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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

The energy decay in self-preserving isotropic turbulence revisited

The assumption of self-preservation allows for an analytical determination of the energy decay in isotropic turbulence. Here, the self-preserving isotropic decay problem is analyzed, yielding a more complete picture of self-serving isotropic turbulence. It is proven rigorously that complete self-serving isotropic turbulence admits two general types of asymptotic solutions: one where the turbulent kinetic energy K approximately t (exp -1) and one where K approximately t (sup alpha) with an exponent alpha greater than 1 that is determined explicitly by the initial conditions. By a fixed point analysis and numerical integration of the exact one-point equations, it is demonstrated that the K approximately t (exp -1) and where K approximately t (sup -alpha) with an exponent alpha greater than 1 that is determined explicitly by the initial conditions. By a fixed point analysis and numerical integration of the exact one-point equations, it is demonstrated that the K approximately t (exp -1) power law decay is the asymptotically consistent high Reynolds number solution; the K approximately 1 (sup -alpha) decay law is only achieved in the limit as t yields infinity and the turbulence Reynolds number vanishes. Arguments are provided which indicate that a K approximately t (exp -1) power law decay is the asymptotic state toward which a complete self-preserving isotropic turbulence is driven at high Reynolds numbers in order to resolve the imbalance between vortex stretching and viscous diffusion.

Speziale, Charles G.↗
NASA NTRS1993

A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations

A new numerical method is developed for the solution of the two-dimensional, steady Navier-Stokes equations. The method that is presented differs in significant ways from the established numerical methods for solving the Navier-Stokes equations. The major differences are described. First, the focus of the present method is on satisfying flux conservation in an integral formulation, rather than on simulating conservation laws in their differential form. Second, the present approach provides a unified treatment of the dependent variables and their unknown derivatives. All are treated as unknowns together to be solved for through simulating local and global flux conservation. Third, fluxes are balanced at cell interfaces without the use of interpolation or flux limiters. Fourth, flux conservation is achieved through the use of discrete regions known as conservation elements and solution elements. These elements are not the same as the standard control volumes used in the finite volume method. Fifth, the discrete approximation obtained on each solution element is a functional solution of both the integral and differential form of the Navier-Stokes equations. Finally, the method that is presented is a highly localized approach in which the coupling to nearby cells is only in one direction for each spatial coordinate, and involves only the immediately adjacent cells. A general third-order formulation for the steady, compressible Navier-Stokes equations is presented, and then a Newton's method scheme is developed for the solution of incompressible, low Reynolds number channel flow. It is shown that the Jacobian matrix is nearly block diagonal if the nonlinear system of discrete equations is arranged approximately and a proper pivoting strategy is used. Numerical results are presented for Reynolds numbers of 100, 1000, and 2000. Finally, it is shown that the present scheme can resolve the developing channel flow boundary layer using as few as six to ten cells per channel width, depending on the Reynolds number.

Scott, James R.↗
NASA NTRS1973

Approximations in the minimum time-to-climb problem

The minimum time-to-climb problem is formulated as a third order system and three approximate solutions based on reduced order systems are presented. The first of these is the often used energy state, the second is the less frequently used two state and the third is a slightly altered form of the second, herein called the modified two state. These three approximations are discussed and compared both qualitatively and, by using a numerical example, quantitatively. The numerical example is also solved by the steepest descent method to provide a basis for comparison. It is concluded that the modified two state approximation is significantly better than the other two. This approximation is used to assess the sensitivity of climb performance to various vehicle parameters and it is found that, as expected, thrust and weight influence the time-to-climb most strongly.

Ardema, M. D.↗
NASA NTRS1994

Numerical investigation of supersonic turbulent boundary layers with high wall temperature

A direct numerical approach has been developed to simulate supersonic turbulent boundary layers. The mean flow quantities are obtained by solving the parabolized Reynolds-averaged Navier-Stokes equations (globally). Fluctuating quantities are computed locally with a temporal direct numerical simulation approach, in which nonparallel effects of boundary layers are partially modeled. Preliminary numerical results obtained at the free-stream Mach numbers 3, 4.5, and 6 with hot-wall conditions are presented. Approximately 5 million grid points are used in all three cases. The numerical results indicate that compressibility effects on turbulent kinetic energy, in terms of dilatational dissipation and pressure-dilatation correlation, are small. Due to the hot-wall conditions the results show significant low Reynolds number effects and large streamwise streaks. Further simulations with a bigger computational box or a cold-wall condition are desirable.

Guo, Y.↗
NASA NTRS1996

Wavelet Sparse Approximate Inverse Preconditioners

There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm.

