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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

On the practical use of high-order methods for hyperbolic systems

The paper tests a number of high order methods on a variety of dynamic problems in one, two, and three space dimensions. The problems covered include wave propagation phenomena as well as an asymptotic approach to a steady state. Consideration is given to both smooth and shocked flows. It is shown that the methods compared require only minor modifications of many existing second-order schemes. Further, the results show that significant gains can be expected from the use of fourth-order methods. Finally, spectral methods are also considered for some of the problems presented.

Turkel, E.↗
DOE OSTI2017

Seismic modeling with radial basis function-generated finite differences (RBF-FD) – a simplified treatment of interfaces

In a previous study of seismic modeling with radial basis function-generated finite differences (RBF-FD), we outlined a numerical method for solving 2-D wave equations in domains with material interfaces between different regions. The method was applicable on a mesh-free set of data nodes. It included all information about interfaces within the weights of the stencils (allowing the use of traditional time integrators), and was shown to solve problems of the 2-D elastic wave equation to 3rd-order accuracy. In the present paper, we discuss a refinement of that method that makes it simpler to implement. It can also improve accuracy for the case of smoothly-variable model parameter values near interfaces. We give several test cases that demonstrate the method solving 2-D elastic wave equation problems to 4th-order accuracy, even in the presence of smoothly-curved interfaces with jump discontinuities in the model parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1999

Global Geochemical Variation on the Lunar Surface: A Three-Element Approach

We present a method for displaying the relative abundances of three important elements (Th, Fe, and Ti) on the same map projection of the lunar surface. Using Th-, Fe-, and Ti-elemental abundances from orbital geochemical data and assigning each element a primary color, a false-color map of the lunar surface was created. This approach is similar to the ternary diagram approach presented by Davis and Spudis with some important differences, discussed later. For the present maps, Th abundances were measured by the Lunar Prospector (LP) Gamma-Ray Spectrometer(GRS).The new LPGRS low-altitude dataset was used in this analysis. Iron and Ti weight percentages were based on Clementine spectral reflectance data smoothed to the LP low altitude footprint. This method of presentation was designed to aid in the location and recognition of three principal lunar compositions: ferroan anorthosite (FAN), mare basalts (MB), and the Mg suite/ KREEP-rich rocks on the lunar surface, with special emphasis on the highlands and specific impact basins. In addition to the recognition of these endmember rock compositions, this method is an attempt to examine the relationship between elemental compositions that do not conform readily to previously accepted or observed endmember rocks in various specific regions of interest, including eastern highlands regions centered on 150 deg longitude, and a northern highlands Th-rich region observed. The LP low-altitude data has full width at half-maximum spatial resolution of about 40 km. The Clementine spectral reflectance datasets were adapted using an equal-area, gaussian smoothing routine to this footprint. In addition, these datasets, reported in weight percent of FeO and of Ti02, were adjusted to Fe and Ti weight percentages. Each dataset was then assigned one of the three primary colors: blue for Th, red for Fe, and green for Ti. For each element, the data range was normalized to represent the ratio of each point to the maximum in the dataset. (To view the color table, go to http://cass.jsc.nasa.gov/meetings/moon99/pdf/8033.pdf.) The full range of lunar longitudes is represented, but due to the lack of coverage of the Clementine data for latitudes > 70 deg and <-70 deg, the data for these regions is excluded. The differences between this approach and the ternary diagram approach of Davis and Spudis eliminate some of the uncertainty and ambiguity of the ternary diagram approach. Rather than using a ratio of Th to Ti normalized to CI chondritic ratios, and a ternary diagram with ternary apexes located at specific endmember compositional values, elemental compositions were used independently, eliminating the errors resulting from dividing numbers that can have high uncertainties, especially at low concentration. The three elements used in this method of presentation were chosen for several reasons. One reason for the inclusion of Th in this study is that it is an accurate indicator of KREEP. Iron and Ti concentrations are both low in highland regolith, causing any small fluctuations in Th to stand out very well. In addition, Fe and Ti are good compositional indicators of different mare basalts. Mixed with red for Fe, the green for Ti produces a yellow signal in high-Ti basalts. While universally high in Fe relative to the surrounding highlands, mare basalts have a diverse range of Ti values, making Ti concentration a valuable asset to the classification and identification of different basalt types. Finally, an important constraint in element selection is the availability of the global data, both from LP and Clementine results. Data for Th, Fe, and Ti are among the highest quality of existing lunar remote-sensing data. In addition, LP data for Fe and Ti will become available, enabling these data to be incorporated into the analysis. Using upper-limit values for end member rock compositions calculated from Korotev et al., attempts were made to locate the different endmember compositions of terranes on this diagram. Most strikingly, ferroan anorthosite (Th < and = 0.37 micro g/g; Fe (wt%)< and =2.29; Ti (wt%) < and = 0.22), which should appear as an almost black, reddish color, does not appear on the diagram at any noticeable frequency. Based on this analysis, the suggestion of extensive FAN regions on the lunar surface is not strong, especially at the presently accepted values for Fe and Th. However, to make sure this effect is not due to systematic errors, a thorough investigation of the precision, accuracy, and uncertainties of the Fe, Ti, and Th abundances needs to be carried out, especially at low concentrations. A particular region of interest is an area of high Th concentrations relative to Fe and Ti content north and east of Humboldtianum Crater. First observed by Lawrence et al., this region does not coincide with any visible impact structure and comprises one of the closest approximations to pure blue (high Th, very low Ti and Fe) on the lunar surface. Such an elemental composition does not lend itself readily to classification, and presents something of an anomaly. More detailed analysis of this region is needed to understand its structure and origin. There seems to be a longitudinal asymmetry in the Th concentrations of the highlands regolith. High-Th, low-Ti, and Fe regions are located between 135 deg and 180 deg longitude and between -30 deg and +30 deg latitude. While the Th levels are not high enough to attract attention in a single elemental display, the variation in the abundance of Th relative to Fe and Ti abundances can be clearly seen. The composition that these data suggest is not well represented in the sample return suite. In addition, these regions were largely missed by the Apollo orbital ground tracks, which only covered the outer edge of the areas of interest. The LP orbital Th data represent the first information about the Th concentrations in these regions of the highlands. Additional information contained in original.

