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At least 73 records · Page 4

A Poisson equation formulation for pressure calculations in penalty finite element models for viscous incompressible flows

The calculation of pressures when the penalty-function approximation is used in finite-element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C0 velocity approximation using a least-squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.

Sohn, J. L.↗

Numerical recovery of certain discontinuous electrical conductivities

The inverse problem of recovering an electrical conductivity of the form Gamma(x) = 1 + (k-1)(sub Chi(D)) (Chi(D) is the characteristic function of D) on a region omega is a subset of 2-dimensional Euclid space from boundary data is considered, where D is a subset of omega and k is some positive constant. A linearization of the forward problem is formed and used in a least squares output method for approximately solving the inverse problem. Convergence results are proved and some numerical results presented.

Bryan, Kurt↗

Development of an efficient analysis for high Reynolds number inviscid/viscid interactions in cascades

An efficient steady analysis for predicting strong inviscid/viscid interaction phenomena such as viscous-layer separation, shock/boundary-layer interaction, and trailing-edge/near-wake interaction in turbomachinery blade passages is described. It uses an inviscid/viscid interaction approach, wherein the flow in the outer inviscid region is assumed to be potential, and that in the inner or viscous-layer region is governed by Prandtl's equations. The inviscid solution is determined using an implicit, least-squares, finite-difference approximation. The viscous-layer solution is obtained using an inverse, finite-difference, space-marching method which is applied along the blade surfaces and the wake streamline. A semiinverse global iteration procedure permits the prediction of boundary-layer separation and other strong-interaction phenomena. Results are presented for two cascades where a range of inlet flow conditions was considered for one of them including conditions leading to large-scale flow separation.

Barnett, M.↗

An analysis for high Reynolds number inviscid/viscid interactions in cascades

An efficient steady analysis for predicting strong inviscid/viscid interaction phenomena such as viscous-layer separation, shock/boundary-layer interaction, and trailing-edge/near-wake interaction in turbomachinery blade passages is needed as part of a comprehensive analytical blade design prediction system. Such an analysis is described. It uses an inviscid/viscid interaction approach, in which the flow in the outer inviscid region is assumed to be potential, and that in the inner or viscous-layer region is governed by Prandtl's equations. The inviscid solution is determined using an implicit, least-squares, finite-difference approximation, the viscous-layer solution using an inverse, finite-difference, space-marching method which is applied along the blade surfaces and wake streamlines. The inviscid and viscid solutions are coupled using a semi-inverse global iteration procedure, which permits the prediction of boundary-layer separation and other strong-interaction phenomena. Results are presented for three cascades, with a range of inlet flow conditions considered for one of them, including conditions leading to large-scale flow separations. Comparisons with Navier-Stokes solutions and experimental data are also given.

Barnett, Mark↗

Parameter identifiability under approximation

The problem of injectivity of the parameter-to-state map is discussed for Galerkin approximations of a linear parabolic equation. A necessary and sufficient condition is derived and illustrated by means of simple examples. Finally, output least squares identifiability of the Galerkin approximations is discussed.

Kunisch, K.↗

Least squares finite element simulation of transonic flows

Finite difference approximation of transonic flow problems is a well-developed and largely successful approach. Nevertheless, there is still a real need to develop finite element methods for applications arising from fluid-structure interactions and problems with complicated boundaries. In this paper a least squares based finite element scheme is introduced. It is shown that, if suitably formulated, such an approach can lead to physically meaningful results. Bottlenecks that arise from such schemes are also discussed.

