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At least 145 records · Page 8

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NASA NTRS1988

Assessment of recent resolution and parameterization changes in the GLA fourth order GCM

The Goddard Laboratory for Atmospheres' fourth-order GCM is under evaluation for the impact on model integrations of enhanced horizontal and vertical resolution, as well as the effects of such novel parameterization schemes as that of gravity-wave-drag, the Arakawa-Schubert (1974) cumulus parameterization, and an explicitly-resolved planetary boundary layer. While the doubling of the GMC's horizontal resolution to 2 deg in latitude and 2.5 deg in longitude has improved the model's predictive skill for 6-7 day forecasts, systematic errors associated with the model's climate drift lead to a deterioration in predictions for longer forecasts.

Helfand, H. M.↗

NASA NTRS1988

Numerical prediction experiments related to the summer 1980 U.S. heat wave

The GLA (Goddard Laboratory for Atmosphere) fourth-order model predictions of the summer 1980 heat wave are examined to assess the skill of the model in numerically forecasting the initiation of the heat wave and the sensitivity of the model predictions to initial conditions and boundary forcing. Results of experiments indicate that the model predictions are sensitive to the initial conditions. The sensitivity of the model to anomalous boundary forcing is found to be generally larger than its sensitivity to initial conditions at extended ranges. The results of the study suggest that models may be useful in forecasting similar events if adequate determinations of the evolving boundary forcing can be made in real time.

Atlas, R.↗

NASA NTRS1989

Stability boundaries for aircraft with unstable lateral-directional dynamics and control saturation

Aircraft that do not possess inherent (aerodynamic) stability must rely on closed-loop control systems for stable operation. Because there are limits on the deflections of an aircraft's control surfaces, the region of stable operation also is bounded. These boundaries are investigated for a lateral-directional example in which vertical fin size is inadequate to provide directional stability and where aileron and rudder deflections are subject to saturation. Fourth-order models are used in this study, with flight control logic based on minimum-control-energy linear-quadratic-regulatory theory. It is found that the stability boundaries can be described by unstable limit cycles surrounding stable equilibrium points. Variations in regions of stability with gain levels and command inputs are illustrated. Current results suggest guidelines for permissible limits on the open-loop instability of an aircraft's lateral-directional modes.

Shrivastava, Prakash C.↗

NASA NTRS1989

Three-dimensional compressible boundary layer calculations to fourth order accuracy on wings and fuselages

Laminar flow control and drag reduction research requires accurate boundary layer solutions as input to the three-dimensional stability analysis procedures currently under development. In support of these major programs, a fourth-order accurate finite difference scheme for solving the three-dimensional, compressible boundary layer equations has been developed and is presented in this paper. The method employs a two-point scheme in the wall normal direction and second order zigzag scheme in the cross flow direction. Accurate procedures to interface with the inviscid results are also presented. The results of applying the procedure to laminar flow on wings and fuselages are presented.

Iyer, Venkit↗

NASA NTRS1989

Three-dimensional computations of cross-flow injection and combustion in a supersonic flow

A low-storage version of the SPARK3D code which is based on the temporally second-order accurate MacCormack (1969) explicit scheme is used to solve the governing equations for three-dimensional chemically reacting flows with finite-rate chemistry. The code includes a fourth-order compact spatial scheme capable of providing higher order spatial accuracy, and it is used to study two-dimensional linear advection, two-dimensional Euler flow, and three-dimensional viscous flow. Also considered are the injection, mixing, and combustion of hydrogen in a supersonic cross stream.

Carpenter, M. H.↗

NASA NTRS1989

Numerical Study of Three-dimensional Spatial Instability of a Supersonic Flat Plate Boundary Layer

The behavior of spatially growing three-dimensional waves in a supersonic boundary layer was studied numerically by solving the complete Navier-Stokes equations. Satisfactory comparison with linear parallel and non-parallel stability theories, and experiment are obtained when a small amplitude inflow disturbance is used. The three-dimensional unsteady Navier-Stokes equations are solved by a finite difference method which is fourth-order and second-order accurate in the convection and viscous terms respectively, and second-order accurate in time. Spanwise periodicity is assumed. The inflow disturbance is composed of eigenfunctions from linear stability theory. By increasing the amplitude of the inflow disturbance, nonlinear effects in the form of a relaxation type oscillation of the time signal of rho(u) are observed.

