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At least 1,081 records · Page 60
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

A Realizable Reynolds Stress Algebraic Equation Model

The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.

Shih, Tsan-Hsing↗
NASA NTRS2007

Probabilistic Analysis for Comparing Fatigue Data Based on Johnson-Weibull Parameters

Probabilistic failure analysis is essential when analysis of stress-life (S-N) curves is inconclusive in determining the relative ranking of two or more materials. In 1964, L. Johnson published a methodology for establishing the confidence that two populations of data are different. Simplified algebraic equations for confidence numbers were derived based on the original work of L. Johnson. Using the ratios of mean life, the resultant values of confidence numbers deviated less than one percent from those of Johnson. It is possible to rank the fatigue lives of different materials with a reasonable degree of statistical certainty based on combined confidence numbers. These equations were applied to rotating beam fatigue tests that were conducted on three aluminum alloys at three stress levels each. These alloys were AL 2024, AL 6061, and AL 7075. The results were analyzed and compared using ASTM Standard E739-91 and the Johnson-Weibull analysis. The ASTM method did not statistically distinguish between AL 6010 and AL 7075. Based on the Johnson-Weibull analysis confidence numbers greater than 99 percent, AL 2024 was found to have the longest fatigue life, followed by AL 7075, and then AL 6061. The ASTM Standard and the Johnson-Weibull analysis result in the same stress-life exponent p for each of the three aluminum alloys at the median or L(sub 50) lives.

Hendricks, Robert C.↗
DOE OSTI2020

Scale Invariance of the Homentropic Inviscid Euler Equations with Application to the Noh Problem

We investigate the inviscid compressible flow (Euler) equations constrained by an ”isentropic” equation of state (EOS), whose functional form in pressure is an arbitrary function of density alone. Under the aforementioned condition, we interrogate using symmetry methods the scale-invariance of the homentropic inviscid Euler equations. We find that under general conditions, we can reduce the inviscid Euler equations into a system of two coupled ordinary differential equations. To exemplify the utility of these results, we formulate two example scale-invariant, self-similar solutions. The first example includes a shock-free expanding bubble scenario, featuring a modified Tait EOS. The second example features the classical Noh problem, coupled to an arbitrary isentropic EOS. In this case, in order to satisfy the conditions set forth in the classical Noh problem, we find that the solution for the flow is given by a transcendental algebraic equation in the shocked density.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

Computational analysis of forebody tangential slot blowing on the high alpha research vehicle

A numerical analysis of forebody tangential slot blowing as a means of generating side force and yawing moment is conducted using an aircraft geometry. The Reynolds-averaged, thin-layer, Navier-Stokes equations are solved using a partially flux-split, approximately-factored algorithm. An algebraic turbulence model is used to determine the turbulent eddy viscosity values. Solutions are obtained using both patched and overset grid systems. In the patched grid model, and actuator plane is used to introduce jet variables into the flow field. The overset grid model is used to model the physical slot geometry and facilitate modeling of the full aircraft configuration. A slot optimization study indicates that a short slot located close to the nose of the aircraft provided the most side force and yawing moment per unit blowing coefficient. Comparison of computed surface pressure with that obtained in full-scale wind tunnel tests produce good agreement, indicating the numerical method and grid system used in the study are valid. Full aircraft computations resolve the changes in vortex burst point due to blowing. A time-accurate full-aircraft solution shows the effect of blowing on the changes in the frequency of the aerodynamic loads over the vertical tails. A study of the effects of freestream Mach number and various jet parameters indicates blowing remains effective through the transonic Mach range. An investigation of the force onset time lag associated with forebody blowing shows the lag to be minimal. The knowledge obtained in this study may be applied to the design of a forebody tangential slot blowing system for use on flight aircraft.

Gee, Ken↗
DOE OSTI2020

Weak scaling of the contact distance between two fluctuating interfaces with system size

A pair of flat parallel surfaces, each freely diffusing along the direction of their separation, will eventually come into contact. If the shapes of these surfaces also fluctuate, then contact will occur when their centers-of-mass remain separated by a nonzero distance ℓ. An example of such a situation is the motion of interfaces between two phases at conditions of thermodynamic coexistence, and in particular the annihilation of domain wall pairs under periodic boundary conditions. Here we present a general approach to calculate the probability distribution of the contact distance ℓ and determine how its most likely value ℓ* depends on the surfaces' lateral size L. Using the Edward-Wilkinson equation as a model for interfaces, we demonstrate that ℓ* scales weakly with system size, i.e., the dependence of ℓ* on L for both (1+1)- and (2+1)-dimensional interfaces is such that lim L→∞ (ℓ*/L) = 0. In particular, for (2+1)-dimensional interfaces ℓ* is an algebraic function of logL, a result that is confirmed by computer simulations of slab-shaped domains formed under periodic boundary conditions. Overall, this weak scaling implies that such domains remain topologically intact until ℓ becomes very small compared to the lateral size of the interface, contradicting expectations from equilibrium thermodynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Evaluation of a nonlinear variational multiscale method for fluid transport problems

