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NASA NTRSDate not supplied

Shock Capturing via Limiting for High-Order Methods Including Discontinuous Galerkin

As is well-known, popular high-order methods such as discontinuous Galerkin (DG) and flux reconstruction (FR) tend to generate oscillations near shocks and discontinuities, which can lead to negative pressure or density, ultimately causing code breakdown. For standard second-order methods, one approach to mitigating oscillations is to impose constraints on the calculated slopes, ensuring they do not become excessively steep. This limiting process is rooted in the idea of preserving monotonicity introduced by Van Leer (1974): when the data are monotone, limiting the slopes result in a monotone piecewise linear solution. However, a drawback of this approach is the loss of accuracy near extrema, where the non-monotone solution is somewhat flattened and achieves only first-order accuracy.

numerical methods↗

NASA NTRS2015

Assessing the Tangent Linear Behaviour of Common Tracer Transport Schemes and Their Use in a Linearised Atmospheric General Circulation Model

The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5). All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have nonlinear behaviour. The piecewise parabolic method (PPM) with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM) is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5.

Tangent Linear Model↗

NASA NTRS1993

Green vegetation, nonphotosynthetic vegetation, and soils in AVIRIS data

The problem of distinguishing between green vegetation, nonphotosynthetic vegetation (NPV, such as dry grass, leaf litter, and woody material), and soils in imaging-spectrometer data is addressed by analyzing an image taken by the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) over the Jasper Ridge Biological Preserve (California) on September 20, 1989, using spectral mixture analysis. Over 98 percent of the spectral variation could be explained by linear mixtures of three endmembers, green vegetation, shade, and soil. NPV, which could not be distinguished from soil when included as an endmember, was discriminated by residual spectra that contained cellulose and lignin absorptions. Distinct communities of green vegetation were distinguished by (1) nonlinear mixing effect caused by transmission and scattering by green leaves, (2) variations in a derived canopy-shade spectrum, and (3) the fraction of NPV.

Roberts, D. A.↗

NASA NTRSDate not supplied

A New Approach for a Wider Class of Entropy Split Methods for Compressible Gas Dynamics and MHD

The high order entropy split methods of Sjögreen & Yee [1, 2] by entropy splitting of the compressible Euler (inviscid) flux derivatives for a thermally-perfect gas are based on Harten’s entropy function [3, 4, 5]. Their derivation takes advantage of the homogeneity property of Euler flux, symmetrizable Euler flux derivatives and energy-norm stability in conjunction with high order classical spatial central, DRP (dispersion relation-preserving) [6, 7, 8] or Padé (compact) spatial discretizations [9] with summation-by-parts (SBP) operators [10]. Our entropy split methods have been proven entropy conserving and stable [1, 11, 12]. Our proofs do not rely on a two-point numerical flux, but rather only a linear difference operator is required to derive these methods. To extend the entropy split method for the MHD, we used the Godunov symmetrizable non-conservative MHD form [12, 13, 14]. These high order entropy split methods not only preserve certain physical properties of the chosen governing equations but are also known to either improve numerical stability, and/or minimize aliasing errors in long time integration of turbulent flow computations without the aid of added numerical dissipation. In our previous published work, extensive error norm comparison with grid refinement was performed to show the high accuracy performance of these methods. These studies also showed how well the entropy split methods conserve the entropy, momentum and mass, and preserve the kinetic energy for long time integration of the various flows [1, 2, 12, 13, 14]. The objective of the present work is to use a new approach to obtain a wider class of entropy split methods consisting of a two-point numerical flux portion and a non-conservative portion in such a way that the homogeneity property of the compressible Euler flux is not required. For high order classical spatial central, DRP (dispersion relation-preserving) or Padé (compact) spatial discretizations, this new approach can be proven to be entropy conservative with conservative spatial dsicretizations while at the same time allowing a wider class of symmetrizable inviscid flux derivatives. We also use this generalization to derive an entropy split scheme that is entropy conserving for the equations of MHD without the homogeneity property using the Godunov symmetrizable ideal MHD formulation [15].

High Order Physical Preserving Methods↗

NASA NTRS1976

Conservation properties of numerical integration methods for systems of ordinary differential equations

If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.