Chan, Tony F.↗
NASA NTRS1984

Error analysis of analytic solutions for self-excited near-symmetric rigid bodies - A numerical study

Analytic error bounds are presented for the solutions of approximate models for self-excited near-symmetric rigid bodies. The error bounds are developed for analytic solutions to Euler's equations of motion. The results are applied to obtain a simplified analytic solution for Eulerian rates and angles. The results of a sample application of the range and error bound expressions for the case of the Galileo spacecraft experiencing transverse torques demonstrate the use of the bounds in analyses of rigid body spin change maneuvers.

Kia, T.↗
NASA NTRS2006

RAISHIN: A High-Resolution Three-Dimensional General Relativistic Magnetohydrodynamics Code

We have developed a new three-dimensional general relativistic magnetohydrodynamic (GRMHD) code, RAISHIN, using a conservative, high resolution shock-capturing scheme. The numerical fluxes are calculated using the Harten, Lax, & van Leer (HLL) approximate Riemann solver scheme. The flux-interpolated, constrained transport scheme is used to maintain a divergence-free magnetic field. In order to examine the numerical accuracy and the numerical efficiency, the code uses four different reconstruction methods: piecewise linear methods with Minmod and MC slope-limiter function, convex essentially non-oscillatory (CENO) method, and piecewise parabolic method (PPM) using multistep TVD Runge-Kutta time advance methods with second and third-order time accuracy. We describe code performance on an extensive set of test problems in both special and general relativity. Our new GRMHD code has proven to be accurate in second order and has successfully passed with all tests performed, including highly relativistic and magnetized cases in both special and general relativity.

Mizuno, Yosuke↗
DOE OSTI2022

Investigation of plasmon relaxation mechanisms using nonadiabatic molecular dynamics

Hot carriers generated from the decay of plasmon excitation can be harvested to drive a wide range of physical or chemical processes. However, their generation efficiency is limited by the concomitant phonon-induced relaxation processes by which the energy in excited carriers is transformed into heat. However, simulations of dynamics of nanoscale clusters are challenging due to the computational complexity involved. Here, in this paper, we adopt our newly developed Trajectory Surface Hopping (TSH) nonadiabatic molecular dynamics algorithm to simulate plasmon relaxation in Au 20 clusters, taking the atomistic details into account. The electronic properties are treated within the Linear Response Time-Dependent Tight-binding Density Functional Theory (LR-TDDFTB) framework. The relaxation of plasmon due to coupling to phonon modes in Au 20 beyond the Born–Oppenheimer approximation is described by the TSH algorithm. The numerically efficient LR-TDDFTB method allows us to address a dense manifold of excited states to ensure the inclusion of plasmon excitation. Starting from the photoexcited plasmon states in Au 20 cluster, we find that the time constant for relaxation from plasmon excited states to the lowest excited states is about 2.7 ps, mainly resulting from a stepwise decay process caused by low-frequency phonons of the Au 20 cluster. Furthermore, our simulations show that the lifetime of the phonon-induced plasmon dephasing process is ~10.4 fs and that such a swift process can be attributed to the strong nonadiabatic effect in small clusters. Our simulations demonstrate a detailed description of the dynamic processes in nanoclusters, including plasmon excitation, hot carrier generation from plasmon excitation dephasing, and the subsequent phonon-induced relaxation process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2003

An Approximate Dissipation Function for Large Strain Rubber Thermo-Mechanical Analyses

Mechanically induced viscoelastic dissipation is difficult to compute. When the constitutive model is defined by history integrals, the formula for dissipation is a double convolution integral. Since double convolution integrals are difficult to approximate, coupled thermo-mechanical analyses of highly viscous rubber-like materials cannot be made with most commercial finite element software. In this study, we present a method to approximate the dissipation for history integral constitutive models that represent Maxwell-like materials without approximating the double convolution integral. The method requires that the total stress can be separated into elastic and viscous components, and that the relaxation form of the constitutive law is defined with a Prony series. Numerical data is provided to demonstrate the limitations of this approximate method for determining dissipation. Rubber cylinders with imbedded steel disks and with an imbedded steel ball are dynamically loaded, and the nonuniform heating within the cylinders is computed.