Thomsen, D. R.↗
DOE OSTI2023

Spatially quasi-periodic bifurcations from periodic traveling water waves and a method for detecting bifurcations using signed singular values

We present a method of detecting bifurcations by locating zeros of a signed version of the smallest singular value of the Jacobian. This enables the use of quadratically convergent root-bracketing techniques or Chebyshev interpolation to locate bifurcation points. Only positive singular values have to be computed, though the method relies on the existence of an analytic or smooth singular value decomposition (SVD). The sign of the determinant of the Jacobian, computed as part of the bidiagonal reduction in the SVD algorithm, eliminates slope discontinuities at the zeros of the smallest singular value. We use the method to search for spatially quasi-periodic traveling water waves that bifurcate from large-amplitude periodic waves. The water wave equations are formulated in a conformal mapping framework to facilitate the computation of the quasi-periodic Dirichlet-Neumann operator. We find examples of pure gravity waves with zero surface tension and overhanging gravity-capillary waves. In both cases, the waves have two spatial quasi-periods whose ratio is irrational. We follow the secondary branches via numerical continuation beyond the realm of linearization about solutions on the primary branch to obtain traveling water waves that extend over the real line with no two crests or troughs of exactly the same shape. The pure gravity wave problem is of relevance to ocean waves, where capillary effects can be neglected. Such waves can only exist through secondary bifurcation as they do not persist to zero amplitude. The gravity-capillary wave problem demonstrates the effectiveness of using the signed smallest singular value as a test function for multi-parameter bifurcation problems. This test function becomes mesh independent once the mesh is fine enough.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

High order filtering methods for approximating hyberbolic systems of conservation laws

In the computation of discontinuous solutions of hyperbolic systems of conservation laws, the recently developed essentially non-oscillatory (ENO) schemes appear to be very useful. However, they are computationally costly compared to simple central difference methods. A filtering method which is developed uses simple central differencing of arbitrarily high order accuracy, except when a novel local test indicates the development of spurious oscillations. At these points, the full ENO apparatus is used, maintaining the high order of accuracy, but removing spurious oscillations. Numerical results indicate the success of the method. High order of accuracy was obtained in regions of smooth flow without spurious oscillations for a wide range of problems and a significant speed up of generally a factor of almost three over the full ENO method.

