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NASA NTRS1981

Sequential decision rules for failure detection

The formulation of the decision making of a failure detection process as a Bayes sequential decision problem (BSDP) provides a simple conceptualization of the decision rule design problem. As the optimal Bayes rule is not computable, a methodology that is based on the Baysian approach and aimed at a reduced computational requirement is developed for designing suboptimal rules. A numerical algorithm is constructed to facilitate the design and performance evaluation of these suboptimal rules. The result of applying this design methodology to an example shows that this approach is a useful one.

Chow, E. Y.↗

NASA NTRS1982

Computation of viscous hypersonic flow over control surfaces

A parabolized Navier-Stokes (PNS) computer code has been used to compute hypersonic flow over control surfaces located on the aft end of generic re-entry configurations. The Beam-Warming implicit numerical algorithm as modified by Schiff and Steger is used to march in the spatial direction. The outer bow shock is treated as a sharp discontinuity; within the shock layer discontinuities are captured. Several different turbulent flow solutions were generated for flap angles varying from -7 deg to 15 deg and angles of attack varying from 0 deg to 20 deg. The present results are qualitatively correct when compared with previous compression corner studies.

Chaussee, D. S.↗

NASA NTRS1982

Unsteady, thermally conductive coronal flow

A numerical algorithm using implicit time-differencing is applied to the solar wind equations allowing, for the first time, solutions including thermal conduction to be found for time-dependent flow traversing the subsonic to supersonic velocity transition region. Sample solutions are shown that demonstate the distinctive differences introduced by including thermal conduction, in comparison to the commonly available solutions assuming polytropic flow. Also, it is found that steady solutions are produced at least as quickly using a time-dependent relaxation to the steady state as when solving the steady-state equations.

Suess, S. T.↗

NASA NTRS1983

Potential of minicomputer/array-processor system for nonlinear finite-element analysis

The potential of using a minicomputer/array-processor system for the efficient solution of large-scale, nonlinear, finite-element problems is studied. A Prime 750 is used as the host computer, and a software simulator residing on the Prime is employed to assess the performance of the Floating Point Systems AP-120B array processor. Major hardware characteristics of the system such as virtual memory and parallel and pipeline processing are reviewed, and the interplay between various hardware components is examined. Effective use of the minicomputer/array-processor system for nonlinear analysis requires the following: (1) proper selection of the computational procedure and the capability to vectorize the numerical algorithms; (2) reduction of input-output operations; and (3) overlapping host and array-processor operations. A detailed discussion is given of techniques to accomplish each of these tasks. Two benchmark problems with 1715 and 3230 degrees of freedom, respectively, are selected to measure the anticipated gain in speed obtained by using the proposed algorithms on the array processor.

Strohkorb, G. A.↗

NASA NTRS1983

Flux-based acceleration of the Euler equations

A new coarse grid acceleration scheme for the Euler equations is presented. This flux based scheme eliminates the need, exhibited by previous accelerators, for computing flux vector Jacobian matrices. The method is derived and implemented in a two dimensional flow algorithm. Numerical results are presented for both subcritical and shocked, supercritical flow. These results demonstrate that the flux based accelerator is more efficient than its Jacobian based counterpart. Generalization to three dimensions is immediate. Construction of flux based accelerators for the Navier-Stokes equations is also discussed.

Johnson, G. M.↗

NASA NTRS1983

Modeling of turbulent separated flows for aerodynamic applications

Steady, high speed, compressible separated flows modeled through numerical simulations resulting from solutions of the mass-averaged Navier-Stokes equations are reviewed. Emphasis is placed on benchmark flows that represent simplified (but realistic) aerodynamic phenomena. These include impinging shock waves, compression corners, glancing shock waves, trailing edge regions, and supersonic high angle of attack flows. A critical assessment of modeling capabilities is provided by comparing the numerical simulations with experiment. The importance of combining experiment, numerical algorithm, grid, and turbulence model to effectively develop this potentially powerful simulation technique is stressed.

Marvin, J. G.↗

NASA NTRS1981

Mesh generation by conformal and quasiconformal mappings

It is pointed out that many recent advances in the finite-difference solution of elliptic equations have been limited to regions whose boundary contours coincide with coordinate lines of the Cartesian coordinate system. The reason for this is related to the fact that in the case of an arbitrary curvilinear coordinate system the original equation becomes much more complex. However, there is no added complexity if an orthogonal coordinate system is generated from a conformal mapping. In the present investigation, a finite difference method developed for the construction of conformal mappings has been generalized to construct quasi-conformal mappings. It is expected that the use of more sophisticated numerical algorithms could lead to improvements in both speed and accuracy. Quasi-conformal mappings have applications not only in the solution of elliptic equations but also in other areas such as orthogonal mesh generation on surfaces and the solution of certain fluid flow problems.