Diverse transport problems, especially those based on fluid flow models, are intrinsically multiscale and nonlinear, characteristics that often lead to intricate dynamics such as the development of instabilities and turbulence. Computational simulations that resolve all scales in these problems are often unfeasible, prompting to coarse-grained simulation strategies in which small-scale features are modeled instead of resolved. Variational Multiscale (VMS) methods, and particularly residual-based Large-Eddy Simulation (LES) approaches, have proven effective and robust for the coarse-grained simulation of complex transport problems. VMS methods avoid the assumption of separable nonlinearity and the reliance on empirical small-scale models by using a variational decomposition of scales together with a residual-based approximation of the small-scales. Evaluation of a nonlinear VMS approach, denoted as VMS n , is presented for the coarse-grained simulation of transient-advective-diffusive-reactive (TADR) transport problems arising from fluid flow models. In contrast to classical VMS approaches that neglect the effect of the small scales on the transport operator, VMS n treats the inter-dependence between large- and small-scales upfront. The treatment of inter-scale coupling involves the solution of a local algebraic nonlinear system describing the evolution of the small-scales. The VMS n approach is complemented with two algebraic approximations of the small-scales: one based on the main diagonal of the transport matrices and another that preserves transport fluxes and is suitable for generic TADR systems. The suitability of the VMS n approach for handling general TADR problems and regimes is evaluated with benchmark incompressible, compressible, and magnetohydrodynamic laminar flow problems, the incompressible Taylor-Green vortex flow, the turbulent free jet, and the two-temperature arc in crossflow. Furthermore, simulation results show that VMS n leads to minor improvements in accuracy with respect to the classical VMS for the laminar flow problems, but to significantly greater accuracy for the turbulent flows and the unsteady plasma flow problems, while using the same cohesive numerical formulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

ROM-Based Surrogate Systems Modeling of EBR-II

We report the System Analysis Module (SAM), developed and maintained by Argonne National Laboratory, is designed to provide whole-plant transient safety analysis capabilities for a number of advanced non-light water reactors, including sodium-cooled fast reactor (SFR), lead-cooled fast reactor (LFR), and molten salt reactor (MSR)/fluoride-salt-cooled high-temperature reactor (FHR) designs. SAM is primarily constructed as a systems-level analysis tool, with the potential to incorporate reduced order models from three-dimensional computational fluid dynamics (CFD) simulations to improve characterization of complex, multidimensional physics. It is recognized that the computational expense associated with CFD can be intractable for various engineering analyses, such as uncertainty quantification, inference, and design optimization. This paper explores the reducibility of a SAM model using recent advances in randomized linear algebra techniques, which attempt to find recurring patterns in the various realizations generated by a model after randomly perturbing all its input parameters. The reduction is described in terms of fewer degrees of freedom (DOFs), referred to as the active DOFs, for the model variables such as input model parameters and model responses. The results indicate that there is significant room for additional reduction that may be leveraged for additional computational gains when employing SAM for engineering-intensive analyses that require repeated model executions. Different from physics-based reduction approaches, the proposed approach allows one to estimate upper bounds on the reduction errors, which are rigorously developed in this work. Finally, different methods for surrogate model construction, such as regression and neural network-based training, are employed to correlate the input and output active DOFs, which are related back to the original variables using matrix-based linear transformations.

42 ENGINEERING↗
NASA NTRS1984

Calculating C-grids with fine and embedded mesh regions

A program for calculating a C-type mesh around airfoil like shapes is described. The Jameson/Caughey approach is used: a parabolic transformation coupled with a shearing transformation. The algebraic algorithm is capable of efficiently generating nearly orthogonal grids. A high degree of grid control is possible. The user may specify grid boundaries, number of grid lines, and location of (and spacing in) trailing edge and leading edge fine mesh areas. The capability of embedding fine mesh regions, for use with new adaptive grid techniques, is being developed. Grids generated by the program were used in Euler flow flow calculatons by W. Usab. Results superior to results calculated on previous O-type grids were obtained. Specifically, calculations converged faster using C-grids rather than 0-grids, total pressure loss spikes at the trailing edge of the airfoil were eliminated, and the Ni method converged with zero artificial smoothing for a subcritical case (resulting overall total pressure loss was then nearly zero). These improvements were attributed to higher grid orthogonality, especially at the trailing edge. The program itself is fairly straightforward. Roughly half of the 800 code lines are comment lines.