Lafon, F.↗
DOE OSTI2016

Bayesian tomography and integrated data analysis in fusion diagnostics

In this article, a Bayesian tomography method using non-stationary Gaussian process for a prior has been introduced. The Bayesian formalism allows quantities which bear uncertainty to be expressed in the probabilistic form so that the uncertainty of a final solution can be fully resolved from the confidence interval of a posterior probability. Moreover, a consistency check of that solution can be performed by checking whether the misfits between predicted and measured data are reasonably within an assumed data error. In particular, the accuracy of reconstructions is significantly improved by using the non-stationary Gaussian process that can adapt to the varying smoothness of emission distribution. The implementation of this method to a soft X-ray diagnostics on HL-2A has been used to explore relevant physics in equilibrium and MHD instability modes. This project is carried out within a large size inference framework, aiming at an integrated analysis of heterogeneous diagnostics.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

Basis adaptive sample efficient polynomial chaos (BASE-PC)

For a large class of orthogonal basis functions, there has been a recent identification of expansion methods for computing accurate, stable approximations of a quantity of interest. Here this paper presents, within the context of uncertainty quantification, a practical implementation using basis adaptation, and coherence motivated sampling, which under assumptions has satisfying guarantees. This implementation is referred to as Basis Adaptive Sample Efficient Polynomial Chaos (BASE-PC). A key component of this is the use of anisotropic polynomial order which admits evolving global bases for approximation in an efficient manner, leading to consistently stable approximation for a practical class of smooth functionals. This fully adaptive, non-intrusive method, requires no a priori information of the solution, and has satisfying theoretical guarantees of recovery. A key contribution to stability is the use of a presented correction sampling for coherence-optimal sampling in order to improve stability and accuracy within the adaptive basis scheme. Theoretically, the method may dramatically reduce the impact of dimensionality in function approximation, and numerically the method is demonstrated to perform well on problems with dimension up to 1000.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A quadratic programming flux correction method for high-order DG discretizations of S transport

In this work, we present a new flux-fixup approach for arbitrarily high-order discontinuous Galerkin (DG) discretizations of the S N transport equation, and we demonstrate the compatibility of this approach with the Variable Eddington Factor (VEF) method. The new fixup approach is sweep-compatible: during a transport sweep (block Gauss-Seidel iteration in which the scattering source is lagged), a local quadratic programming (QP) problem is solved in each spatial element to ensure that the solution satisfies certain physical constraints, including local particle balance. In this paper, we describe two choices of physical constraints, resulting in two variants of the method: QP Zero (QPZ) and QP Maximum Principle (QPMP). In QPZ, the finite element coefficients of the solution are constrained to be nonnegative. In QPMP, they are constrained to adhere to an approximate discrete maximum principle. There are two primary takeaways in this paper. First, when the positive Bernstein basis is used for DG discretization, the QPMP method eliminates negativities, preserves high-order accuracy for smooth problems, and significantly dampens unphysical oscillations in the solution. The latter feature – the dampening of unphysical oscillations – is an improvement upon standard, simpler fixup approaches such as the approach described in (denoted as the “zero and rescale” (ZR) method in this paper). This improvement comes at a moderate computational cost, but it is not prohibitive. Our results show that, even in an unrealistic worst-case scenario where 83% of the spatial elements require a fixup, the computational cost of performing a transport sweep with fixup is only ~31% greater than performing one without fixup. The second takeaway is that the VEF method can be used to accelerate the convergence of transport sweeps even when a fixup is applied. When optically thick regions are present, transport sweeps converge slowly, regardless of whether a fixup is applied, and acceleration is needed. However, attempting to apply standard diffusion synthetic acceleration (DSA) to fixed-up transport sweeps results in divergence for optically thick problems. Our results show that the same is not true for VEF. When VEF is combined with fixed-up transport sweeps, the result is a scheme that produces a nonnegative solution, converges independently of the mean free path, and, in the case of the QPMP fixup, adheres to an approximate discrete maximum principle.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Design of optimally smoothing multi-stage schemes for the Euler equations

In this paper, a method is developed for designing multi-stage schemes that give optimal damping of high-frequencies for a given spatial-differencing operator. The objective of the method is to design schemes that combine well with multi-grid acceleration. The schemes are tested on a nonlinear scalar equation, and compared to Runge-Kutta schemes with the maximum stable time-step. The optimally smoothing schemes perform better than the Runge-Kutta schemes, even on a single grid. The analysis is extended to the Euler equations in one space-dimension by use of 'characteristic time-stepping', which preconditions the equations, removing stiffness due to variations among characteristic speeds. Convergence rates independent of the number of cells in the finest grid are achieved for transonic flow with and without a shock. Characteristic time-stepping is shown to be preferable to local time-stepping, although use of the optimally damping schemes appears to enhance the performance of local time-stepping. The extension of the analysis to the two-dimensional Euler equations is hampered by the lack of a model for characteristic time-stepping in two dimensions. Some results for local time-stepping are presented.