Mastin, C. W.↗

NASA NTRS1983

A computational investigation of supersonic axisymmetric flow over boattails containing a centered propulsive jet

The influence of underexpanded jets on a supersonic afterbody flow field is investigated using computational techniques. The thin-shear-layer formulation of the compressible, Reynolds-averaged Navier-Stokes equations is solved using a time-dependent, implicit numerical algorithm. Solutions are obtained for supersonic flow over an axisymmetric conical afterbody containing a centered propulsive jet where the free-stream Mach number is 2.0 and the jet exit Mach number is 2.5. Exhaust-jet static pressures are considered in the range of 2 to 9 times the free-stream static pressure and with nozzle-exit half-angles from 15 deg to 43 deg. Comparisons are made with experimental results for base pressure, separation distance, afterbody pressure distribution, anf flow-field structure. Although good quantitative agreement with experimental separation distance and base pressure level is not observed, the parametric trends induced by exhaust-jet pressure level and nozzle-exit angle are well predicted, as are the flow-field details in the vicinity of the afterbody and in the exhaust plume.

Deiwert, G. S.↗

NASA NTRS1982

Determination of the horizontal and vertical distribution of clouds from infrared satellite sounding data

A numerical algorithm, based on a physical inversion of the radiative transfer equation, is developed to retrieve the global distribution of the horizontal cloud cover, the cloud-top pressure levels and their temperature. The algorithm makes use of infrared and microwave temperature sounding data to derive the clear-column vertical temperature profiles and then uses the same infrared sounding data to obtain the corresponding cloud parameters. Experimental verification of this method is carried out using data from the High resolution Infrared Sounder (HIRS) and the Microwave Sounding Unit (MSU) operating on the NOAA weather satellite system.

Chahine, M. T.↗

NASA NTRS1983

Investigation, Development, and Evaluation of Performance Proving for Fault-tolerant Computers

A number of methodologies for verifying systems and computer based tools that assist users in verifying their systems were developed. These tools were applied to verify in part the SIFT ultrareliable aircraft computer. Topics covered included: STP theorem prover; design verification of SIFT; high level language code verification; assembly language level verification; numerical algorithm verification; verification of flight control programs; and verification of hardware logic.

Levitt, K. N.↗

NASA NTRS1979

Solution of 3-dimensional time-dependent viscous flows. Part 1: Investigation of candidate algoriths

There is considerable interest in developing a numerical scheme for solving the time dependent viscous compressible three dimensional flow to aid in the design of helicopter rotors. Numerical algorithms are examined to determine their overall suitability for the efficient and routine solution of an appropriate system of partial differential equations. It is concluded that a consistently split time linearized block implicit scheme using either quintic B spline collocation or the generalized operator compact implicit approach to generate a fourth order accurate algorithm is particularly well suited for use on the present problem. High cell Reynolds number behavior leads to favoring the generalized operator compact implicit approach over the quintic B spline collocation method.

Weinberg, B. C.↗

NASA NTRS1984

Research on output feedback control of systems with ill-conditioned dynamics

The accuracy of a two time scale approach to the output feedback regulator design problem is examined. An approximate quadratic performance index which reflects a two time scale decomposition of the system dynamics is developed. A sequential numerical algorithm is defined which obtains output feedback gains minimizing a broad class of performance indices, including the standard LQ case. A procedure for optimally zeroing selected gain elements in an output feedback gain matrix is developed and demonstrated. A summary of conference and journal publications from this research is also provided.

Calise, A. J.↗

NASA NTRS1984

Numerical simulation of the interaction of a vortex with stationary airfoil in transonic flow

A perturbation form of an implicit conservative, noniterative numerical algorithm for the two-dimensional thin layer Navier-Stokes and Euler equations is used to compute the interaction flow-field of a vortex with stationary airfoil. A Lamb-like analytical vortex having a finite core is chosen to interact with a thick (NACA 0012) and a thin (NACA 64A006) airfoil independently in transonic flow. Two different configurations of vortex interaction are studied, viz., (1) when the vortex is fixed at one location in the flowfield, and (2) when the vortex is convecting past the airfoil at freestream velocity. Parallel computations of this interacting flowfield are also done using a version of the Transonic Small Disturbance Code (ATRAN2). A special treatment of the leading edge region for thin airfoils is included in this code. With this, the three methods gave qualitatively similar results for the weaker interactions considered in this study. However, the strongest interactions considered proved to be beyond the capabilities of the small disturbance code. The results also show a far greater influence of the vortex on the airfoil flowfield when the vortex is stationary than when it is convecting with the flow.

