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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Hyperbolic conservation laws and numerical methods

The mathematical structure of hyperbolic systems and the scalar equation case of conservation laws are discussed. Linear, nonlinear systems and the Riemann problem for the Euler equations are also studied. The numerical methods for conservation laws are presented in a nonstandard manner which leads to large time steps generalizations and computations on irregular grids. The solution of conservation laws with stiff source terms is examined.

Leveque, Randall J.↗
NASA NTRS1991

Flux-vector splitting algorithm for chain-rule conservation-law form

A flux-vector splitting algorithm with Newton-Raphson iteration was developed for the 'full compressible' Navier-Stokes equations cast in chain-rule conservation-law form. The algorithm is intended for problems with deforming spatial domains and for problems whose governing equations cannot be cast in strong conservation-law form. The usefulness of the algorithm for such problems was demonstrated by applying it to analyze the unsteady, two- and three-dimensional flows inside one combustion chamber of a Wankel engine under nonfiring conditions. Solutions were obtained to examine the algorithm in terms of conservation error, robustness, and ability to handle complex flows on time-dependent grid systems.

Shih, T. I.-P.↗
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 NTRS1993

Conservative high-order-accurate finite-difference methods for curvilinear grids

Two fourth-order-accurate finite-difference methods for numerically solving hyperbolic systems of conservation equations on smooth curvilinear grids are presented. The first method uses the differential form of the conservation equations; the second method uses the integral form of the conservation equations. Modifications to these schemes, which are required near boundaries to maintain overall high-order accuracy, are discussed. An analysis that demonstrates the stability of the modified schemes is also provided. Modifications to one of the schemes to make it total variation diminishing (TVD) are also discussed. Results that demonstrate the high-order accuracy of both schemes are included in the paper. In particular, a Ringleb-flow computation demonstrates the high-order accuracy and the stability of the boundary and near-boundary procedures. A second computation of supersonic flow over a cylinder demonstrates the shock-capturing capability of the TVD methodology. An important contribution of this paper is the dear demonstration that higher order accuracy leads to increased computational efficiency.

Rai, Man M.↗
NASA NTRS1992

Soil conservation applications with C-band SAR

Soil conservation programs are becoming more important as the growing human population exerts greater pressure on this non-renewable resource. Indeed, soil degradation affects approximately 10 percent of Canada's agricultural land with an estimated loss of 6,000 hectares of topsoil annually from Ontario farmland alone. Soil loss not only affects agricultural productivity but also decreases water quality and can lead to siltation problems. Thus, there is a growing demand for soil conservation programs and a need to develop an effective monitoring system. Topography and soil type information can easily be handled within a geographic information system (GIS). Information about vegetative cover type and surface roughness, which both experience considerable temporal change, can be obtained from remote sensing techniques. For further development of the technology to produce an operational soil conservation monitoring system, an experiment was conducted in Oxford County, Ontario which investigated the separability of fall surface cover type using C-band Synthetic Aperture Radar (SAR) data.

Brisco, B.↗
NASA NTRS1994

An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws

This dissertation addresses various issues for model classes of hyperbolic conservation laws. The basic approach developed in this work employs a new family of adaptive, hp-version, finite element methods based on a special discontinuous Galerkin formulation for hyperbolic problems. The discontinuous Galerkin formulation admits high-order local approximations on domains of quite general geometry, while providing a natural framework for finite element approximations and for theoretical developments. The use of hp-versions of the finite element method makes possible exponentially convergent schemes with very high accuracies in certain cases; the use of adaptive hp-schemes allows h-refinement in regions of low regularity and p-enrichment to deliver high accuracy, while keeping problem sizes manageable and dramatically smaller than many conventional approaches. The use of discontinuous Galerkin methods is uncommon in applications, but the methods rest on a reasonable mathematical basis for low-order cases and has local approximation features that can be exploited to produce very efficient schemes, especially in a parallel, multiprocessor environment. The place of this work is to first and primarily focus on a model class of linear hyperbolic conservation laws for which concrete mathematical results, methodologies, error estimates, convergence criteria, and parallel adaptive strategies can be developed, and to then briefly explore some extensions to more general cases. Next, we provide preliminaries to the study and a review of some aspects of the theory of hyperbolic conservation laws. We also provide a review of relevant literature on this subject and on the numerical analysis of these types of problems.

