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NASA NTRS1992

Non-LTE radiative transfer with lambda-acceleration - Convergence properties using exact full and diagonal lambda-operators

We investigate the convergence properties of Lambda-acceleration methods for non-LTE radiative transfer problems in planar and spherical geometry. Matrix elements of the 'exact' A-operator are used to accelerate convergence to a solution in which both the radiative transfer and atomic rate equations are simultaneously satisfied. Convergence properties of two-level and multilevel atomic systems are investigated for methods using: (1) the complete Lambda-operator, and (2) the diagonal of the Lambda-operator. We find that the convergence properties for the method utilizing the complete Lambda-operator are significantly better than those of the diagonal Lambda-operator method, often reducing the number of iterations needed for convergence by a factor of between two and seven. However, the overall computational time required for large scale calculations - that is, those with many atomic levels and spatial zones - is typically a factor of a few larger for the complete Lambda-operator method, suggesting that the approach should be best applied to problems in which convergence is especially difficult.

Macfarlane, J. J.↗

NASA NTRS1992

Improving the efficiency of aerodynamic shape optimization procedures

The computational efficiency of an aerodynamic shape optimization procedure which is based on discrete sensitivity analysis is increased through the implementation of two improvements. The first improvement involves replacing a grid point-based approach for surface representation with a Bezier-Bernstein polynomial parameterization of the surface. Explicit analytical expressions for the grid sensitivity terms are developed for both approaches. The second improvement proposes the use of Newton's method in lieu of an alternating direction implicit (ADI) methodology to calculate the highly converged flow solutions which are required to compute the sensitivity coefficients. The modified design procedure is demonstrated by optimizing the shape of an internal-external nozzle configuration. A substantial factor of 8 decrease in computational time for the optimization process was achieved by implementing both of the design improvements.

Burgreen, Greg W.↗

NASA NTRS1993

Vibration of thermally buckled composite plates with initial deflections using triangular elements

A consistent finite element formulation is presented for the analysis of thermal postbuckling and free vibration of thermally buckled thin, laminated composite plates subjected to large temperature change. The influence of moderately large initial imperfections in deflection on the thermal postbuckling deflection and the vibration characteristics of the buckled plate is also investigated. The finite element equations of motion are derived from the principle of virtual work. These equations can be mathematically separated into two sets and solved in sequence. The first set of equations yields the particular solution of static thermal postbuckling deflection, and the second set of equations gives the homogeneous solution of vibration characteristics on the buckled plate. The first set of static equations is solved by using Newton-Raphson iteration method. The tangent stiffness matrix in the final iteration is equal to the total stiffness matrix of the second set of dynamic equations. This feature saves tremendous computation time in comparing with using the conventional approach. The influence of lamination angle, temperature distribution, plate planform of arbitrary shape, and boundary support conditions on postbuckling and vibration behavior are investigated.

Zhou, R. C.↗

NASA NTRS1993

Structural design utilizing updated, approximate sensitivity derivatives

A method to improve the computational efficiency of structural optimization algorithms is investigated. In this method, the calculations of 'exact' sensitivity derivatives of constraint functions are performed only at selected iterations during the optimization process. The sensitivity derivatives utilized within other iterations are approximate derivatives which are calculated using an inexpensive derivative update formula. Optimization results are presented for an analytic optimization problem (i.e., one having simple polynomial expressions for the objective and constraint functions) and for two structural optimization problems. The structural optimization results indicate that up to a factor of three improvement in computation time is possible when using the updated sensitivity derivatives.

Scotti, Stephen J.↗

NASA NTRS1993

A numerical treatment of geodynamic viscous flow problems involving the advection of material interfaces

Effective numerical treatment of multicomponent viscous flow problems involving the advection of sharp interfaces between materials of differing physical properties requires correction techniques to prevent spurious diffusion and dispersion. We develop a particular algorithm, based on modern shock-capture techniques, employing a two-step nonlinear method. The first step involves the global application of a high-order upwind scheme to a hyperbolic advection equation used to model the distribution of distinct material components in a flow field. The second step is corrective and involves the application of a global filter designed to remove dispersion errors that result from the advection of discontinuities (e.g., material interfaces) by high-order, minimally dissipative schemes. The filter introduces no additional diffusion error. Nonuniform viscosity across a material interface is allowed for by the implementation of a compositionally weighted-inverse interface viscosity scheme. The combined method approaches the optimal accuracy of modern shock-capture techniques with a minimal increase in computational time and memory. A key advantage of this method is its simplicity to incorporate into preexisting codes be they finite difference, element, or volume of two or three dimensions.