Srinivasan, G. R.↗

NASA NTRS1983

Impact of new computing systems on finite element computations

Recent advances in computer technology that are likely to impact finite element computations are reviewed. The characteristics of supersystems, highly parallel systems, and small systems (mini and microcomputers) are summarized. The interrelations of numerical algorithms and software with parallel architectures are discussed. A scenario is presented for future hardware/software environment and finite element systems. A number of research areas which have high potential for improving the effectiveness of finite element analysis in the new environment are identified.

Noor, A. K.↗

NASA NTRS1984

Theoretical analysis of aircraft afterbody flow

The strongly interactive flow field about aircraft afterbodies is investigated using computational techniques by which the thin-shear-layer formulation of the compressible, Reynolds-averaged Navier-Stokes equations is solved. A time-dependent implicit numerical algorithm is used to obtain solutions for a variety of afterbody and nozzle geometries, within the class of bodies of revolution, for both subsonic and supersonic external flow, and for sonic and supersonic underexpanded jets. Only centered nozzles with either a sharp lip or a blunt base are considered. In all cases, computed results are compared with experimental data taken at flight Reynolds numbers for like-flow conditions. Turbulence closure is realized using algebraic eddy-viscosity concepts. A new and unique adaptive-grid technique is used to resolve flow regimes with large gradients and to improve the accuracy and efficiency of the computational scheme. Special singular point boundary conditions are used for similar purposes, and are especially effective for highly under-expanded jets. For all cases considered, except one with a very large base-to-nozzle-exit-diameter ratio, the agreement with experimental measurements is excellent. For geometries with large base regions, enhancements in the turbulence transport model are necessary to support improvements in the flow-field simulation.

Deiwert, G. S.↗

NASA NTRS1984

Design of an optimal output feedback control system with modal insensitivity

This paper deals with the design of an output feedback controller which results in selected modal insensitivity, and at the same time optimizes a quadratic performance index representative of desired system performance for nominal plant parameter values. The approach taken here is to characterize the class of attainable eigenvectors for a given set of eigenvalues (distinct or non-distinct) which lie in a subspace called the 'Modal Insensitivity Subspace'. A constraint is established on the feedback matrix which results in modal insensitivity. Necessary conditions for optimality subject to the constraint on the feedback matrix are given. This forms the basis for a numerical algorithm to compute the optimal feedback gain which analyzed for convergence. To illustrate the procedure, a design is carried out using the lateral dynamics of an L-1011 aircraft.

Raman, K. V.↗

NASA NTRS1984

Microwave radiances from precipitating clouds containing aspherical ice, combined phase, and liquid hydrometeors

A numerical algorithm based on Eddington's second approximation to the equation of radiative transfer has been developed in order to compute the radiances with horizontal and vertical polarization that emerge from precipitating clouds. This algorithm yields a rapid solution to problems pertaining to clouds with vertically inhomogeneous structure. Precipitating clouds containing liquid, mixtures of phases, and ice hydrometeors are modelled. It is shown that the lower-frequency radiances are sensitive to liquid precipitation at low altitudes while the higher-frequency radiances are more sensitive to the ice hydrometeors at the cloud tops. The extinction coefficients of aspherical hydrometeors are presented as a function of rainfall rates. The fact that vertically polarized radiances are warmer than horizontally polarized ones at high rainfall rates, with the difference diminishing at lower frequencies, is due to aspherical ice hydrometeors in the upper regions of precipitating clouds.

Wu, R.↗

NASA NTRS1984

Estimation of electric fields and current from ground-based magnetometer data

Recent advances in numerical algorithms for estimating ionospheric electric fields and currents from groundbased magnetometer data are reviewed and evaluated. Tests of the adequacy of one such algorithm in reproducing large-scale patterns of electrodynamic parameters in the high-latitude ionosphere have yielded generally positive results, at least for some simple cases. Some encouraging advances in producing realistic conductivity models, which are a critical input, are pointed out. When the algorithms are applied to extensive data sets, such as the ones from meridian chain magnetometer networks during the IMS, together with refined conductivity models, unique information on instantaneous electric field and current patterns can be obtained. Examples of electric potentials, ionospheric currents, field-aligned currents, and Joule heating distributions derived from ground magnetic data are presented. Possible directions for future improvements are also pointed out.

Kamide, Y.↗