Bey, Kim S.↗
NASA NTRS1994

Practical formulation of a positively conservative scheme

Approximate Riemann solvers have been highly successful for computing the Euler/Navier-Stokes equations, but linearized Riemann solvers are known to fail occasionally by predicting non-physical states with negative density or internal energy. Positively conservative schemes, in contrast, guarantee physical solutions from realistic input. The Harten-Lax-van Leer-Einfeldt (HLLE) scheme is a typical example of a positively conservative scheme. However, the HLLE scheme is highly dissipative at contact discontinuities and shear layers and thus it is not applicable to practicle simulations. An existing modification to the HLLE scheme, known as HLLEM, enhances the resolution to that of the Roe scheme. However, this modification violates the positivity of density and internal energy. Precise derivation of the modification yields a quatratic inequality and thus requires a case-by-case treatment. This Note describes a new, modified HLLE scheme that satisfies the positively conservative condition approximately. Sample computationa are included to demonstrate the resolution and the robustness of the scheme.

Obayashi, Shigeru↗
NASA NTRS2001

Energy Stable Flux Formulas For The Discontinuous Galerkin Discretization Of First Order Nonlinear Conservation Laws

We consider the discontinuous Galerkin (DG) finite element discretization of first order systems of conservation laws derivable as moments of the kinetic Boltzmann equation. This includes well known conservation law systems such as the Euler For the class of first order nonlinear conservation laws equipped with an entropy extension, an energy analysis of the DG method for the Cauchy initial value problem is developed. Using this DG energy analysis, several new variants of existing numerical flux functions are derived and shown to be energy stable.

Barth, Timothy↗
NASA NTRS2001

On the Conservation and Convergence to Weak Solutions of Global Schemes

In this paper we discuss the issue of conservation and convergence to weak solutions of several global schemes, including the commonly used compact schemes and spectral collocation schemes, for solving hyperbolic conservation laws. It is shown that such schemes, if convergent boundedly almost everywhere, will converge to weak solutions. The results are extensions of the classical Lax-Wendroff theorem concerning conservative schemes.

Carpenter, Mark H.↗
NASA NTRS2003

A Discrete Constraint for Entropy Conservation and Sound Waves in Cloud-Resolving Modeling

Ideal cloud-resolving models contain little-accumulative errors. When their domain is so large that synoptic large-scale circulations are accommodated, they can be used for the simulation of the interaction between convective clouds and the large-scale circulations. This paper sets up a framework for the models, using moist entropy as a prognostic variable and employing conservative numerical schemes. The models possess no accumulative errors of thermodynamic variables when they comply with a discrete constraint on entropy conservation and sound waves. Alternatively speaking, the discrete constraint is related to the correct representation of the large-scale convergence and advection of moist entropy. Since air density is involved in entropy conservation and sound waves, the challenge is how to compute sound waves efficiently under the constraint. To address the challenge, a compensation method is introduced on the basis of a reference isothermal atmosphere whose governing equations are solved analytically. Stability analysis and numerical experiments show that the method allows the models to integrate efficiently with a large time step.

Zeng, Xi-Ping↗
NASA NTRS2004

Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. A discussion on the Discontinuous Spectral Difference (SD) Method, locations of the unknowns and flux points and numerical results are also presented.

Liu, Yen↗
NASA NTRS2002

Conservation of the plastid sedimentation zone in all moss genera with known gravitropic protonemata

Moss protonemata from several species are known to be gravitropic. The characterization of additional gravitropic species would be valuable to identify conserved traits that may relate to the mechanism of gravitropism. In this study, four new species were found to have gravitropic protonemata, Fissidens adianthoides, Fissidens cristatus, Physcomitrium pyriforme, and Barbula unguiculata. Comparison of upright and inverted apical cells of P. pyriforme and Fissidens species showed clear axial sedimentation. This sedimentation is highly regulated and not solely dependent on amyloplast size. Additionally, the protonemal tip cells of these species contained broad subapical zones that displayed lateral amyloplast sedimentation. The conservation of a zone of lateral sedimentation in a total of nine gravitropic moss species from five different orders supports the idea that this sedimentation serves a specialized and conserved function in gravitropism, probably in gravity sensing.