Chen, T. F.↗

Aerodynamic parameter estimation via Fourier modulating function techniques

Parameter estimation algorithms are developed in the frequency domain for systems modeled by input/output ordinary differential equations. The approach is based on Shinbrot's method of moment functionals utilizing Fourier based modulating functions. Assuming white measurement noises for linear multivariable system models, an adaptive weighted least squares algorithm is developed which approximates a maximum likelihood estimate and cannot be biased by unknown initial or boundary conditions in the data owing to a special property attending Shinbrot-type modulating functions. Application is made to perturbation equation modeling of the longitudinal and lateral dynamics of a high performance aircraft using flight-test data. Comparative studies are included which demonstrate potential advantages of the algorithm relative to some well established techniques for parameter identification. Deterministic least squares extensions of the approach are made to the frequency transfer function identification problem for linear systems and to the parameter identification problem for a class of nonlinear-time-varying differential system models.

Pearson, A. E.↗

Geodetic and Astrometric Measurements with Very-Long-Baseline Interferometry

The use of very-long-baseline interferometry (VLBI) observations for the estimation of geodetic and astrometric parameters is discussed. Analytic models for the dependence of delay and delay rate on these parameters are developed and used for parameter estimation by the method of weighted least squares. Results are presented from approximately 15,000 delay and delay-rate observations, obtained in a series of nineteen VLBI experiments involving a total of five stations on two continents. The closure of baseline triangles is investigated and found to be consistent with the scatter of the various baseline-component results. Estimates are made of the wobble of the earth's pole and of the irregularities in the earth's rotation rate. Estimates are also made of the precession constant and of the vertical Love number, for which a value of 0.55 + or - 0.05 was obtained.

Robertson, D. S.↗

Estimation of time- and state-dependent delays and other parameters in functional differential equations

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Murphy, K. A.↗

Estimation of time- and state-dependent delays and other parameters in functional differential equations

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Murphy, K. A.↗

Polynomial compensation, inversion, and approximation of discrete time linear systems

The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.

Baram, Yoram↗

Analysis of the distribution of pitch angles in model galactic disks - Numerical methods and algorithms

An automated mathematical method capable of successfully isolating the many different features in prototype and observed spiral galaxies and of accurately measuring the pitch angles and lengths of these individual features is developed. The method is applied to analyze the evolution of specific features in a prototype galaxy exhibiting flocculent spiral structure. The mathematical-computational method was separated into two components. Initially, the galaxy was partitioned into dense regions constituting features using two different methods. The results obtained using these two partitioning algorithms were very similar, from which it is inferred that no numerical biasing was evident and that capturing of the features was consistent. Standard least-squares methods underestimated the true slope of the cloud distribution and were incapable of approximating an orientation of 45 deg. The problems were overcome by introducing a superior fit least-squares method, developed with the intention of calculating true orientation rather than a regression line.

Russell, William S.↗

Pole placement with constant gain output feedback

Given a linear time invariant multivariable system with m inputs and p outputs, it was shown that p closed loop poles of the system can be preassigned arbitrarily using constant gain output feedback provided (A circumflex, B circumflex) is controllable. These data show that if (A circumflex, B circumflex, C circumflex) is controllable and observable, and Rank B circumflex = m, Rank C circumflex = p, then max (m,p) poles of the system can be assigned arbitarily using constant gain output feedback. Further, it is shown that in some cases more than max (m,p) poles can be arbitrarily assigned. A least square design technique is outlined to approximate the desired pole locations when it is not possible to place all the poles.

Sridhar, B.↗

Pole-placement with constant gain output feedback

Davison (1970) has demonstrated that it is possible to assign max (m, p) poles of a linear time-invariant controllable and observable multivariable system arbitrarily close to desired locations by using constant gain output feedback. A new proof of Davison's theorem on pole placement is developed, and a system design procedure is described which offers some advantages over Davison's method. It is shown that in some cases more than max (m, p) poles can be assigned arbitrarily, and a least square design procedure is proposed to approximate the desired pole locations when it is not possible to place all the poles.

