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At least 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Multigrid Relaxation of a Factorizable, Conservative Discretization of the Compressible Flow Equations

The second-order factorizable discretization of the compressible Euler equations developed by Sidilkover is extended to conservation form on general curvilinear body-fitted grids. The discrete equations are solved by symmetric collective Gauss-Seidel relaxation and FAS multigrid. Solutions for flow in a channel with Mach numbers ranging from 0.0001 to a supercritical Mach number are shown, demonstrating uniform convergence rates and no loss of accuracy in the incompressible limit. A solution for the flow around the leading edge of a semi-infinite parabolic body demonstrates that the scheme maintains rapid convergence for a flow containing a stagnation point.

Roberts, Thomas W.↗
NASA NTRS2001

Analysis of Preconditioning and Relaxation Operators for the Discontinuous Galerkin Method Applied to Diffusion

The explicit stability constraint of the discontinuous Galerkin method applied to the diffusion operator decreases dramatically as the order of the method is increased. Block Jacobi and block Gauss-Seidel preconditioner operators are examined for their effectiveness at accelerating convergence. A Fourier analysis for methods of order 2 through 6 reveals that both preconditioner operators bound the eigenvalues of the discrete spatial operator. Additionally, in one dimension, the eigenvalues are grouped into two or three regions that are invariant with order of the method. Local relaxation methods are constructed that rapidly damp high frequencies for arbitrarily large time step.

Atkins, H. L.↗
NASA NTRS1994

On the Dynamics of Computing a Chemically Relaxed Nonequilibrium Flow

In order to gain insights into the strong dependence of numerical solutions on initial data for finite time steps, a set of nonlinear test problems rich enough to capture the behavior of difference schemes were recently identified and the numerical basins of attraction for these problems were computed using commonly used time discretizations in CFD. Our study revealed a wealth of surprisingly nonlinear behavior of numerical schemes that were not observed before, in particular for the implicit time discretizations that are commonly used in CFD. The goal of this work is to apply these tools to study a practical model from non-equilibrium flowfield relaxation. This type of problem arises in chemically nonequilibrium hypersonic flows such as in a shock tube experiment or an expanding nozzle. Here we consider a reacting mixture of (N2, N) for an inviscid one-dimensional steady model. Preliminary numerical results indicate that, aside from the possibility of spurious numerical solutions being introduced by the time discretizations, limitations on the model for physical or accurate solutions may also play a part in the dynamics observed.

Sweby, P. K.↗
NASA NTRS1995

Multilayer Relaxation Features on (100) and (111) Surfaces of Beta-SiC

Multilayer relaxation features were investigated for beta-SiC surfaces. Calculations include (1 x 1), (2 x 1) and c(2 x 2) phases of the (100) surface, and the (1 x 1) structure of the (111) surface. For both C- and Si-terminated surfaces, variations in the top three interlayer spacings were calculated. The largest vertical displacement was calculated for the top interlayer spacing of the (111) surface. In general, it was found that top interlayer spacings contract, while the second interlayer spacings expand moderately. The third interlayer spacings, on the other hand, were found to exhibit very small amounts of contractions. Dimerization energies and bond distances were also calculated for reconstructed phases of the (100) surface. Calculated results were compared with data from the literature.

Halicioglu, Timur↗
NASA NTRS2002

Elliptic Relaxation of a Tensor Representation for the Redistribution Terms in a Reynolds Stress Turbulence Model

A formulation to include the effects of wall proximity in a second-moment closure model that utilizes a tensor representation for the redistribution terms in the Reynolds stress equations is presented. The wall-proximity effects are modeled through an elliptic relaxation process of the tensor expansion coefficients that properly accounts for both correlation length and time scales as the wall is approached. Direct numerical simulation data and Reynolds stress solutions using a full differential approach are compared for the case of fully developed channel flow.

Carlson, J. R.↗
NASA NTRS2002

Viscosity Relaxation in Molten HgZnTe

Because of its narrow electronic band-gap, HgZnTe solid solutions have been proposed as effective detectors for infrared radiation. To produce the best single crystals of these materials for this application, knowledge of the phase diagram that governs the freezing of the liquid is essential. Besides the phase diagram, however, some information concerning the thermophysical properties of the melt, such as viscosity, density, specific heat, and enthalpy of mixing, can also be useful. Of these thermophysical properties, the viscosity is perhaps of the most interest scientifically. Measurements using the oscillating cup method have shown that the isothermal melt requires tens of hours of equilibration time before a steady value of the viscosity can be achieved. Over this equilibration time, which depends upon temperature, the viscosity can increase by as much as a factor of two before reaching a steady state. We suggest that this relaxation phenomenon may be due to a slight polymerization of Te atoms in the melt.