Maestrello, Lucio↗

NASA NTRS1989

Effect of spatial resolution on apparent sensitivity to initial conditions of a decaying flow as it becomes turbulent

Grids with 32(exp 3), 64(exp 3), and 128(exp 3) points are used in numerical solutions for a decaying flow. The sensitivity of initially neighboring solutions to small changes in initial conditions increases as the spatial resolution improves. A fourth-order finite-difference method is used for the solutions with 32(exp 3) and 64(exp 3) grid points, and a pseudospectral method is used for 128(exp 3) grid points. The latter solutions appear to be rather well-resolved, in spite of the formation of steep velocity gradients in the flow.

Deissler, Robert G.↗

NASA NTRS1990

Some Aspects of Essentially Nonoscillatory (ENO) Formulations for the Euler Equations, Part 3

An essentially nonoscillatory (ENO) formulation is described for hyperbolic systems of conservation laws. ENO approaches are based on smart interpolation to avoid spurious numerical oscillations. ENO schemes are a superset of Total Variation Diminishing (TVD) schemes. In the recent past, TVD formulations were used to construct shock capturing finite difference methods. At extremum points of the solution, TVD schemes automatically reduce to being first-order accurate discretizations locally, while away from extrema they can be constructed to be of higher order accuracy. The new framework helps construct essentially non-oscillatory finite difference methods without recourse to local reductions of accuracy to first order. Thus arbitrarily high orders of accuracy can be obtained. The basic general ideas of the new approach can be specialized in several ways and one specific implementation is described based on: (1) the integral form of the conservation laws; (2) reconstruction based on the primitive functions; (3) extension to multiple dimensions in a tensor product fashion; and (4) Runge-Kutta time integration. The resulting method is fourth-order accurate in time and space and is applicable to uniform Cartesian grids. The construction of such schemes for scalar equations and systems in one and two space dimensions is described along with several examples which illustrate interesting aspects of the new approach.

Chakravarthy, Sukumar R.↗

NASA NTRS1990

Analysis and mitigation of numerical dissipation in inviscid and viscid computation of vortex-dominated flows

The conservative unsteady Euler equations for the flow relative motion in the moving frame of reference are used to solve for the steady and unsteady flows around sharp-edged delta wings. The resulting equations are solved by using an implicit approximately-factored finite volume scheme. Implicit second-order and explicit second- and fourth-order dissipations are added to the scheme. The boundary conditions are explicitly satisfied. The grid is generated by locally using a modified Joukowski transformation in cross flow planes at the grid chord stations. The computational applications cover a steady flow around a delta wing whose results serve as the initial conditions for the unsteady flow around a pitching delta wing about a large angle of attack. The steady results are compared with the experimental data and the periodic solution is achieved within the third cycle of oscillation.

Kandil, Osama A.↗

NASA NTRS1990

Global simulation of the solar wind-magnetosphere interaction - The importance of its numerical validity

This paper examines the global interaction of the solar wind with the geomagnetic field, using a newly developed three-dimensional high-precision MHD simulation code which employs the fourth-order Runge-Kutta-Gill scheme in time and the direct finite-difference method in space, and which allows much less numerical error than the conventional code. The simulation reveals in detail the formation processes of the magnetosphere and the bow shock, as well as the plasma sheet formation process. It is shown that, contrary to the conventional understanding, no Kelvin-Helmholtz instability occurs along the magnetopause in an ideal MHD.

Watanabe, K.↗

NASA NTRS1990

Numerical methods for hypersonic boundary layer stability

Four different schemes for solving compressible boundary layer stability equations are developed and compared, considering both the temporal and spatial stability for a global eigenvalue spectrum and a local eigenvalue search. The discretizations considered encompass: (1) a second-order-staggered finite-difference scheme; (2) a fourth-order accurate, two-point compact scheme; (3) a single-domain Chebychev spectral collocation scheme; and (4) a multidomain spectral collocation scheme. As Mach number increases, the performance of the single-domain collocation scheme deteriorates due to the outward movement of the critical layer; a multidomain spectral method is accordingly designed to furnish superior resolution of the critical layer.

Malik, M. R.↗

NASA NTRS1990

Assessing the impact of different satellite retrieval methods on forecast available potential energy

The effects of the inclusion of satellite temperature retrieval data, and of different satellite retrieval methods, on forecasts made with the NASA Goddard Laboratory for Atmospheres (GLA) fourth-order model were investigated using, as the parameter, the available potential energy (APE) in its isentropic form. Calculation of the APE were used to study the differences in the forecast sets both globally and in the Northern Hemisphere during 72-h forecast period. The analysis data sets used for the forecasts included one containing the NESDIS TIROS-N retrievals, the GLA retrievals using the physical inversion method, and a third, which did not contain satellite data, used as a control; two data sets, with and without satellite data, were used for verification. For all three data sets, the Northern Hemisphere values for the total APE showed an increase throughout the forecast period, mostly due to an increase in the zonal component, in contrast to the verification sets, which showed a steady level of total APE.