Johnson, Arthur R.↗
NASA NTRS2018

The Magellan Evolution of Galaxies Spectroscopic and Ultraviolet Reference Atlas (MegaSaura). II. Stacked Spectra

We stack the rest-frame ultraviolet spectra of N = 14 highly magnified gravitationally lensed galaxies at redshifts 1.6 < z < 3.6. The resulting new composite spans 900 < lambda rest < 3000 Angstrom, with a peak signal-to-noise ratio of 103 per spectral resolution element (approximately 100 km s (exp -1)). It is the highest signalto-noise ratio, highest spectral resolution composite spectrum of z approximately 2-3 galaxies yet published. The composite reveals numerous weak nebular emission lines and stellar photospheric absorption lines that can serve as new physical diagnostics, particularly at high redshift with the James Webb Space Telescope (JWST). We report equivalent widths to aid in proposing for and interpreting JWST spectra. We examine the velocity profiles of strong absorption features in the composite, and in a matched composite of z approximately 0 COS/HST galaxy spectra. We find remarkable similarity in the velocity profiles at z approximately 0 and z approximately 2, suggesting that similar physical processes control the outflows across cosmic time. While the maximum outflow velocity depends strongly on ionization potential, the absorptionweighted mean velocity does not. As such, the bulk of the high-ionization absorption traces the low-ionization gas, with an additional blueshifted absorption tail extending to at least approximately 2000 km s (exp -1). We interpret this tail as arising from the stellar wind and photospheres of massive stars. Starburst99 models are able to replicate this high-velocity absorption tail. However, these theoretical models poorly reproduce several of the photospheric absorption features, indicating that improvements are needed to match observational constraints on the massive stellar content of star-forming galaxies at z approximately 2. We publicly release our composite spectra.

Rigby, J. R.↗
DOE OSTI2022

Nuclear cusps and singularities in the nonadditive kinetic potential bifunctional from analytical inversion

The non-additive kinetic potential $v^{\text{NAD}}$ is a key quantity in density-functional theory (DFT) embedding methods, such as frozen density embedding theory and partition DFT. $v^{\text{NAD}}$ is a bi-functional of electron densities $\rho_{\rm B}$ and $\rho_{\rm tot} = \rho_{\rm A} + \rho_{\rm B}$. It can be evaluated using approximate kinetic-energy functionals, but accurate approximations are challenging. The behavior of $v^{\text{NAD}}$ in the vicinity of the nuclei has long been questioned, and singularities were seen in some approximate calculations. In this article, the existence of singularities in $v^{\text{NAD}}$ is analyzed analytically for various choices of $\rho_{\rm B}$ and $\rho_{\rm tot}$, using the nuclear cusp conditions for the density and Kohn-Sham potential. It is shown that no singularities arise from smoothly partitioned ground-state Kohn-Sham densities. We confirm this result by numerical calculations on diatomic test systems HeHe, HeLi$^+$, and H$_2$, using analytical inversion to obtain a numerically exact $v^{\rm NAD}$ for the local density approximation. We examine features of $v^{\rm NAD}$ which can be used for development and testing of approximations to $v^{\rm NAD}[\rho_{\rm B},\rho_{\rm tot}]$ and kinetic-energy functionals.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1996

Intergalactic Hydrogen Clouds at Low Redshift: Connections to Voids and Dwarf Galaxies

We provide new post-COSTAR data on one sightline (Mrk 421) and updated data from another (I Zw 1) from our Hubble Space Telescope (HST) survey of intergalactic Ly(alpha) clouds located along sightlines to four bright quasars passing through well-mapped galaxy voids (16000 km/s pathlength) and superclusters (18000 km/s). We report two more definite detections of low-redshift Ly(alpha) clouds in voids: one at 3047 km/s (heliocentric) toward Mrk 421 and a second just beyond the Local Supercluster at 2861 km/s toward I Zw 1, confirming our earlier discovery of Ly(alpha) absorption clouds in voids (Stocke et al., ApJ, 451, 24). We have now identified ten definite and one probable low-redshift neutral hydrogen absorption clouds toward four targets, a frequency of approximately one absorber every 3400 km/s above 10(exp 12.7/sq cm column density. Of these ten absorption systems, three lie within voids; the probable absorber also lies in a void. Thus, the tendency of Ly(alpha) absorbers to 'avoid the voids' is not as clear as we found previously. If the Ly(alpha) clouds are approximated as homogeneous spheres of 100 kpc radius, their masses are approximately 10(exp 9)solar mass (about 0.01 times that of bright L* galaxies) and they are 40 times more numerous, comparable to the density of dwarf galaxies and of low-mass halos in numerical CDM simulations. The Ly(alpha) clouds contribute a fraction Omega(sub cl)approximately equals 0.003/h(sub 75) to the closure density of the universe, comparable to that of luminous matter. These clouds probably require a substantial amount of nonbaryonic dark matter for gravitational binding. They may represent extended haloes of low-mass protogalaxies which have not experienced significant star formation or low-mass dwarf galaxies whose star formation ceased long ago, but blew out significant gaseous material.