NASA Discipline Plant Biology↗
NASA NTRS2004

The Conservation of Structure and Mechanism of Catalytic Action in a Family of Thiamin Pyrophosphate (TPP)-dependent Enzymes

Thiamin pyrophosphate (TPP)-dependent enzymes are a divergent family of TPP and metal ion binding proteins that perform a wide range of functions with the common decarboxylation steps of a -(O=)C-C(OH)- fragment of alpha-ketoacids and alpha- hydroxyaldehydes. To determine how structure and catalytic action are conserved in the context of large sequence differences existing within this family of enzymes, we have carried out an analysis of TPP-dependent enzymes of known structures. The common structure of TPP-dependent enzymes is formed at the interface of four alpha/beta domains from at least two subunits, which provide for two metal and TPP-binding sites. Residues around these catalytic sites are conserved for functional purpose, while those further away from TPP are conserved for structural reasons. Together they provide a network of contacts required for flip-flop catalytic action within TPP-dependent enzymes. Thus our analysis defines a TPP-action motif that is proposed for annotating TPP-dependent enzymes for advancing functional proteomics.

Dominiak, P.↗
NASA NTRS2000

Three Conservation Applications of Astronaut Photographs of Earth: Tidal Flat Loss (Japan), Elephant Impacts on Vegetation (Botswana), and Seagrass and Mangrove Monitoring (Australia)

NASA photographs taken from low Earth orbit can provide information relevant to conservation biology. This data source is now more accessible due to improvements in digitizing technology, Internet file transfer, and availability of image processing software. We present three examples of conservation-related projects that benefited from using orbital photographs. (1) A time series of photographs from the Space Shuttle showing wetland conversion in Japan was used as a tool for communicating about the impacts of tidal flat loss. Real-time communication with astronauts about a newsworthy event resulted in acquiring current imagery. These images and the availability of other high resolution digital images from NASA provided timely public information on the observed changes. (2) A Space Shuttle photograph of Chobe National Park in Botswana was digitally classified and analyzed to identify the locations of elephant-impacted woodland. Field validation later confirmed that areas identified on the image showed evidence of elephant impacts. (3) A summary map from intensive field surveys of seagrasses in Shoalwater Bay, Australia was used as reference data for a supervised classification of a digitized photograph taken from orbit. The classification was able to distinguish seagrasses, sediments and mangroves with accuracy approximating that in studies using other satellite remote sensing data. Orbital photographs are in the public domain and the database of nearly 400,000 photographs from the late 1960s to the present is available at a single searchable location on the Internet. These photographs can be used by conservation biologists for general information about the landscape and in quantitative applications.

Lulla, Kamlesh P.↗
NASA NTRS2015

Comprehensive Non-Destructive Conservation Documentation of Lunar Samples Using High-Resolution Image-Based 3D Reconstructions and X-Ray CT Data

