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NASA NTRS1992

Numerical simulation of conservation laws

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially from the well established methods, i.e., finite difference, finite volume, finite element and spectral methods, in both concept and methodology. The key features of the current scheme include: (1) direct discretization of the integral forms of conservation laws, (2) treating space and time on the same footing, (3) flux conservation in space and time, and (4) unified treatment of the convection and diffusion fluxes. The model equation considered in the initial study is the standard one dimensional unsteady constant-coefficient convection-diffusion equation. In a stability study, it is shown that the principal and spurious amplification factors of the current scheme, respectively, are structurally similar to those of the leapfrog/DuFort-Frankel scheme. As a result, the current scheme has no numerical diffusion in the special case of pure convection and is unconditionally stable in the special case of pure diffusion. Assuming smooth initial data, it will be shown theoretically and numerically that, by using an easily determined optimal time step, the accuracy of the current scheme may reach a level which is several orders of magnitude higher than that of the MacCormack scheme, with virtually identical operation count.

Chang, Sin-Chung↗

NASA NTRS1991

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I - The dynamics of time discretization and its implications for algorithm development in computational fluid dynamics

Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

Yee, H. C.↗

NASA NTRS1992

Low Mach number two-dimensional hydrodynamic turbulence - Energy budgets and density fluctuations in a polytropic fluid

Theory suggests that three distinct types of turbulence can occur in the low Mach number limit of polytropic flow: nearly incompressible flows dominated by vorticity, nearly pure acoustic turbulence dominated by compression, and flows characterized by near statistical equipartition of vorticity and compressions. Distinctions between these kinds of turbulence are investigated here by direct numerical simulation of two-dimensional compressible hydrodynamic turbulence. Dynamical scalings of density fluctuations, examination of the ratio of transverse to longitudinal velocity fluctuations, and spectral decomposition of the fluctuations are employed to distinguish the nature of these low Mach number solutions. A strong dependence on the initial data is observed, as well as a tendency for enhanced effects of compressibility at later times and at higher wave numbers, as suggested by theories of nearly incompressible flows.

Ghosh, S.↗

NASA NTRS1991

Nonlinear symmetric instability and intraseasonal oscillations in the tropical atmosphere

Symmetric inertial instability (SII) is studied as a mechanism for stratospheric and tropospheric phenomena in the equatorial regions. The linear and nonlinear dynamics of SII in a two-layer, zonally symmetric model on an equatorial beta plane, in the presence of a basic flow with horizontal and vertical shear, with and without dissipative effects are investigated. Linear symmetric instabilities are, in accordance with previously published results, purely exponential, that is, nonoscillatory. Nonlinear SII, studied here for the first time on a planetary scale, can produce finite-amplitude oscillatory behavior, periodic or chaotic. The period of oscillations in the inviscid case depends on the initial data. In the presence of dissipative effects, all solutions tend to a limit cycle or to a strange attractor. The dominant period in this case, over a wide range of parameters and whether vertical shear is present or not, is in the intraseasonal, 20-30-day range. It appears therefore that nonlinear SII might be a contributing mechanism to low-frequency oscillations in the tropical atmosphere.

Zhao, J.-X.↗

NASA NTRS1992

A regularization method for extrapolation of solar potential magnetic fields

The mathematical basis of a Tikhonov regularization method for extrapolating the chromospheric-coronal magnetic field using photospheric vector magnetograms is discussed. The basic techniques show that the Cauchy initial value problem can be formulated for potential magnetic fields. The potential field analysis considers a set of linear, elliptic partial differential equations. It is found that, by introducing an appropriate smoothing of the initial data of the Cauchy potential problem, an approximate Fourier integral solution is found, and an upper bound to the error in the solution is derived. This specific regularization technique, which is a function of magnetograph measurement sensitivities, provides a method to extrapolate the potential magnetic field above an active region into the chromosphere and low corona.

Gary, G. A.↗

NASA NTRS1992

Z306 molecular contamination ad hoc committee results

LDEF external surfaces which did not receive significant amounts of atomic oxygen were observed to be coated with a brown contamination, apparently the result of a condensed organic residue darkened due to UV radiation exposure. During the initial Materials Special Investigation Group (MSIG) Meeting after LDEF deintegration, held in Seattle - July 1990, this organic contamination was the subject of much discussion. The amount of contamination was thought to be significant and its source was immediately believed to be the Z306 black thermal control coating used to coat the entire inner surface of LDEF. Due to the size of the structure, it was not feasible to bake-out the coating. However, initial data on the contamination film was confusing in that significant amounts of silicon was observed by several different researchers. Silicon (from silicone) was not expected to be a potential outgassing product of the Z306 polyurethane coating. To investigate the connection between external contamination and the interior paint, a MSIG ad hoc committee was formed.