Whittaker, Linda M.↗

NASA NTRS1990

Two-dimensional atmospheric transport and chemistry model - Numerical experiments with a new advection algorithm

Extensive testing of the advective scheme proposed by Prather (1986) has been carried out in support of the California Institute of Technology-Jet Propulsion Laboratory two-dimensional model of the middle atmosphere. The original scheme is generalized to include higher-order moments. In addition, it is shown how well the scheme works in the presence of chemistry as well as eddy diffusion. Six types of numerical experiments including simple clock motion and pure advection in two dimensions have been investigated in detail. By comparison with analytic solutions, it is shown that the new algorithm can faithfully preserve concentration profiles, has essentially no numerical diffusion, and is superior to a typical fourth-order finite difference scheme.

Shia, Run-Lie↗

NASA NTRS1990

Outgoing long-wave radiation computed from HIRS2/MSU soundings

Fields of outgoing long-wave radiation (OLR) have been computed using geophysical parameters retrieved from analysis of HIRS2/MSU sounding data as input to a modified version of the Wu-Kaplan radiation code used in the Goddard Laboratory for Atmospheres fourth-order general circulation model. Monthly mean results for 1979 agree with monthly mean OLR fields measured by the Nimbus 7 earth radiation budget (ERB) broadband narrow field of view instrument within standard deviations of 6.3 W/sq m but with a global mean bias of 8.0 W/sq m. Results are shown for July 1979. The areas of disagreement between high-resolution infrared radiation sounder OLR and ERB OLR are small but spatially coherent with patterns which may be related to sampling differences. The difference patterns are much less extensive than those between OLR derived from advanced very high resolution radiometer 11-micron observations and ERB OLR.

Wu, Man-Li C.↗

NASA NTRS1990

Computation of vortex-dominated flow for a delta wing undergoing pitching oscillation

The conservative, unsteady Euler equations for the flow relative to a moving frame of reference are used to solve for the three-dimensional steady and unsteady flows around a sharp-edged delta wing. The resulting equations are solved by using an implicit, approximately factored, finite-volume scheme. Implicit second-order and explicit second- and fourth-order dissipations are added to the scheme. The boundary conditions are explicitly satisfied. The grid is generated by locally using a modified Joukowski transformation in crossflow planes at the grid-chord stations. The computational applications cover a steady flow around a delta wing, whose results serve as the initial conditions for the unsteady flow around a pitching delta wing at a large mean angle of attack. The steady results are compared with the experimental data, and the unsteady results are compared with results of a flux-difference splitting scheme.

Kandil, Osama A.↗

NASA NTRS1989

The breakup of trailing-line vortices

It is now known that Batchelor's trailing-line vortex is extremely unstable to small amplitude disturbances for swirl numbers in the neighborhood of 0.83. The results of numerical calculations are presented that show the response of the vortex in this range of swirl numbers to finite amplitude, temporal, helical disturbances. Phenomena observed include: (1) ejection of axial vorticity and momentum from the core resulting in the creation of secondary, separate vortices; (2) a great intensification of core axial vorticity and a weakening of core momentum; and (3) the production of azimuthal vorticity in the form of a tightly wrapped spiral wave. The second phenomenon eventually stablizes the vortex, which then smooths and gradually returns to an axisymmetric state. The calculations are mixed spectral-finite-difference, fourth-order accurate, and have been carried out at Reynolds numbers of 1000 to 2000. Some linearized results are also discussed in an attempt to explain the process of vortex intensification.

Jacqmin, David↗

NASA NTRS1990

Analysis of spectral projectors in one-dimensional domains

A class of projection operators with values in a subspace of polynomials is analyzed. These projection operators are related to the Hilbert spaces involved in the numerical analysis of spectral methods. They are, in the first part of the paper, the standard Sobolev spaces and, in the second part, some weighted Sobolev spaces, the weight of which is related to the orthoronality relation satisfied by the Chebyshev polynomials. These results are used to study the approximation of a model fourth-order problem.

Maday, Y.↗

NASA NTRS1990

An improved fully stressed design algorithm for plate/shell structures

The stress-ratio algorithm associated with fully stressed design philosophy has been used as a convenient tool to achieve minimum weight design of strength-limited structures. The algorithm is effective and converges quickly for many cases. However, it presents extremely slow oscillatory iteration histories for plate-thickness design problems that involve transverse bending loads. Modification of the basic algorithm presented in this paper provides an effective remedy to this problem when both membrane and bending loads are present. The modified resizing algorithm requires numerical solutions of a fourth-order algebraic equation. No additional data, beyond the ordinary static analysis results, are required.

Miura, H.↗