Established contemporary conservation methods within the fields of Natural and Cultural Heritage encourage an interdisciplinary approach to preservation of heritage material (both tangible and intangible) that holds "Outstanding Universal Value" for our global community. NASA's lunar samples were acquired from the moon for the primary purpose of intensive scientific investigation. These samples, however, also invoke cultural significance, as evidenced by the millions of people per year that visit lunar displays in museums and heritage centers around the world. Being both scientifically and culturally significant, the lunar samples require a unique conservation approach. Government mandate dictates that NASA's Astromaterials Acquisition and Curation Office develop and maintain protocols for "documentation, preservation, preparation and distribution of samples for research, education and public outreach" for both current and future collections of astromaterials. Documentation, considered the first stage within the conservation methodology, has evolved many new techniques since curation protocols for the lunar samples were first implemented, and the development of new documentation strategies for current and future astromaterials is beneficial to keeping curation protocols up to date. We have developed and tested a comprehensive non-destructive documentation technique using high-resolution image-based 3D reconstruction and X-ray CT (XCT) data in order to create interactive 3D models of lunar samples that would ultimately be served to both researchers and the public. These data enhance preliminary scientific investigations including targeted sample requests, and also provide a new visual platform for the public to experience and interact with the lunar samples. We intend to serve these data as they are acquired on NASA's Astromaterials Acquisistion and Curation website at http://curator.jsc.nasa.gov/. Providing 3D interior and exterior documentation of astromaterial samples addresses the increasing demands for accessability to data and contemporary techniques for documentation, which can be realized for both current collections as well as future sample return missions.

Blumenfeld, E. H.↗
NASA NTRS2018

Integrating Science & Management: Florida Scrub-Jay Conservation along the Central Florida's Atlantic Coast

Florida scrub-jays are a species listed under the Endangered Species Act. The NASA Ecology program has been a partner for conservation, recovery, and translocation across the species range. The objectives of this talk are to update members of the Archie Carr Working Group recovery, conservation, and translocation activities and describe how the Archie Carr National Wildlife Refuge and nearby conservation lands relate to species recovery actions.

translocation↗
NASA NTRS2018

Violation of Field Line Conservation and Associated Spatial Scales in Particle-In-Cell Simulations and MMS Data

For the first time, space flight technology exists to detect, in situ, violation of magnetic field line conservation. The violation of magnetic line conservation on scales smaller than the system size is a necessary and sufficient condition for finite magnetic field reconnection. We demonstrate that violation of line conservation produces a detectable, structured signature both in particle-in-cell simulations of reconnection and in data from the Magnetospheric Multi-Scale mission. In particle-in-cell simulations of asymmetric reconnection, the quantity-which we call M-that identifies this violation achieves significant values in electron skin depth-scale layers that extend away from the separator, with higher values emerging on the low-density, high-magnetic-field side of the current sheet. At the separator, M owes largely to perpendicular gradients in the parallel electric field, while it attains its highest values away from the separator in dispersed, layered structures associated with gradients in the perpendicular nonideal electric field and electron transport. Sub-ion scale bipolar forms of the quantity also appear further from the separator. In two MMS burst data intervals detecting the electron diffusion region, we find that M exceeds measurement uncertainties both at the separator and near the separatrices. One interval has highly sheared reconnecting fields and the other a stronger guide field. For one event, we determine the location and scale of M and the inner electron diffusion region relative to electron outflows and the magnetic separatrices. The measure can therefore serve as a potent diagnostic for magnetic reconnection in space measurements.

Wendel, Deirdre E.↗
NASA NTRS2022

Adiabatic Evolution Due to the Conservative Scalar Self-force During Orbital Resonances

We calculate the scalar self-force experienced by a scalar point-charge orbiting a Kerr black holealongrθ-resonant geodesics. We use the self-force to calculate the averaged rate of change of thecharge’s orbital energy⟨ ̇E⟩, angular momentum⟨ ̇Lz⟩, and Carter constant⟨ ̇Q⟩, which togethercapture the leading-order adiabatic, secular evolution of the point-charge. Away from resonances,only the dissipative (time antisymmetric) components of the self-force contribute to⟨ ̇E⟩,⟨ ̇Lz⟩, and⟨ ̇Q⟩. We demonstrate, using a new numerical code, that duringrθresonances conservative (timesymmetric) scalar perturbations also contribute to⟨ ̇Q⟩and, thus, help drive the adiabatic evolutionof the orbit. Furthermore, we observe that the relative impact of these conservative contributionsto⟨ ̇Q⟩is particularly strong for eccentric 2:3 resonances. These results provide the first conclusivenumerical evidence that conservative scalar perturbations of Kerr spacetime are nonintegrable duringrθresonances.

Zachary Nasipak↗