Rosenbaum, J. S.↗

NASA NTRS1993

Giant radiating dyke swarms on Earth and Venus

On Earth, giant radiating dyke swarms are usually preserved as fan-shaped fragments which have been dismembered from their original configuration by subsequent plate tectonic rifting events. Analysis of the largest fragments and consideration of their original configuration has led to the idea that many swarms are plume related, and that dyke swarms radiate away from plume centers. Magellan radar data reveal abundant intact giant radiating swarms on Venus which are similar in scale and pattern to those on Earth. The absence of intense weathering and plate tectonic processes on Venus accounts for the preservation of the primary radiating patterns. It is characteristic of both Earth and Venus that giant radiating dikes are emplaced laterally for distances of at least 2000 km away from plume centers. At distances beyond the influence of the plume on both Earth and Venus, the radiating dyke pattern is often swept into a linear pattern aligned with the regional stress field. There is tremendous potential synergism between the characterization and analysis of terrestrial dyke swarms (where significant erosion has revealed their structure and emplacement directions at depth) and the giant swarms of Venus (where the complete circumferential structure is preserved, and the surface fracture systems above near surface dikes and the nature of the central source regions are revealed). In this study, we report on the characteristics of radial dyke swarms on Earth and Venus and draw some preliminary comparisons from the two perspectives. In summary, on both planets there is evidence for plume-related magmatic centers associated with vertical and lateral injection of magma over considerable distances (up to at least 2000 km). The abundance of very broadly radiating swarms on Venus supports the notion that the swarms on Earth were radiating over broad sectors at the time of intrusion but were dissected by later events. The Venus data show that a swarm can change from radiating (proximal) to regional (distal) subparallel orientations. An implication for Earth is that many regional linear swarms which do not have a radiating pattern may be due to fragmentation of the swarm during later plate tectonic rifting. Completion of the global classification and census of Venus features, comparison to the terrestrial synthesis, and documentation of the mode of emplacement of dikes in these environments (buffered and unbuffered conditions) should lead to additional general insight into mechanisms of formation and evolution and their relation to plumes.

Ernst, Richard E.↗

NASA NTRS2007

Alfven Waves and Turbulence in the Solar Atmosphere and Solar Wind

We solve the problem of propagation and dissipation of Alfvenic turbulence in a model solar atmosphere consisting of a static photosphere and chromosphere, transition region, and open corona and solar wind using a phenomenological model for the turbulent dissipation based on wave reflection. We show that most of the dissipation for a given wave frequency spectrum occurs in the lower corona, and the overall rms amplitude of the fluctuations evolves in a way consistent with observations. The frequency spectrum for a Kolmogorov-like slope is not found to change dramatically from the photosphere to the solar wind; however, it does preserve signatures of transmission throughout the lower atmospheric layers, namely, oscillations in the spectrum at high frequencies reminiscent of the resonances found in the linear case. These may disappear once more realistic couplings for the nonlinear terms are introduced or if time-dependent variability of the lower atmospheric layer is introduced.

turbulence↗

NASA NTRS2020

Searching for Evidence of Life in Deep Time and Space

Cyanobacterial mats provide insights into ancient benthic microbial communities and their biosignatures. Thick mats occupy hypersaline saltern ponds at Guerrero Negro, Baja California, Mexico. Mat biota maintains rapid rates of biogeochemical processes under steep and rapidly changing environmental gradients. Cycling of C, O, and S all increased identically with temperature, indicating the tight coupling of these cycles. An enormous microbial diversity exhibits a highly structured spatial distribution of populations. Combined universal clone libraries from all mat layers indicated Bacteria/Archaea/Eukarya ratios of 57:7:1. More than 10,000 unique bacterial sequences were present. The relative abundance of Archaea increased with depth - below 10 cm, solvent-extractable archaeal lipids were twice as abundant as bacterial lipids. Only 15 species of Eukarya were found among 890 clones analyzed. Degradation of the mats’ insoluble macromolecular organic fraction (IMOM) by hydropyrolysis released a complex variety of linear, branched and polycyclic alkane structures, e.g., hopanes, methylhopanes and steranes. Covalent binding of these biosignatures into IMOM aids their long-term geological preservation. Mars rover missions revealed evidence of long-lived fluvial lacustrine systems and organics in associated mudstones. NASA’s Mars 2020 rover mission will examine sediments in Jezero crater, including a delta and shoreline carbonate deposits, environments that on Earth have sustained microbial mats.

Des Marais, David J.↗

NASA NTRS1986

Feedback maximization

Consideration is given to synthesis methods for feedback systems with nonlinear dynamic compensation, which permits increased feedback while preserving robustness, global stability, good transient responses, and stability of the output processes. Material needed for the realization of design goals from the areas of linear systems, nonlinear oscillation, and stability of nonlinear systems is covered. The three main parts of the book are: (1) linear feedback systems, (2) nonlinear feedback system analysis, and (3) synthesis methods for globally stable Nyquist-stable feedback systems with increased feedback.