Van Leer, Bram↗
NASA NTRS1989

Multigrid calculation of three-dimensional turbomachinery flows

Research was performed in the general area of computational aerodynamics, with particular emphasis on the development of efficient techniques for the solution of the Euler and Navier-Stokes equations for transonic flows through the complex blade passages associated with turbomachines. In particular, multigrid methods were developed, using both explicit and implicit time-stepping schemes as smoothing algorithms. The specific accomplishments of the research have included: (1) the development of an explicit multigrid method to solve the Euler equations for three-dimensional turbomachinery flows based upon the multigrid implementation of Jameson's explicit Runge-Kutta scheme (Jameson 1983); (2) the development of an implicit multigrid scheme for the three-dimensional Euler equations based upon lower-upper factorization; (3) the development of a multigrid scheme using a diagonalized alternating direction implicit (ADI) algorithm; (4) the extension of the diagonalized ADI multigrid method to solve the Euler equations of inviscid flow for three-dimensional turbomachinery flows; and also (5) the extension of the diagonalized ADI multigrid scheme to solve the Reynolds-averaged Navier-Stokes equations for two-dimensional turbomachinery flows.

Caughey, David A.↗
NASA NTRS1987

Experience in grid optimization

Two optimization methods for solving a variational problem in grid generation are described and evaluated. The smoothness, cell volumes, and orthogonality of the variational integrals are examined. The Jacobi-Newton iterative method is compared to the Fletcher-Reeves conjugate gradient method. It is observed that a combination of the Jacobi-Newton iteration and the direct solution of the variational problem produces an algorithm which is easy to program and requires less storage and computer time/iteration than the conjugate gradient method.

Mastin, C. W.↗
NASA NTRS1989

Computing Viscoplastic Behavior Of A Material

Finite-element implementation developed for Robinson's unified model of viscoplasticity. Implemented via MARC general-purpose finite-element computer program by incorporating all of nonlinearity of material into initial load vector and treating vector as pseudo body force in finite-element equilibrium equations. In technique, each finite increment split into several equal subincrements, constitutive equations integrated by explicit Euler forward-difference method. HYPELA subroutine in MARC includes adaptive integration scheme selecting optimal sizes of subincrements. Spline function smooths discontinuous boundaries in Robinson's model to facilitate finite-element numerical calculations. Method used to calculate elastic, plastic, and creep deformations in solid materials at various temperatures; also used to study thermomechanical behavior of such things as hot pressure vessels and highly stressed components in engines.

Arya, V. K.↗
NASA NTRS2001

Use of a genetic algorithm for the analysis of eye movements from the linear vestibulo-ocular reflex

It is common in vestibular and oculomotor testing to use a single-frequency (sine) or combination of frequencies [sum-of-sines (SOS)] stimulus for head or target motion. The resulting eye movements typically contain a smooth tracking component, which follows the stimulus, in which are interspersed rapid eye movements (saccades or fast phases). The parameters of the smooth tracking--the amplitude and phase of each component frequency--are of interest; many methods have been devised that attempt to identify and remove the fast eye movements from the smooth. We describe a new approach to this problem, tailored to both single-frequency and sum-of-sines stimulation of the human linear vestibulo-ocular reflex. An approximate derivative is used to identify fast movements, which are then omitted from further analysis. The remaining points form a series of smooth tracking segments. A genetic algorithm is used to fit these segments together to form a smooth (but disconnected) wave form, by iteratively removing biases due to the missing fast phases. A genetic algorithm is an iterative optimization procedure; it provides a basis for extending this approach to more complex stimulus-response situations. In the SOS case, the genetic algorithm estimates the amplitude and phase values of the component frequencies as well as removing biases.