Loyd, B.↗
DOE OSTI2026

Particle-hole symmetric slave-boson method for the mixed valence problem

We introduce an analytic slave-boson method for treating the finite-𝑈 Anderson impurity model. Our approach introduces two bosons to track both 𝑄 ⇌ 𝑄 ± 1 valence fluctuations and reduces to a single symmetric 𝑠 boson in the effective action, encoding all the high-energy atomic physics information in the boson's kinematics, while the low-energy part of the action remains unchanged across finite-𝑈, infinite-𝑈, and Kondo limits. We recover the infinite-𝑈- and Kondo-limit actions from our approach and show that the Kondo resonance already develops in the normal state when the slave boson has yet to condense. We show that the slave rotor and 𝑠 boson have the same algebraic structure, and we establish a unified functional integral framework connecting the 𝑠-boson and slave-rotor representations for the single-impurity Anderson model.

Anderson impurity model↗
NASA NTRS1996

Robust Stabilization of Uncertain Systems Based on Energy Dissipation Concepts

Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear time-invariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the time-domain and the frequency-domain, in terms of linear matrix inequalities (LMls) and algebraic Riccati equations (ARE's). A novel characterization of strictly dissipative LTI systems is introduced in this report. Sufficient conditions in terms of dissipativity and strict dissipativity are presented for (1) stability of the feedback interconnection of dissipative LTI systems, (2) stability of dissipative LTI systems with memoryless feedback nonlinearities, and (3) quadratic stability of uncertain linear systems. It is demonstrated that the framework of dissipative LTI systems investigated in this report unifies and extends small gain, passivity, and sector conditions for stability. Techniques for selecting power functions for characterization of uncertain plants and robust controller synthesis based on these stability results are introduced. A spring-mass-damper example is used to illustrate the application of these methods for robust controller synthesis.

Gupta, Sandeep↗
DOE OSTI2025

Randomized Algorithms for Symmetric Nonnegative Matrix Factorization

Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a matrix with a product of a nonnegative, low-rank matrix and it transpose. To design faster and more scalable algorithms for SymNMF we develop two randomized algorithms for its computation. The first method uses randomized matrix sketching to compute an initial low-rank approximation to the input matrix and proceeds to uses this as a low-rank input to rapidly compute a SymNMF. The second methods uses randomized leverage score sampling to approximately solve constrained least squares problems. Many successful methods for SymNMF rely on (approximately) solving sequences of constrained least squares problems. Here, we prove theoretically that leverage score sampling can approximately solve constrained least squares problems to e-accuracy. Finally we demonstrate both methods work in practice by applying them to graph clustering tasks on large real world data sets. These experiments show that our methods approximately maintain solution quality and achieve significant speed ups for both large dense and large sparse problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

tapir: A tool for topologies, amplitudes, partial fraction decomposition and input for reductions

The demand for precision predictions in the field of high energy physics has dramatically increased over recent years. Experiments conducted at the LHC, as well as precision measurements at the intensity frontier such as Belle II require equally precise theoretical predictions to make full use of the acquired data. To match the experimental precision, second-, third- and, for certain quantities, even higher-order calculations in perturbative quantum field theory are required. To facilitate such calculations, computer software automating as many steps as possible is required. Yet, each calculation poses different challenges and thus, a high level of configurability is required. In this context we present tapir: a tool for identification, manipulation and minimization of Feynman integral families. It is designed to integrate in toolchains based on the computer algebra system FORM, the use of which is common practice in the field. tapir can be used to reduce the complexity of multi-loop problems with cut-filters, topology mapping, partial fraction decomposition and alike. Program Title:tapir CPC Library link to program files:https://doi.org/10.17632/ptc9t46xyn.1 Developer's repository link:https://gitlab.com/tapir-devs/tapir Licensing provisions: GPLv3 Programming language:python 3, C++ Nature of problem: Multi-loop computations require the automatization of a large number of different tasks related to Feynman integral topologies. Among them are the identification and minimization of integral topologies, partial fraction decomposition of topologies in the case of linearly dependent propagators as well as mapping scalar products of loop momenta to scalar functions. Solution method: The minimization of topologies is performed by comparison of their respective Nickel indices [1], even further minimization utilizes Pak's algorithm [2]. To efficiently map scalar products of loop momenta to scalar functions FORM [3] code is generated. Additional comments including restrictions and unusual features: Minimization based on Pak's algorithm slows down for many lines and scales. A coarser minimization using the Nickel indices, however, is still possible. [1]B. Nickel, D. Meiron, G.A.J. Baker, Compilation of 2-pt and 4-pt graphs for continuous spin model, Report, University of Guelph, 1977.[2]A. Pak, J. Phys. Conf. Ser. 368 (2012) 012049, https://doi.org/10.1088/1742-6596/368/1/012049, arXiv:1111.0868.[3]B. Ruijl, T. Ueda, J. Vermaseren, FORM version 4.2, arXiv:1707.06453, 7 2017.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