Lurie, B. J.↗

NASA NTRS1997

Algorithmic Extensions of Low-Dispersion Scheme and Modeling Effects for Acoustic Wave Simulation

Accurate computation of acoustic wave propagation may be more efficiently performed when their dispersion relations are considered. Consequently, computational algorithms which attempt to preserve these relations have been gaining popularity in recent years. In the present paper, the extensions to one such scheme are discussed. By solving the linearized, 2-D Euler and Navier-Stokes equations with such a method for the acoustic wave propagation, several issues were investigated. Among them were higher-order accuracy, choice of boundary conditions and differencing stencils, effects of viscosity, low-storage time integration, generalized curvilinear coordinates, periodic series, their reflections and interference patterns from a flat wall and scattering from a circular cylinder. The results were found to be promising en route to the aeroacoustic simulations of realistic engineering problems.

Kaushik, Dinesh K.↗

NASA NTRS1979

An accurate method for two-point boundary value problems

A second-order method for solving two-point boundary value problems on a uniform mesh is presented where the local truncation error is obtained for use with the deferred correction process. In this simple finite difference method the tridiagonal nature of the classical method is preserved but the magnitude of each term in the truncation error is reduced by a factor of two. The method is applied to a number of linear and nonlinear problems and it is shown to produce more accurate results than either the classical method or the technique proposed by Keller (1969).

Walker, J. D. A.↗

NASA NTRS2020

Ancient Martian aeolian sand dune deposits recorded in the stratigraphy of Valles Marineris and implications for past climates

Aeolian sediment transport, deposition, and erosion have been ongoing throughout Mars’ history. This record of widespread aeolian processes is preserved in landforms and geologic units that retain important clues about past environmental conditions including wind patterns. In this study we describe landforms within Melas Chasma, Valles Marineris, that occur in distinct groups with linear to crescentic shapes, arranged with a characteristic wavelength; some possess slope profiles analogous to modern sand dunes, yet show evidence for lithification. Based on the features’ dimensions, asymmetry, and spatial patterns relative to modern equivalents, we interpret these landforms to be two classes of aeolian bedforms: decameter-scale mega-ripples and sand dunes. The presence of superposed erosional features and depositional units indicates these landforms were cemented and likely ancient. Melas paleo-dunes are found atop Hesperian-aged layered deposits, but we estimate them to be younger, likely lithified in the Amazonian period. Although a range of degradation was observed, some paleo-dunes are >10 m tall and maintain steep lee sides (>25°), an uncommon scenario for terrestrial examples as other geologic processes lead to dune obliteration. The preserved paleo-bedform geometries are largely consistent with those of modern aeolian indicators, suggesting no major shifts in wind regime or contributing boundary conditions. Finally, we propose their appearance and context require sequential periods of dune migration, stabilization following catastrophic burial, cementation, differential erosion, exposure, and burial. The presence of wholly preserved duneforms appears to be more common on Mars compared to the Earth and may signal something important about Martian landscape evolution. Plain Language Summary Wind-driven sand dunes are common on modern Mars and the presence of certain sedimentary rock layers indicates these landforms occurred there in the past. Here, we explore features in the canyons of Valles Marineris which show characteristics frequently attributed to dunes, yet evidence for their lithification and burial is clear. Their horizontal extent, height, shape, slopes, and collective spatial patterns led to our interpretation of them as lithified dune fields. The heavily eroded appearance along with superposed elements such as craters and boulders led to the conclusion that these are relatively ancient landforms. Despite this erosion This level of preservation is rare for terrestrial sand dunes due to erosion and tectonics, thus providing an opportunity to reconstruct the various factors contributing to their history. Understanding the circumstances that led to the preservation of these ancient duneforms will yield crucial information regarding planetary sedimentary processes and the geologic history of the region.

Matthew Chojnacki↗

NASA NTRS2014

Performance of the Linear Ion Trap Mass Spectrometer for the Mars Organic Molecule Analyzer (MOMA) Investigation on the 2018 Exomars Rover

The 2018 ExoMars rover mission includes the Mars Organic Molecule Analyzer (MOMA) investigation. MOMA will examine the chemical composition of samples acquired from depths of up to two meters below the martian surface, where organics may be protected from degradation derived from cosmic radiation and/or oxidative chemical reactions. When combined with the complement of instruments in the rover's Pasteur Payload, MOMA has the potential to reveal the presence of a wide range of organics preserved in a variety of mineralogical environments, and to begin to understand the structural character and potential origin of those compounds. The MOMA investigation is led by the Max Planck Institute for Solar System Research (MPS) with the mass spectrometer subsystem provided by NASA GSFC. MOMA's linear ion trap mass spectrometer (ITMS) is designed to analyze molecular composition of: (i) gas evolved from pyrolyzed powder samples and separated in a gas chromatograph; and, (ii) ions directly desorbed from crushed solid samples at Mars ambient pressure, as enabled by a pulsed UV laser system, fast-actuating aperture valve and capillary ion inlet. Breadboard ITMS and associated electronics have been advanced to high end-to-end fidelity in preparation for flight hardware delivery to Germany in 2015.

