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At least 109 records · Page 6

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NASA NTRS1983

Improving the convergence rate of parabolic ADI methods

The rate of convergence to steady state of parabolic Alternating Direction Implicit (ADI) solvers is analyzed in terms of the L(2)-norms of the residuals. The analysis allows one to predict the number of iterations necessary for convergence as function of the Courant number, Lambda. A simple modification of existing ADI codes is devised. It improves the convergence rate substantially and is insensitive to the Courant number in a large range of Lambda.

Abarbanel, S. S.↗

NASA NTRS1983

Convergence characteristics of nonlinear vortex-lattice methods for configuration aerodynamics

Nonlinear panel methods have no proof for the existence and uniqueness of their solutions. The convergence characteristics of an iterative, nonlinear vortex-lattice method are, therefore, carefully investigated. The effects of several parameters, including 1) the surface-paneling method, 2) the integration method of the trajectories of the wake vortices, 3) vortex-grid refinement , and 4) the initial conditions for the first iteration on the computed aerodynamic coefficients and on the flow field details are presented. The convergence of the iterative-solution procedure is usually rapid. The solution converges with grid refinement to a constant value, but the final value is not unique and varies with the wing surface-paneling and wake-discretization methods within some range in the vicinity of the experimental result.

Seginer, A.↗

NASA NTRS1984

The effect of channel convergence on heat transfer in a passage with short pin fins

Array averaged heat transfer coefficients were obtained for two configurations of short pin fins in a converging channel and for two flat plate configurations in a converging channel. The effect of flow acceleration due to channel convergence and the effect of varying pin length on the heat transfer was determined. Results are presented in the form of Nusselt number versus Reynolds number for the four geometries tested.

Brigham, B. A.↗

NASA NTRS1985

Static internal performance of a two-dimensional convergent nozzle with thrust-vectoring capability up to 60 deg

An investigation was conducted at wind-off conditions in the static-test facility of the Langley 16-Foot Transonic Tunnel to determine the internal performance characteristics of a two-dimensional convergent nozzle with a thrust-vectoring capability up to 60 deg. Vectoring was accomplished by a downward rotation of a hinged upper convergent flap and a corresponding rotation of a center-pivoted lower convergent flap. The effects of geometric thrust-vector angle and upper-rotating-flap geometry on internal nozzle performance characteristics were investigated. Nozzle pressure ratio was varied from 1.0 (jet off) to approximately 5.0.

Leavitt, L. D.↗

NASA NTRS1985

Convergence to steady state of solutions of Burgers' equation

Consider the initial boundary value problem for Burgers' equation. It is shown that its solutions converge, in time, to a unique steady state. The speed of the convergence depends on the boundary conditions and can be exponentially slow. Methods to speed up the rate of convergence are also discussed.

Kreiss, G.↗

NASA NTRS1987

The convergence of spectral methods for nonlinear conservation laws

The convergence of the Fourier method for scalar nonlinear conservation laws which exhibit spontaneous shock discontinuities is discussed. Numerical tests indicate that the convergence may (and in fact in some cases must) fail, with or without post-processing of the numerical solution. Instead, a new kind of spectrally accurate vanishing viscosity is introduced to augment the Fourier approximation of such nonlinear conservation laws. Using compensated compactness arguments, it is shown that this spectral viscosity prevents oscillations, and convergence to the unique entropy solution follows.

Tadmor, Eitan↗

NASA NTRS1986

The Nazca-South American convergence rate and the recurrence of the great 1960 Chilean earthquake

The seismic slip rate along the Chile Trench estimated from the slip in the great 1960 earthquake and the recurrence history of major earthquakes has been interpreted as consistent with the subduction rate of the Nazca plate beneath South America. The convergence rate, estimated from global relative plate motion models, depends significantly on closure of the Nazca - Antarctica - South America circuit. NUVEL-1, a new plate motion model which incorporates recently determined spreading rates on the Chile Rise, shows that the average convergence rate over the last three million years is slower than previously estimated. If this time-averaged convergence rate provides an appropriate upper bound for the seismic slip rate, either the characteristic Chilean subduction earthquake is smaller than the 1960 event, the average recurrence interval is greater than observed in the last 400 years, or both. These observations bear out the nonuniformity of plate motions on various time scales, the variability in characteristic subduction zone earthquake size, and the limitations of recurrence time estimates.

Stein, S.↗

NASA NTRS1986

Improving the convergence rate to steady state of parabolic ADI methods

The present, residuals' L(2)-norms analysis of the rate of convergence to steady state for parabolic ADI solvers allows the prediction of the number of iterations required for convergence, as a function of the Courant number alpha. A modification of current ADI codes is presented which significantly improves the convergence rate and is insensitive to the Courant number over a large range of alpha. This corrected algorithm is tested for the cases of Dirichlet problems for uniform grids of many mesh sizes, mixed Dirichlet-Neumann problems, and problems defined on stretched grids and/or problems with variable coefficients.