James K. Baird↗
NASA NTRS2002

Competing Classical and Quantum Effects in Shape Relaxation of a Metallic Island

Pb islands grown on a silicon substrate transform at room temperature from the initially flattop facet geometry into an unusual ring, shape with a volume-preserving mass transport process catalysed by the tip electrical field of a scanning tunnelling microscope. The formation of such ring shape morphology results from the competing classical and quantum effects in the shape relaxation. The latter also leads to a sequential regrowth on alternating, strips of the same facet defined by the underlying substrate steps, showing for the first time the dynamical impact of the quantum size effect on the stability of a nanostructure.

Okamoto, Rowland H.↗
NASA NTRS2002

Elliptic Relaxation of a Tensor Representation of the Pressure-Strain and Dissipation Rate

A formulation to include the effects of wall-proximity in a second moment closure model is presented that utilizes a tensor representation for the redistribution term in the Reynolds stress equations. The wall-proximity effects are modeled through an elliptic relaxation process of the tensor expansion coefficients that properly accounts for both correlation length and time scales as the wall is approached. DNS data and Reynolds stress solutions using a full differential approach at channel Reynolds number of 590 are compared to the new model.

Carlson, John R.↗
NASA NTRS2002

Effect of the Chemical State of the Surface on the Relaxation of the Surface Shell Atoms in SiC and GaN Nanocrystals

The effect of the chemical state of the surface of nanoparticles on the relaxation in the near-surface layer was examined using the concept of the apparent lattice parameter (alp) determined for different diffraction vectors Q. The apparent lattice parameter is a lattice parameter determined either from an individual Bragg reflection, or from a selected region of the diffraction pattern. At low diffraction vectors the Bragg peak positions are affected mainly by the structure of the near-surface layer, while at high Q-values only the interior of the nano-grain contributes to the diffraction pattern. Following the measurements on raw (as prepared) powders we investigated powders cleaned by annealing at 400C under vacuum, and the same powders wetted with water. Theoretical alp-Q plots showed that the structure of the surface layer depends on the sample treatment. Semi-quantitative analysis based on the comparison of the experimental and theoretical alp-Q plots was performed. Theoretical alp-Q relations were obtained from the diffraction patterns calculated for models of nanocrystals with a strained surface layer using the Debye functions.

Palosz, B.↗
NASA NTRS1999

A Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.

White, J. A.↗
NASA NTRS1999

Distributed Relaxation Multigrid and Defect Correction Applied to the Compressible Navier-Stokes Equations

The distributed-relaxation multigrid and defect- correction methods are applied to the two- dimensional compressible Navier-Stokes equations. The formulation is intended for high Reynolds number applications and several applications are made at a laminar Reynolds number of 10,000. A staggered- grid arrangement of variables is used; the coupled pressure and internal energy equations are solved together with multigrid, requiring a block 2x2 matrix solution. Textbook multigrid efficiencies are attained for incompressible and slightly compressible simulations of the boundary layer on a flat plate. Textbook efficiencies are obtained for compressible simulations up to Mach numbers of 0.7 for a viscous wake simulation.

Thomas, J. L.↗
NASA NTRS1995

MRI of bone marrow in the distal radius: in vivo precision of effective transverse relaxation times

The effective transverse relaxation time T2* is influenced by the presence of trabecular bone, and can potentially provide a measure of bone density as well as bone structure. We determined the in vivo precision of T2* in repeated bone marrow measurements. The T2* measurements of the bone marrow of the distal radius were performed twice within 2 weeks in six healthy young volunteers using a modified water-presaturated 3D Gradient-Recalled Acquisition at Steady State (GRASS) sequence with TE 7, 10, 12, 20, and 30; TR 67; flip angle (FA) 90 degrees. An axial volume covering a length of 5.6 cm in the distal radius was measured. Regions of interest (ROIs) were determined manually and consisted of the entire trabecular bone cross-section extending proximally from the radial subchondral endplate. Reproducibility of T2* and area measurements was expressed as the absolute precision error (standard deviation [SD] in ms or mm2) or as the relative precision error (SD/mean x 100, or coefficient of variation [CV] in %) between the two-point measurements. Short-term precision of T2* and area measurements varied depending on section thickness and location of the ROI in the distal radius. Absolute precision errors for T2* times were between 1.3 and 2.9 ms (relative precision errors 3.8-9.5 %) and for area measurements between 20 and 55 mm2 (relative precision errors 5.1-16.4%). This MR technique for quantitative assessment of trabecular bone density showed reasonable reproducibility in vivo and is a promising future tool for the assessment of osteoporosis.

NASA Discipline Musculoskeletal↗
NASA NTRS1997

Distributed-Memory Computing With the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA)

The Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA), a Navier-Stokes solver, has been modified for use in a parallel, distributed-memory environment using the Message-Passing Interface (MPI) standard. A standard domain decomposition strategy is used in which the computational domain is divided into subdomains with each subdomain assigned to a processor. Performance is examined on dedicated parallel machines and a network of desktop workstations. The effect of domain decomposition and frequency of boundary updates on performance and convergence is also examined for several realistic configurations and conditions typical of large-scale computational fluid dynamic analysis.