linear ion trap mass spectrometer↗

NASA NTRS1993

Linearization of Attitude-Control Error Dynamics

Direction cosines and quaternions are useful for representing rigid-body attitude because they exhibit no kinematic singularities. Each utilizes more variables than the minimum three degrees of freedom required to specify attitude. Therefore, application of a nonlinear inversion procedure to either formulation introduces singularities. Furthermore, in designing an attitude-control system, it is not appropriate to express attitude error as a difference of direction cosines (or quaternions). One should employ a measure of attitude error that not only is minimal but preserves orthogonal rotation properties as well. This note applies an inversion procedure to an appropriate measure of attitude error, so that the singularity occurs when the error reaches +/- 180 deg. This approach leads to the realization of a new model-follower attitude-control system that exhibits exact linear attitude-error dynamics.

Bach, Ralph↗

NASA NTRS2001

Advanced Aerodynamic Design of Passive Porosity Control Effectors

This paper describes aerodynamic design work aimed at developing a passive porosity control effector system for a generic tailless fighter aircraft. As part of this work, a computational design tool was developed and used to layout passive porosity effector systems for longitudinal and lateral-directional control at a low-speed, high angle of attack condition. Aerodynamic analysis was conducted using the NASA Langley computational fluid dynamics code USM3D, in conjunction with a newly formulated surface boundary condition for passive porosity. Results indicate that passive porosity effectors can provide maneuver control increments that equal and exceed those of conventional aerodynamic effectors for low-speed, high-alpha flight, with control levels that are a linear function of porous area. This work demonstrates the tremendous potential of passive porosity to yield simple control effector systems that have no external moving parts and will preserve an aircraft's fixed outer mold line.

Hunter, Craig A.↗

NASA NTRS2003

Aeroelastic System Development Using Proper Orthogonal Decomposition and Volterra Theory

This research combines Volterra theory and proper orthogonal decomposition (POD) into a hybrid methodology for reduced-order modeling of aeroelastic systems. The out-come of the method is a set of linear ordinary differential equations (ODEs) describing the modal amplitudes associated with both the structural modes and the POD basis functions for the uid. For this research, the structural modes are sine waves of varying frequency, and the Volterra-POD approach is applied to the fluid dynamics equations. The structural modes are treated as forcing terms which are impulsed as part of the uid model realization. Using this approach, structural and uid operators are coupled into a single aeroelastic operator. This coupling converts a free boundary uid problem into an initial value problem, while preserving the parameter (or parameters) of interest for sensitivity analysis. The approach is applied to an elastic panel in supersonic cross ow. The hybrid Volterra-POD approach provides a low-order uid model in state-space form. The linear uid model is tightly coupled with a nonlinear panel model using an implicit integration scheme. The resulting aeroelastic model provides correct limit-cycle oscillation prediction over a wide range of panel dynamic pressure values. Time integration of the reduced-order aeroelastic model is four orders of magnitude faster than the high-order solution procedure developed for this research using traditional uid and structural solvers.

Lucia, David J.↗

NASA NTRS1997

Quantification of urinary uric acid in the presence of thymol and thimerosal by high-performance liquid chromatography

A high-performance liquid chromatographic method was developed as an alternative to automated enzymatic analysis of uric acid in human urine preserved with thymol and/or thimerosal. Uric acid (tR = 10 min) and creatinine (tR = 5 min) were separated and quantified during isocratic elution (0.025 M acetate buffer, pH 4.5) from a mu Bondapak C18 column. The uric-acid peak was identified chemically by incubating urine samples with uricase. The thymol/thimerosal peak appeared at 31 min during the washing step and did not interfere with the analysis. We validated the high-performance liquid chromatographic method for linearity, precision and accuracy, and the results were found to be excellent.

NASA Discipline Regulatory Physiology↗

NASA NTRS1992

An IIR median hybrid filter

A new class of nonlinear filters, the so-called class of multidirectional infinite impulse response median hybrid filters, is presented and analyzed. The input signal is processed twice using a linear shift-invariant infinite impulse response filtering module: once with normal causality and a second time with inverted causality. The final output of the MIMH filter is the median of the two-directional outputs and the original input signal. Thus, the MIMH filter is a concatenation of linear filtering and nonlinear filtering (a median filtering module). Because of this unique scheme, the MIMH filter possesses many desirable properties which are both proven and analyzed (including impulse removal, step preservation, and noise suppression). A comparison to other existing median type filters is also provided.

Bauer, Peter H.↗