Non-NASA Center↗
DOE OSTI2015

Colloidal nanocrystals and method of making

A tight confinement nanocrystal comprises a homogeneous center region having a first composition and a smoothly varying region having a second composition wherein a confining potential barrier monotonically increases and then monotonically decreases as the smoothly varying region extends from the surface of the homogeneous center region to an outer surface of the nanocrystal. A method of producing the nanocrystal comprises forming a first solution by combining a solvent and at most two nanocrystal precursors; heating the first solution to a nucleation temperature; adding to the first solution, a second solution having a solvent, at least one additional and different precursor to form the homogeneous center region and at most an initial portion of the smoothly varying region; and lowering the solution temperature to a growth temperature to complete growth of the smoothly varying region.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Multimodal Bayesian registration of noisy functions using Hamiltonian Monte Carlo

Functional data registration is a necessary processing step for many applications. The observed data can be inherently noisy, often due to measurement error or natural process uncertainty; which most functional alignment methods cannot handle. A pair of functions can also have multiple optimal alignment solutions, which is not addressed in current literature. In this paper, a flexible Bayesian approach to functional alignment is presented, which appropriately accounts for noise in the data without any pre-smoothing required. Additionally, by running parallel MCMC chains, the method can account for multiple optimal alignments via the multi-modal posterior distribution of the warping functions. To most efficiently sample the warping functions, the approach relies on a modification of the standard Hamiltonian Monte Carlo to be well-defined on the infinite-dimensional Hilbert space. In this work, this flexible Bayesian alignment method is applied to both simulated data and real data sets to show its efficiency in handling noisy functions and successfully accounting for multiple optimal alignments in the posterior; characterizing the uncertainty surrounding the warping functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Spanning the Gap From Bulk to Bin: A Novel Spectral Microphysics Method

Microphysics methods for climate models and numerical weather prediction typically track one, two, or three moments of a droplet size distribution for various categories of liquid, ice, and aerosol. Such methods rely on conversion parameters between these categories, which introduces uncertainty into predictions. While higher-fidelity options such as bin and Lagrangian schemes exist, they require too many degrees of freedom for climate modeling applications and introduce numerical challenges. Here we introduce a flexible spectral microphysics method based on collocation of basis functions. This method generalizes to a linear bulk scheme when using few basis functions and to a smoothed bin scheme with more degrees of freedom. Tested in an idealized box setting, the method improves spectral accuracy for droplet collision-coalescence and may eliminate the need for precipitation autoconversion rates required by bulk methods; furthermore, it generalizes well to multimodal distributions with less complexity than a bin method. The potential to extend this collocation representation to multiple hydrometeor classes suggests a path forward to unify liquid, ice, and aerosol microphysics in a single, flexible, computational framework for climate modeling.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2011

Two-Point Turbulence Closure Applied to Variable Resolution Modeling

Variable resolution methods have become frontline CFD tools, but in order to take full advantage of this promising new technology, more formal theoretical development is desirable. Two general classes of variable resolution methods can be identified: hybrid or zonal methods in which RANS and LES models are solved in different flow regions, and bridging or seamless models which interpolate smoothly between RANS and LES. This paper considers the formulation of bridging methods using methods of two-point closure theory. The fundamental problem is to derive a subgrid two-equation model. We compare and reconcile two different approaches to this goal: the Partially Integrated Transport Model, and the Partially Averaged Navier-Stokes method.

Girimaji, Sharath S.↗
DOE OSTI2025

A Smoothed Augmented Lagrangian Framework for Convex Optimization with Nonsmooth Constraints

Augmented Lagrangian (AL) methods have proven remarkably useful in solving optimization problems with complicated constraints. The last decade has seen the development of overall complexity guarantees for inexact AL variants. Yet, a crucial gap persists in addressing nonsmooth convex constraints. To this end, we present a smoothed augmented Lagrangian (AL) framework where nonsmooth terms are progressively smoothed with a smoothing parameter $\eta _k$ . The resulting AL subproblems are $\eta _k$ -smooth, allowing for leveraging accelerated schemes. By a careful selection of the inexactness level $\epsilon _k$ (for inexact subproblem resolution), the penalty parameter $\rho _k$ , and smoothing parameter $\eta _k$ at epoch k, we derive rate and complexity guarantees of $\tilde{\mathcal {O}}(1/{\varepsilon }^{3/2})$ and $\tilde{\mathcal {O}}(1/{\varepsilon })$ in convex and strongly convex regimes for computing an ${\varepsilon }$ -optimal solution, when $\rho _k$ increases at a geometric rate, a significant improvement over the best available guarantees for AL schemes for convex programs with nonsmooth constraints. Analogous guarantees are developed for settings with $\rho _k = \rho$ as well as $\eta _k = \eta$ . Preliminary numerics on a fused Lasso problem display promise.

augmented Lagrangian↗