Abarbanel, Saul S.↗

NASA NTRS1986

Necessary and sufficient conditions for parameter convergence in adaptive control

Using Generalized Harmonic Analysis, a complete description of parameter convergence in Model Reference Adaptive Control (MRAC) is given in terms of the spectrum of the exogenous reference input signal. Roughly speaking, if the reference signal 'contains enough frequencies' then the parameter vector converges to its correct value. If not, it converges to an easily characterizable subspace in parameter space.

Boyd, Stephen↗

NASA NTRS1987

On the role of sea surface temperature gradients in forcing low-level winds and convergence in the tropics

The potential contribution of the SST gradient-driven flow to the low-level (p not less than 700 mb) convergence over tropical oceans is determined using a simple one-layer model of the trade cumulus boundary layer wherein surface temperature gradients are mixed vertically (consistent with the ECMWF analyzed data). The influence of the layers above 700 mb is intentionally suppressed. The results of the study demonstrate the importance of taking account of the fact that cumulonimbus convection takes a small but finite time to adjust to low-level convergence. Failure to consider this effect leads to unreasonably large equatorial convergence.

Lindzen, Richard S.↗

NASA NTRS1988

Analysis of the convergence history of flow through nozzles with shocks

Acceleration techniques such as Wynn's (1986) epsilon algorithm and analysis techiques such as eigensystem analysis are used here to study numerically the convergence properties of an iterative scheme applied to the quasi-one-dimensional Euler and Navier-Stokes equations for flow through nozzles with shocks. The convergence and stability properties are studied by analyzing the dependence of convergence of the code on the discretization technique, boundary conditions, time-step, number of grid points, and the physics of the problem.

Cheer, A. Y.↗

NASA NTRS1988

Determination of convergence rates across the Ventura Basin, Southern California, using GPS and historical triangulation

Comparison of angles from historical triangulation observations dating as far back as 1932 with Global Positions System (GPS) measurements taken in 1987 indicates that rapid convergence may be taking place on decade timescales in the central and eastern part of the Ventura basin, an east-west trending trough bounded by thrust faults. Changes in angles over this time were analyzed using Prescott's modified Frank's method and in terms of a model which assumes that the regions to the north and south of the basin are rigid blocks undergoing relative motion. For the two block model, inversion of the observed angle changes over the last 28 years for the relative motion vector leads to north-south convergence across the basin of 30 + or - 5 mm/yr, with a left lateral component of 10 + or - 1 mm/yr in the Fillmore-Santa Paula area in the central part of the basin. The modified Frank's method yields strain rates of approximately 2 microrad/yr in both the east and central parts of the basin for measurements spanning the 1971 San Fernando earthquake. Assuming no east-west strain yeilds north-south compression of approximately 3.5 + or - .2 cm/yr. Comparison of triangulation data prior to the earthquake shows no strain outside the margin of error. The convergence rates determined by geodetic techniques are consistent with geologic observations in the area. Such large geodetic deformation rates, with no apparent near-surface creep on the major thrust, can be understood if these faults become subhorizontal at relatively shallow depths and if the subhorizontal portions of the faults are creeping. An alternative explanation of the large displacement rates might be that the pumping of oil in the vicinity of the benchmarks caused large horizontal motions, although it is unlikely that meter scale horizontal motions are due to oil withdrawal. These and other hypotheses are evaluated to better constrain the tectonics of this active region.

Donnellan, Andrea↗

NASA NTRS1988

Eddies, streams, and convergence zones in turbulent flows

Recent studies of turbulent shear flows have shown that many of their important kinematical and dynamical properties can be more clearly understood by describing the flows in terms of individual events or streamline patterns. These events or flow regions are studied because they are associated with relatively large contributions to certain average properties of the flow, for example kinetic energy, Reynolds stress, or to particular processes in the flow, such as mixing and chemical reactions, which may be concentrated at locations where streamlines converge for fast chemical reactions (referred to as convergence or C regions), or in recirculating eddying regions for slow chemical reactions. The aim of this project was to use the numerical simulations to develop suitable criteria for defining these eddying or vortical zones. The C and streaming (S) zones were defined in order to define the whole flow field. It is concluded that homogeneous and sheared turbulent flow fields are made up of characteristic flow zones: eddy, C, and S zones. A set of objective criteria were found which describe regions in which the streamlines circulate, converge or diverge, and form high streams of high velocity flow.