Shull, J. Michael↗
NASA NTRS1972

A discrete variable approximation to minimum weight panel designs subject to a supersonic flutter-speed constraint.

A numerical technique is presented that determines the minimum-weight thickness distribution for a one-dimensional, simply supported panel subjected to a parallel supersonic flow on one side. An aeroelastic eigenvalue, which characterizes flutter speed, is held constant. The governing differential equations are approximated by sets of difference equations adjoined to the weight function via a penalty function. A conjugate gradient method then solves the resulting sequence of unconstrained minimization problems. Numerical results are obtained without imposing a minimum thickness constraint; the effect of constant inplane tensile and compressive stresses is also investigated.

Pierson, B. L.↗
DOE OSTI2021

A Butterfly-Accelerated Volume Integral Equation Solver for Broad Permittivity and Large-Scale Electromagnetic Analysis

In this work, a butterfly-accelerated volume integral equation (VIE) solver is proposed for fast and accurate electromagnetic (EM) analysis of scattering from heterogeneous objects. The proposed solver leverages the hierarchical off-diagonal butterfly (HOD-BF) scheme to construct the system matrix and obtain its approximate inverse, used as a preconditioner. Complexity analysis and numerical experiments validate the O(N log 2 N) construction cost of the HOD-BF-compressed system matrix and O(N log 1.5 N) inversion cost for the preconditioner, where N is the number of unknowns in the high-frequency EM scattering problem. For many practical scenarios, the proposed VIE solver requires less memory and computational time to construct the system matrix and obtain its approximate inverse compared to a H matrix-accelerated VIE solver. The accuracy and efficiency of the proposed solver have been demonstrated via its application to the EM analysis of large-scale canonical and real-world structures comprising of broad permittivity values and involving millions of unknowns.

42 ENGINEERING↗
NASA NTRS1973

The particle resonance in spiral galaxies - Nonlinear effects.

A theory is developed to account for the nonlinear effects, near the particle resonance, found by numerical integration. There are four equilibrium points in the rotating frame of reference: two of them unstable, at the minima of potential (L1, L2), and two stable, at the maxima of potential (L4, L5). Many particles are trapped in librating orbits around L4, L5. Using the lowest-order terms of a 'third integral' of motion near L4, L5, the behavior of the trapped orbits is determined, and the approximate theoretical results are compared with the orbits found numerically by computer. An estimate of the trapped mass is given. It amounts to about 30% of the total mass between 9 and 11 kpc when the particle resonance is at r sub s = 10 kpc and the maximum force due to the spiral is 4% of the axisymmetric force. Some effects due to these mass concentrations are found numerically and theoretically.

Contopoulos, G.↗
NASA NTRS1989

Markov reliability models for digital flight control systems

The reliability of digital flight control systems can often be accurately predicted using Markov chain models. The cost of numerical solution depends on a model's size and stiffness. Acyclic Markov models, a useful special case, are particularly amenable to efficient numerical solution. Even in the general case, instantaneous coverage approximation allows the reduction of some cyclic models to more readily solvable acyclic models. After considering the solution of single-phase models, the discussion is extended to phased-mission models. Phased-mission reliability models are classified based on the state restoration behavior that occurs between mission phases. As an economical approach for the solution of such models, the mean failure rate solution method is introduced. A numerical example is used to show the influence of fault-model parameters and interphase behavior on system unreliability.

Mcgough, John↗
DOE OSTI2023

Simplified Models of the Bicarbonate Buffer for Scaled Simulations of CO 2 Electrolyzers

Bicarbonate electrolytes are used in a range of chemical processes; however, resolved simulation of these electrolytes is difficult, as disparate reaction time scales lead to numerical stiffness and the formation of fine boundary layers. Based on several physically motivated approximations, we reduce the full set of chemical reactions within a bicarbonate electrolyte to a simpler subset, eliminating the numerical stiffness. We supported this simplification via a two-variable singular perturbation expansion and demonstrated that under neutral conditions (6 < pH < 10) typically found within a fluid-fed CO 2 electrolyzer, the simplifications lead to negligible error. Here, we also discuss two alternative simplifications, one valid at high pH and another valid at arbitrary pH. These simplifications reduce the condition number of the matrices resulting from spatiotemporal discretization by up to 10 orders of magnitude and enable three-dimensional (3D) simulation of CO 2 electrolyzers containing carbonate solutions.

10 SYNTHETIC FUELS↗