Riley, Christopher J.↗
NASA NTRS1996

Effects of H2O Vapor on Vibrational Relaxation in Expanding and Contracting Flows

As opposed to previous explanations based on the effects of anharmonicity of simple diatomic molecules, traces of water vapor are suggested to be the most likely cause of the anomalously fast vibrational relaxation of such gases observed in supersonic and hypersonic nozzles. The mechanism is the strong V-VR coupling with H2O molecules that dramatically facilitates the collisional transfer of vibrational energy. Slight moisture content is thus a real world aspect of gas dynamics that must be considered in characterizations of shock tubes, reflected shock tunnels, and expansion tubes.

Meador, Willard E.↗
NASA NTRS1996

Magnetic resonance imaging of the calcaneus: preliminary assessment of trabecular bone-dependent regional variations in marrow relaxation time compared with dual X-ray absorptiometry

RATIONALE AND OBJECTIVES: Marrow transverse relaxation time (T2*) in magnetic resonance (MR) imaging may be related to the density and structure of the surrounding trabecular network. We investigated regional variations of T2* in the human calcaneus and compared the findings with bone mineral density (BMD), as measured by dual X-ray absorpiometry (DXA). Short- and long-term precisions were evaluated first to determine whether MR imaging would be useful for the clinical assessment of disease status and progression in osteoporosis. METHODS: Gradient-recalled echo MR images of the calcaneus were acquired at 1.5 T from six volunteers. Measurements of T2* were compared with BMD and (for one volunteer) conventional radiography. RESULTS: T2* values showed significant regional variation; they typically were shortest in the superior region of the calcaneus. There was a linear correlation between MR and DXA measurements (r = .66 for 1/T2* versus BMD). Differences in T2* attributable to variations in analysis region-of-interest placement were not significant for five of the six volunteers. Sagittal MR images had short- and long-term precision errors of 4.2% and 3.3%, respectively. For DXA, the precision was 1.3% (coefficient of variation). CONCLUSION: MR imaging may be useful for trabecular bone assessment in the calcaneus. However, given the large regional variations in bone density and structure, the choice of an ROI is likely to play a major role in the accuracy, precision, and overall clinical efficacy of T2* measurements.

Non-NASA Center↗
NASA NTRS2004

Constraints on Early Mars Evolution and Dichotomy Origin from Relaxation Modeling of Dichotomy Boundary in the Ismenius Region

The Martian dichotomy is a global feature separating the northern and southern hemispheres. The 3.5 - 4 Gyr old feature is manifested by a topographic difference of 2-6 km and crustal thickness difference of approx. 15 - 30 km between the two hemispheres. In the Ismenius region, sections of the boundary are characterized by a single scarp with a slope of approx. 20 deg. - 23 deg. and are believed to be among the most well preserved parts of the dichotomy boundary. The origin of the dichotomy is unknown. Endogenic hypotheses do not predict the steep slopes (scarps) of the dichotomy boundary. Exogenic models for forming the northern lowlands by impact cratering, associate the scarps along the dichotomy boundary with craters' rims, but are not globally consistent with the topography and gravity. In order to better understand the origin of the Martian dichotomy, it is necessary to know if the steep scarps along the boundary represent the original shape of the dichotomy. Smrekar et al. presented evidence showing that the boundary scarp in Ismenius is a fault along which the highland crust was down faulted. We test whether the relaxation process could produce faulting along the dichotomy boundary and examine the crustal and mantle conditions that would allow for faulting to occur within 1 Gyr and preserve the long wavelength topography over another 3 Gyr. We approach the problem by a combination of numerical and semi-analytical modeling. We test different viscosity profiles and crustal thicknesses by comparing our modeled magnitude, location and timing of plastic strain and displacements to detailed geologic observations in the Ismenius region.

Guest, A.↗
NASA NTRS2005

Constraints on Thermal Evolution of Mars from Relaxation Models of Crustal and Topographic Dichotomy

The early thermal evolution of Mars is largely unconstrained. Models such as degree one convection [1,2,3], plate tectonics [4], and a transition to stagnant lid [5] have been proposed to explain formation of the dichotomy, the Tharsis rise, crustal production, and dynamo evolution. Here we model both the early deformation of the dichotomy and the long-term preservation as a means of examining the plausibility of a range of early thermal evolution models. Constraints include the preservation of crustal thickness and topographic differences between the northern and southern hemispheres and the geologic history of the dichotomy [6]). Our previous modeling indicates that the lower crust must have been weak enough to allow for relaxation early on, but the Martian interior had to cool fast enough to preserve the crustal difference and the associated topographic difference (~5 km) over approx. 3-3.5 Gyr [7].

Guest, A.↗