Golden, Johnny L.↗

NASA NTRS1992

Materials surface contamination analysis

The original research objective was to demonstrate the ability of optical fiber spectrometry to determine contamination levels on solid rocket motor cases in order to identify surface conditions which may result in poor bonds during production. The capability of using the spectral features to identify contaminants with other sensors which might only indicate a potential contamination level provides a real enhancement to current inspection systems such as Optical Stimulated Electron Emission (OSEE). The optical fiber probe can easily fit into the same scanning fixtures as the OSEE. The initial data obtained using the Guided Wave Model 260 spectrophotometer was primarily focused on determining spectra of potential contaminants such as HD2 grease, silicones, etc. However, once we began taking data and applying multivariate analysis techniques, using a program that can handle very large data sets, i.e., Unscrambler 2, it became apparent that the techniques also might provide a nice scientific tool for determining oxidation and chemisorption rates under controlled conditions. As the ultimate power of the technique became recognized, considering that the chemical system which was most frequently studied in this work is water + D6AC steel, we became very interested in trying the spectroscopic techniques to solve a broad range of problems. The complexity of the observed spectra for the D6AC + water system is due to overlaps between the water peaks, the resulting chemisorbed species, and products of reaction which also contain OH stretching bands. Unscrambling these spectral features, without knowledge of the specific species involved, has proven to be a formidable task.

Workman, Gary L.↗

NASA NTRS1992

Investigation of passive atmospheric sounding using millimeter and submillimeter wavelength channels

Activities within the period from January 1, 1992 through June 30, 1992 by Georgia Tech researchers in millimeter and submillimeter wavelength tropospheric remote sensing have been centered around the integration and initial data flights of the MIR on board the NASA ER-2. Georgia Tech contributions during this period include completion of the MIR flight software and implementation of a 'quick-view' graphics program for ground based calibration and analysis of the MIR imagery. In the current configuration, the MIR has channels at 90, 150, 183 +/- 1,3,7, and 220 GHz. Provisions for three additional channels at 325 +/-1,3 and 9 GHZ have been made, and a 325-GHz receiver is currently being built by the ZAX Millimeter Wave Corporation for use in the MIR. The combination of the millimeter wave and submillimeter wave channels aboard a single well-calibrated instrument will provide the necessary aircraft radiometric data for radiative transfer and cloud and water vapor retrieval studies. A paper by the PI discussing the potential benefits of passive millimeter and submillimeter wave observations for cloud, water vapor and precipitation measurements has recently been accepted for publication (Gasiewski, 1992), and is included as Appendix A. The MIR instrument is a joint project between NASA/GSFC and Georgia Tech. Other Georgia Tech contributions to the MIR and its related scientific uses have included basic system design studies, performance analyses, and circuit and radiometric load design.

Gasiewski, Albin J.↗

NASA NTRS1993

Remote surface inspection system

This paper reports on an on-going research and development effort in remote surface inspection of space platforms such as the Space Station Freedom (SSF). It describes the space environment and identifies the types of damage for which to search. This paper provides an overview of the Remote Surface Inspection System that was developed to conduct proof-of-concept demonstrations and to perform experiments in a laboratory environment. Specifically, the paper describes three technology areas: (1) manipulator control for sensor placement; (2) automated non-contact inspection to detect and classify flaws; and (3) an operator interface to command the system interactively and receive raw or processed sensor data. Initial findings for the automated and human visual inspection tests are reported.

Hayati, S.↗

NASA NTRS1992

The Coronal Ultraviolet Berkeley Spectrometer (CUBS)

We describe an instrument package to remotely measure thermospheric, exospheric, and plasmaspheric structure and composition. This instrument was flown aboard the second test flight of the Black Brant XII sounding rocket on December 5, 1989, which attained an apogee of 1460 km. The experiment package consisted of a spectrophotometer to measure He I 584 A, O II 834 A, O I 989 A, hydrogen Lyman beta (1025 A), hydrogen Lyman alpha (1216 A), and O I 1304 A transitions, and a photometer to measure the He II 304 A emission. The optical design of the spectrophotometer was identical to that of the Berkeley Extreme Ultraviolet (EUV) Airglow Rocket Spectrometer payload, flown on September 30, 1988 aboard the maiden flight of the Black Brant XII rocket. We present the initial data analysis and describe directions we will go toward the completion of our study.

Bush, Brett C.↗

NASA NTRS1992

An airborne system for collecting polarization imagery

This paper describes a recently completed electrooptical camera flying onboard the NASA ER-2 high altitude aircraft. The device includes a six-position filter wheel which can be fitted with a combination of polarizing and/or spectral filters. An alternate configuration will include a polarizing filter which can be rotated to any angle under computer control. The camera mount in the nose of the ER-2 can tilt forward or aft up to 40 degrees, both for bidirectional reflectance studies and for image motion compensation (the aircraft moves 34 meters between frame acquisitions). The ground resolution is nominally 5 meters from and altitude of 20 km. Spectral responsivity is that of the silicon imaging array (Kodak KAF-1400). Initial data sets were acquired in support of the International Satellite Cloud Climatology Program Regional Experiment of November, 1991, and will be used to study cirrus cloud properties.

