuously for a period of 5 hours and 37 minutes, providing spectra of the 570 A to 850 A wavelength region of the airglow. Five diurnal cycles of the 584 A emission of neutral helium and the 834 A emission of ionized atomic oxygen were recorded. The experiment also recorded ion events and pressure pulses associated with thruster firings. The experiment is to fly again on Mission 41-F.

Conway, R. R.↗

Uniformly high-order accurate non-oscillatory schemes, 1

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws was begun. These schemes share many desirable properties with total variation diminishing schemes (TVD), but TVD schemes have at most first order accuracy, in the sense of truncation error, at extreme of the solution. A uniformly second order approximation was constucted, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Harten, A.↗

On the inclusion principle and spillover effect in the identification of distributed structures

Distributed structures are Distributed-Parameter Systems (DPS) and must be modeled by large-dimensional systems. Practical limitations require that only a subset of the modes be actively controlled. Control of the residual (uncontrolled) modes is known as control spillover, and it can degrade the system performance. The contamination of the sensor signals by the residual modes is known as observation spillover and it can destabilize the system. An analogous effect exists in the identification problem. Distributed structures must be represented by discretized (finite-dimensional) models or lumped-parameter systems. The contamination of the measurements by the residual (unmodeled) modes is referred to as identification spillover, and it is the object of this study. To study the effects of identification spillover, we use a variational formulation to obtain the natural frequencies and mode shapes. This formulation has direct application to DPS. The identification technique consists of finding the stationary values of a pseudo-Rayleigh quotient.

Norris, Mark. A.↗

Experimental Feedback Control of Flow Induced Cavity Tones

An experimental study of the application of discrete-time, linear quadratic control design methods to the cavity tone problem is described. State space models of the dynamics from a synthetic jet actuator at the leading edge of the cavity to two pressure sensors in the cavity were computed from experimental data. Variations in model order, control order, control bandwidth, and properties of a Kalman state estimator were studied. Feedback control reduced the levels of multiple cavity tones at Mach 0.275, 0.35, and 0.45. Closed loop performance was often limited by excitation of sidebands of cavity tones, and creation of new tones in the spectrum. State space models were useful for explaining some of these limitations, but were not able to account for non-linear dynamics, such as interactions between tones at different frequencies.

Cabell, Randolph H.↗

Time variation of the meteoritic contribution to the atmosphere of Mars

The meteoritic contribution to the planets of the inner solar system varies significantly with time. During the first billion years, the flux of meteoritic material was significantly greater than present. Over the past 3.6 billion years, the background flux has been relatively constant, but shorter periods of significantly enhanced flux are associated with discrete events such as major impacts of large bodies onto the planets or their moons and passage through cometary debris streams. The topics covered include the following (1) the last 3.6 billion years; (2) large impacts; (3) passage through comet tail; and (4) major collision in the main-belt.

Flynn, G. J.↗

Discrete control of linear distributed systems with application to the deformable primary mirror of a large orbiting telescope

One of the more significant technological problems associated with the orbital operation of large astronomical telescope's is the fabrication and maintenance of the primary mirror surface to the tolerance required for diffraction-limited performance. An interesting approach to the solution of this problem involves continuously measuring and automatically correcting the optical surface of a thin deformable mirror by means of discrete actuators located on its rear surface: The realization of diffraction-limited performance from a telescope in space by this method rests on the ability of the designer to achieve extremely accurate control of a highly complex, interacting, multivariable system. This paper presents the results of a detailed study of the discrete control of linear distributed systems with specific application to the design of a practical controller for a plant representative of a telescope primary mirror for an orbiting astronomical observatory. The problem of controlling the distributed plant is treated by employing modal techniques to represent variations in the optical figure. Distortion of the mirror surface, which arises primarily from thermal gradients, is countered by actuators working against a backing structure to apply a corrective force distribution to the controlled surface. Each displacement actuator is in series with a spring attached to the mirror by means of a pad intentionally introduced to restrict the excitation of high-order modes. Control is then exerted over a finite number (equal.to the number of actuators) of the most significant modes. Through the application of the modal expansion technique the mirror equation of motion is transformed tb a set of uncoupled, linear, time-invariant, ordinary differential equations. The desired dynamic response and static accuracy may then be achieved by the application of classical single-variable design techniques. The formulation of a quadratic performance index which incorporates a measure of image quality permits determination of the trade-off between the-number of actuators and optical purity. A criterion for defining actuator placement and pad size is presented which minimizes the tendency of the controller to excite the unmonitored modes.

Jeremiah F Creedon↗