Lenardic, A.↗

NASA NTRS1993

An optimal GPS data processing technique for precise positioning

A mathematical formula to optimally combine dual-frequency GPS pseudorange and carrier phase (integrated Doppler) data streams into a single data stream is derived in closed form. The data combination reduces the data volume and computing time in the filtering process for parameter estimation by a factor of 4 while preserving the full data strength for precise positioning. The resulting single data stream is that of carrier phase measurements with both data noise and bias uncertainty strictly defined. With this mathematical formula the single stream of optimally combined GPS measurements can be efficiently formed by simple numerical calculations. Carrier phase ambiguity resolution, when feasible, is strengthened due to the preserved full data strength with the optimally combined data and the resulting longer wavelength for the ambiguity to be resolved.

Wu, Sien-Chong↗

NASA NTRS1993

Application of the multigrid solution technique to hypersonic entry vehicles

A multigrid solution procedure has been incorporated in a version of the Langley Aerothermodynamic Upwind Relaxation Algorithm. The multigrid scheme is based on the Full Approximation Storage approach and uses Full Multigrid to obtain a well defined fine mesh starting solution. Predictions were obtained using standard transfer operators and a 'V-cycle' was used to control grid sequencing. Computed hypersonic flow solutions compared with experimental data for a 15 degree sphere cone, blended-wing body, and shuttle-like geometries are presented. It is shown that the algorithm accurately predicts heating rates, and when compared with the single grid algorithm computes solutions in one-third the computational time.

Greene, Francis A.↗

NASA NTRS1993

A fast recursive algorithm for molecular dynamics simulation

The present recursive algorithm for solving molecular systems' dynamical equations of motion employs internal variable models that reduce such simulations' computation time by an order of magnitude, relative to Cartesian models. Extensive use is made of spatial operator methods recently developed for analysis and simulation of the dynamics of multibody systems. A factor-of-450 speedup over the conventional O(N-cubed) algorithm is demonstrated for the case of a polypeptide molecule with 400 residues.

Jain, A.↗

NASA NTRS1993

Aerodynamic shape optimization using preconditioned conjugate gradient methods

In an effort to further improve upon the latest advancements made in aerodynamic shape optimization procedures, a systematic study is performed to examine several current solution methodologies as applied to various aspects of the optimization procedure. It is demonstrated that preconditioned conjugate gradient-like methodologies dramatically decrease the computational efforts required for such procedures. The design problem investigated is the shape optimization of the upper and lower surfaces of an initially symmetric (NACA-012) airfoil in inviscid transonic flow and at zero degree angle-of-attack. The complete surface shape is represented using a Bezier-Bernstein polynomial. The present optimization method then automatically obtains supercritical airfoil shapes over a variety of freestream Mach numbers. Furthermore, the best optimization strategy examined resulted in a factor of 8 decrease in computational time as well as a factor of 4 decrease in memory over the most efficient strategies in current use.

Burgreen, Greg W.↗

NASA NTRS1993

The optical counterpart of the bright nearby millisecond pulsar PSR J0437-4715

Optical imaging of the field of PSR J0437-4715 reveals a candidate optical counterpart less than 1 arcsec from the radio source location. The color and magnitude of this star are consistent with a 0.2-solar mass helium white dwarf with T(eff) about 4400 K at a distance of 150 parsecs. Such an object is expected as the binary companion of the neutron star, given the orbital characteristics determined from the radio observations. The cooling time for the white dwarf is greater than the characteristic spin-down age of the pulsar, which suggests that, in some cases, spin-down times computed from pulsar periods and period derivatives may not in fact represent an upper limit to the pulsar age. No luminosity variations over the orbital period are observed, down to a limit of a few tenths of a magnitude.

Bailyn, Charles D.↗

NASA NTRS1992

Application of a neural network to simulate analysis in an optimization process

A new experimental software package called NETS/PROSSS aimed at reducing the computing time required to solve a complex design problem is described. The software combines a neural network for simulating the analysis program with an optimization program. The neural network is applied to approximate results of a finite element analysis program to quickly obtain a near-optimal solution. Results of the NETS/PROSSS optimization process can also be used as an initial design in a normal optimization process and make it possible to converge to an optimum solution with significantly fewer iterations.

Rogers, James L.↗

NASA NTRS1993

Light scattering by size-shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength

Rigorously light scattering by size-shape distributions of randomly oriented axially symmetric particles are calculated by the T-matrix method, as extended to randomly oriented scatterers. The computational scheme is described along with a newly developed convergence procedure that makes it possible to substantially reduce computer time and storage requirements. The elements of the Stokes scattering matrix for a power-law size distribution of randomly oriented moderately aspherical spheroids are shown to be much smoother than and differ substantially from those of equivalent monodisperse spheroids; averaging over orientations does not eliminate the necessity of averaging over particle sizes. The angular-scattering behavior of the ensembles of nonspherical particles is found to be significantly different from that of the equivalent polydisperse spheres.

Mishchenko, Michael I.↗

NASA NTRS1989

Experiment and simulation for CSI: What are the missing links?