Hildum, Edward A.↗

NASA NTRS1993

Effective equations and the inverse cascade theory for Kolmogorov flows

We study the two-dimensional Kolmogorov flows in the limit as the forcing frequency goes to infinity. Direct numerical simulation indicates that the low frequency energy spectrum evolves to a universal kappa (exp -4) decay law. We derive effective equations governing the behavior of the large scale flow quantities. We then present numerical evidence that with smooth initial data, the solution to the effective equation develops a kappa (exp -4) type singularity at a finite time. This gives a convenient explanation for the kappa (exp -4) decay law exhibited by the original Kolmogorov flows.

Weinan, E.↗

NASA NTRS1993

Computational analysis of off-design waveriders

Comprehensive inviscid and viscous numerical simulations of hypersonic flow past nonconical rounded-nose waveriders are presented. The flow fields and aerodynamic forces at off-design conditions are determined inviscidly by a space-marching CFD code with the initial-data plane provided by a time-marching Navier-Stokes CFD code. Off-design conditions include off-design Mach numbers, angles of attack, and rounded leading edges. A wide range of waverider configurations is investigated and compared. These calculations show the effects of viscous interactions, which are influential near the leading edges, and determine the viscous drag. The inviscid calculations show that L/D decreases as freestream M increases (with alpha = 0). At the on-design Mach numbers, the maximum L/D may occur at slight positive or negative alpha, depending on the shape of the waverider, and zero lift occurs at a negative alpha approximately equal to half of the body thickness. The effects of slight leading-edge blunting produce only local effects in the flow field and small losses in L/D.

He, X.↗

NASA NTRS1993

Navier-Stokes relaxation to sinh-Poisson states at finite Reynolds numbers

A mathematical framework is proposed in which it seems possible to justify the computationally-observed relaxation of a two-dimensional Navier-Stokes fluid to a 'most probable', or maximum entropy, state. The relaxation occurs at large but finite Reynolds numbers, and involves substantial decay of higher-order ideal invariants such as enstrophy. A two-fluid formulation, involving interpenetrating positive and negative vorticity fluxes (continuous and square integrable) is developed, and is shown to be intimately related to the passive scalar decay problem. Increasing interpenetration of the two fluids corresponds to the decay of vorticity flux due to viscosity. It is demonstrated numerically that, in two dimensions, passive scalars decay rapidly, relative to mean-square vorticity (enstrophy). This observation provides a basis for assigning initial data to the two-fluid field variables.

Montgomery, David↗

NASA NTRS1993

Remote surface inspection system

Hayati, Samad↗

NASA NTRS1993

Finite difference schemes for long-time integration

Finite difference schemes for the evaluation of first and second derivatives are presented. These second order compact schemes were designed for long-time integration of evolution equations by solving a quadratic constrained minimization problem. The quadratic cost function measures the global truncation error while taking into account the initial data. The resulting schemes are applicable for integration times fourfold, or more, longer than similar previously studied schemes. A similar approach was used to obtain improved integration schemes.

Haras, Zigo↗

NASA NTRS1993

Mars Operational Environmental Satellite (MOES): A post-Mars Observer discovery mission

Mars Operational Environmental Satellite (MOES) is a Discovery concept mission that is designed to observe the global short-term weather phenomena on Mars in a systematic fashion. Even after the Mariner, Viking, and, soon, Mars Observer missions, crucial aspects of the martian atmosphere will remain unobserved systematically. Achieving a better understanding of the cycles of dust, water vapor, and ices on Mars requires detailed information about atmospheric transports of those quantities associated with the weather systems, particularly those arising in mid latitudes during fall and winter. It also requires a quantitive understanding of the processes responsible for the onset and evolution of dust storms on all scales. Whereas on Earth the system of geosynchronous and polar orbiting satellites provides continuous coverage of the weather systems, on Mars the time history of important events such as regional and global dust storms remains unobserved. To understand the transport of tracers in the martian atmosphere and particularly to identify their sources and sinks, it is necessary to have systematic global, synoptic observations that have yet to be attained. Clearly these requirements are not easy to achieve from a single spacecraft in orbit, but if we focus on specific regions of the planet, e.g., polar vs. low and mid latitudes, then it is possible to attain a nearly ideal coverage at a reasonable spatial and temporal resolution with a system of just two satellites. Mars Observer is about to yield good coverage of the polar latitudes, so we focus initially on the region not covered well in terms of diurnal coverage, and in terms of desired observations will provide the initial data for the numerical models of the martian weather and climate that can be verified only with better temporal and spatial data.

Limaye, Sanjay S.↗

NASA NTRS1994

Local reduction of certain wave operators to one-dimensional form

It is noted that certain common linear wave operators have the property that linear variation of the initial data gives rise to one-dimensional evolution in a plane defined by time and some direction in space. The analysis is given For operators arising in acoustics, electromagnetics, elastodynamics, and an abstract system.

Roe, Philip↗