Hunt, J. C. R.↗

NASA NTRS1989

Architecture of orogenic belts and convergent zones in Western Ishtar Terra, Venus

Linear mountain belts in Ishtar Terra were recognized from Pioneer-Venus topography, and later Arecibo images showed banded terrain interpreted to represent folds. Subsequent analyses showed that the mountains represented orogenic belts, and that each had somewhat different features and characteristics. Orogenic belts are regions of focused shortening and compressional deformation and thus provide evidence for the nature of such deformation, processes of crustal thickening (brittle, ductile), and processes of crustal loss. Such information is important in understanding the nature of convergent zones on Venus (underthrusting, imbrication, subduction), the implications for rates of crustal recycling, and the nature of environments of melting and petrogenesis. The basic elements of four convergent zones and orogenic belts in western Ishtar Terra are identified and examined, and then assess the architecture of these zones (the manner in which the elements are arrayed), and their relationships. The basic nomenclature of the convergent zones is shown.

Head, James W.↗

NASA NTRS1990

Convergence of the SMI and the diagonally loaded SMI algorithms with weak interference

Approximations for the power levels at the output of an adaptive array that uses the diagonally loaded sample-matrix inversion (SMI) algorithm are derived. Diagonal loading is a technique where the diagonal of the covariance matrix is augmented with a positive or negative constant prior to inversion. This paper examines how the signal-to-interference-plus-noise ratio (SINR) and signal-to-interference ratio (SIR) at the array output vary with the number of samples taken when the input signals are CW. It is shown that positive loading produces more rapid convergence with a reduction in output SIR. Negative loading provides an improved SIR level, but positive loading produces more rapid convergence. Negative loading provides an improved SIR level, but the output power levels are erratic and slow to converge. Simulation results which verify the theoretical procedure are given.

Ganz, Matthew W.↗

NASA NTRS1990

Global convergence of inexact Newton methods for transonic flow

In computational fluid dynamics, nonlinear differential equations are essential to represent important effects such as shock waves in transonic flow. Discretized versions of these nonlinear equations are solved using iterative methods. In this paper an inexact Newton method using the GMRES algorithm of Saad and Schultz is examined in the context of the full potential equation of aerodynamics. In this setting, reliable and efficient convergence of Newton methods is difficult to achieve. A poor initial solution guess often leads to divergence or very slow convergence. This paper examines several possible solutions to these problems, including a standard local damping strategy for Newton's method and two continuation methods, one of which utilizes interpolation from a coarse grid solution to obtain the initial guess on a finer grid. It is shown that the continuation methods can be used to augment the local damping strategy to achieve convergence for difficult transonic flow problems. These include simple wings with shock waves as well as problems involving engine power effects. These latter cases are modeled using the assumption that each exhaust plume is isentropic but has a different total pressure and/or temperature than the freestream.

Young, David P.↗

NASA NTRS1991

Approximate effect of parameter pseudonoise intensity on rate of convergence for EKF parameter estimators

When using parameter estimation methods based on extended Kalman filter (EKF) theory, it is common practice to assume that the unknown parameter values behave like a random process, such as a random walk, in order to guarantee their identifiability by the filter. The present work is the result of an ongoing effort to quantitatively describe the effect that the assumption of a fictitious noise (called pseudonoise) driving the unknown parameter values has on the parameter estimate convergence rate in filter-based parameter estimators. The initial approach is to examine a first-order system described by one state variable with one parameter to be estimated. The intent is to derive analytical results for this simple system that might offer insight into the effect of the pseudonoise assumption for more complex systems. Such results would make it possible to predict the estimator error convergence behavior as a function of the assumed pseudonoise intensity, and this leads to the natural application of the results to the design of filter-based parameter estimators. The results obtained show that the analytical description of the convergence behavior is very difficult.

Hill, Bryon K.↗

NASA NTRS1993

On the accuracy of limiters and convergence to steady state solutions

This paper addresses the practical problem of obtaining convergence to steady state solutions when limiters are used in conjunction with upwind schemes on unstructured grids. The base scheme forms a gradient and limits it by imposing monotonicity conditions in the reconstruction stage. It is shown by analysis in one dimension that such an approach leads to various schemes meeting TVD requirements in one dimension. It is further shown that these formally second order accurate schemes are less than second order accurate in practice because of the action of the limiter function in smooth regions of the solution. Modifications are proposed to the limiter that restore the second order accuracy. In multiple dimensions these schemes produce steady state solutions that are monotone and devoid of oscillations. However, convergence stalls after a few orders of reduction in the residual. With the modified limiter, on the other hand, it is shown that converged steady state solutions can be obtained.

Venkatakrishnan, V.↗