Viewgraphs on experiment and simulation for control structure interaction (CSI) are presented. Topics covered include: control structure interaction; typical control/structure interaction system; CSI problem classification; actuator/sensor models; modeling uncertainty; noise models; real-time computations; and discrete versus continuous.

Belvin, W. Keith↗

NASA NTRS1994

Anticipatory Neurofuzzy Control

Technique of feedback control, called "anticipatory neurofuzzy control," developed for use in controlling flexible structures and other dynamic systems for which mathematical models of dynamics poorly known or unknown. Superior ability to act during operation to compensate for, and adapt to, errors in mathematical model of dynamics, changes in dynamics, and noise. Also offers advantage of reduced computing time. Hybrid of two older fuzzy-logic control techniques: standard fuzzy control and predictive fuzzy control.

Mccullough, Claire L.↗

NASA NTRS1990

Random search optimization based on genetic algorithm and discriminant function

The general problem of optimization with arbitrary merit and constraint functions, which could be convex, concave, monotonic, or non-monotonic, is treated using stochastic methods. To improve the efficiency of the random search methods, a genetic algorithm for the search phase and a discriminant function for the constraint-control phase were utilized. The validity of the technique is demonstrated by comparing the results to published test problem results. Numerical experimentation indicated that for cases where a quick near optimum solution is desired, a general, user-friendly optimization code can be developed without serious penalties in both total computer time and accuracy.

Kiciman, M. O.↗

NASA NTRS1993

The effects of orbital and climatic variations on Martian surface heat flow

Large changes in the orbital elements of Mars on timescales of 10(exp 4) to 10(exp 6) years will cause widely varying climate, specifically surface temperatures, as a result of varying insolation. These surface temperature oscillations will produce subsurface thermal gradients which contribute to the total surface heat flux. We investigate the thermal behavior of the Martian regolith on orbital timescales and show that this climatological surface heat flux is spatially variable and contributes significantly to the total surface heat flux at many locations. We model the thermal behavior of the Martian regolith by calculating the mean annual surface temperatures for each epoch (spaced 1000 years apart to resolve orbital variations) for the past 200,000 years at a chosen location on the surface. These temperatures are used as a boundary condition for the deeper regolith and subsurface temperature oscillation are then computed. The surface climatological heat flux due to past climate changes can then be found from the temperature gradient between the surface and about 150 m depth (a fraction of the thermal skin depth on these timescales). This method provides a fairly accurate determination of the climatological heat flow component at a point; however, this method is computationally time consuming and cannot be applied to all points on the globe. To map the spatial variations in the surface heat flow we recognize that the subsurface temperature structure will be largely dominated by the most recent surface temperature oscillations. In fact, the climate component of the surface heat flow will be approximately proportional to the magnitude of the most recent surface temperature change. By calculating surface temperatures at all points globally for the present epoch and an appropriate past epoch, and combining these results with a series of more precise calculations described above, we estimate the global distribution of climatological surface heat flow.

Mellon, Michael T.↗

NASA NTRS1993

Thin-layer and full Navier-Stokes calculations for turbulent supersonic flow over a cone at an angle of attack

The proper use of a computational fluid dynamics code requires a good understanding of the particular code being applied. In this report the application of CFL3D, a thin-layer Navier-Stokes code, is compared with the results obtained from PARC3D, a full Navier-Stokes code. In order to gain an understanding of the use of this code, a simple problem was chosen in which several key features of the code could be exercised. The problem chosen is a cone in supersonic flow at an angle of attack. The issues of grid resolution, grid blocking, and multigridding with CFL3D are explored. The use of multigridding resulted in a significant reduction in the computational time required to solve the problem. Solutions obtained are compared with the results using the full Navier-Stokes equations solver PARC3D. The results obtained with the CFL3D code compared well with the PARC3D solutions.

Smith, Crawford F.↗

NASA NTRS1993

Linear and nonlinear PSE for compressible boundary layers

Compressible stability of growing boundary layers is studied by numerically solving the partial differential equations under a parabolizing approximation. The resulting parabolized stability equations (PSE) account for nonparallel as well as nonlinear effects. Evolution of disturbances in compressible flat-plate boundary layers are studied for freestream Mach numbers ranging from 0 to 4.5. Results indicate that the effect of boundary-layer growth is important for linear disturbances. Nonlinear calculations are performed for various Mach numbers. Two-dimensional nonlinear results using the PSE approach agree well with those from direct numerical simulations using the full Navier-Stokes equations while the required computational time is less by an order of magnitude. Spatial simulation using PSE were carried out for both the fundamental and subharmonic type breakdown for a Mach 1.6 boundary layer. The promising results obtained show that the PSE method is a powerful tool for studying boundary-layer instabilities and for predicting transition over a wide range of Mach numbers.

Chang, Chau-Lyan↗