Sridhar, B.↗

Observation of a driver gas-tangential discontinuity

A complete analysis of an interplanetary disturbance of Nov. 19, 1970 using the Apollo 12-SIDE (Suprathermal Ion Detector Experiment) is presented. The SIDE detectors were pointing at 26.3 degrees from the normal solar-wind direction during the observations. The data were least-squares fitted (using a parabolic hypersurface approximation) to a convected Maxwell-Boltzmann distribution function. The results of the fit combined with two other experiments showed a drastic change in the wind speed (from an steady 352 km/sec down to 219 km/sec), direction, and temperature. Except for a delta-function increase at the onset, the density remained constant. There was a considerable enhancement in the abundance of He and probably of heavier elements. The interplanetary magnetic field exhibited a jump of 21 gamma with a change in latitude from -56 to -76 degrees in solar ecliptic coordinates. It is concluded that the disturbance was due to the driver gas-tangential discontinuity of a solar flare-induced shock wave. The characteristic of the tangential discontinuity fit well with theoretical prediction.

Medrano, R. A.↗

On the Formulation of Weakly Singular Displacement/Traction Integral Equations; and Their Solution by the MLPG Method

In this paper, a very simple method is used to derive the weakly singular traction boundary integral equation based on the integral relationships for displacement gradients. The concept of the MLPG method is employed to solve the integral equations, especially those arising in solid mechanics. A moving Least Squares (MLS) interpolation is selected to approximate the trial functions in this paper. Five boundary integral Solution methods are introduced: direct solution method; displacement boundary-value problem; traction boundary-value problem; mixed boundary-value problem; and boundary variational principle. Based on the local weak form of the BIE, four different nodal-based local test functions are selected, leading to four different MLPG methods for each BIE solution method. These methods combine the advantages of the MLPG method and the boundary element method.

Atluri, Satya N.↗

Simulation of a Periodic Jet in a Crossflow with a RANS Solver Using an Unstructured Grid

A second-order unstructured-grid code, developed and used primarily for steady aerodynamic simulations, is applied to the synthetic jet in a cross flow. The code, FUN3D, is a vertex-centered finite-volume method originally developed by Anderson[1, 2], and is currently supported by members of the Fast Adaptive Aerospace Tools team at NASA Langley. Used primarily for design[3] and analysis[4] of steady aerodynamic configurations, FUN3D incorporates a discrete adjoint capability, and supports parallel computations using MPI. A detailed description of the FUN3D code can be found in the references given above. The code is under continuous development and contains a variety of flux splitting algorithms for the inviscid terms, two methods for computing gradients, several turbulence models, and several solution methodologies; all in varying states of development. Only the most robust and reliable components, based on experiences with steady aerodynamic simulations, were employed in this work. As applied in this work, FUN3D solves the Reynolds averaged Navier-Stokes equations using the one equation turbulence model of Spalart and Allmaras[5]. The spatial discretization is formed on unstructured meshes using a vertex-centered approach. The inviscid terms are evaluated by a flux-difference splitting formulation using least-squares reconstruction and Roe-type approximate Riemann fluxes. Green-Gauss gradient evaluations are used for viscous and turbulence modeling terms. The discrete spatial operator is combined with a backward time operator which is then solved iteratively using point or line Gauss-Seidel and local time stepping in a pseudo time. For steady flows, the physical time step is set to infinity and the pseudo time step is ramped up with the iteration count. A second-order backward in time operator is used for time accurate flows with 20 to 50 steps in the pseudo time applied at each physical time step. For this effort, FUN3D was modified to support spatially varying boundary and initial conditions, and unsteady boundary conditions. Also, a specialized in/out flow boundary condition was implemented to model the action of the diaphragm. This boundary condition is described below in more detail. The grids were generated using the internally developed codes GridEX[6] for meshing the surfaces and inviscid regions of the domain, and for CAD access; and MesherX[7] for meshing the viscous regions. Grid spacing in on the surfaces and in the inviscid regions are indirectly controlled by specifying sources. The viscous layers are generated using an advancing layer technique. MeshersX allows the user to control the spatial variation of the first step off the surface, growth rates, and the termination criterion by providing small problem dependent subroutines.

Atkins, H. L.↗