A parallel, distributed memory implementation of the adaptive sampling configuration interaction method

The many-body simulation of quantum systems is an active field of research that involves several different methods targeting various computing platforms. Many methods commonly employed, particularly coupled cluster methods, have been adapted to leverage the latest advances in modern high-performance computing. Selected configuration interaction (sCI) methods have seen extensive usage and development in recent years. However, the development of sCI methods targeting massively parallel resources has been explored only in a few research works. Here, we present a parallel, distributed memory implementation of the adaptive sampling configuration interaction approach (ASCI) for sCI. In particular, we will address the key concerns pertaining to the parallelization of the determinant search and selection, Hamiltonian formation, and the variational eigenvalue calculation for the ASCI method. Load balancing in the search step is achieved through the application of memory-efficient determinant constraints originally developed for the ASCI-PT2 method. The presented benchmarks demonstrate near optimal speedup for ASCI calculations of Cr 2 (24e, 30o) with 10 6 , 10 7 , and 3 × 10 8 variational determinants on up to 16 384 CPUs. Importantly, to the best of the authors’ knowledge, this is the largest variational ASCI calculation to date.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1990

On the Response of the Special Sensor Microwave/Imager to the Marine Environment: Implications for Atmospheric Parameter Retrievals

A reasonably rigorous basis for understanding and extracting the physical information content of Special Sensor Microwave/Imager (SSM/I) satellite images of the marine environment is provided. To this end, a comprehensive algebraic parameterization is developed for the response of the SSM/I to a set of nine atmospheric and ocean surface parameters. The brightness temperature model includes a closed-form approximation to microwave radiative transfer in a non-scattering atmosphere and fitted models for surface emission and scattering based on geometric optics calculations for the roughened sea surface. The combined model is empirically tuned using suitable sets of SSM/I data and coincident surface observations. The brightness temperature model is then used to examine the sensitivity of the SSM/I to realistic variations in the scene being observed and to evaluate the theoretical maximum precision of global SSM/I retrievals of integrated water vapor, integrated cloud liquid water, and surface wind speed. A general minimum-variance method for optimally retrieving geophysical parameters from multichannel brightness temperature measurements is outlined, and several global statistical constraints of the type required by this method are computed. Finally, a unified set of efficient statistical and semi-physical algorithms is presented for obtaining fields of surface wind speed, integrated water vapor, cloud liquid water, and precipitation from SSM/I brightness temperature data. Features include: a semi-physical method for retrieving integrated cloud liquid water at 15 km resolution and with rms errors as small as approximately 0.02 kg/sq m; a 3-channel statistical algorithm for integrated water vapor which was constructed so as to have improved linear response to water vapor and reduced sensitivity to precipitation; and two complementary indices of precipitation activity (based on 37 GHz attenuation and 85 GHz scattering, respectively), each of which are relatively insensitive to variations in other environmental parameters.

Petty, Grant W.↗
NASA NTRS1993

DUKSUP - A high thrust trajectory optimization code

Designing missions on expendable launch vehicles (ELV's) includes determining launch vehicle performance capabilities and trajectory characteristics over the range of mission requirements for suitable launch periods. This analysis depends on mathematically modeling both the launch vehicle and the mission requirements. Generally the result is a mathematical model that is described by an objective function to be optimized subject to an assortment of algebraic and dynamic constraints. About 30 years ago, engineers at Lewis Research Center (LeRC) undertook the task of creating a software code to solve 3D versions of such problems and based it on the Calculus of Variations/Optimal Control Theory. One of these codes, DUKSUP, has been in use at LeRC for nearly 25 years, during which time it has played an important role in a large number of studies and actual missions. Currently it is being used by about 12 analysts in the Center's Advanced Space Analysis Office (ASAO) to do mission design, feasibility studies, corroboration of contractor data and planning studies for the Space Exploration Initiative (SEI). Today, it is one of the few ELV mission analysis production codes based on variational methods. With future ELV missions in mind, ASAO is presently creating a new code to upgrade DUKSUP's capabilities.

Balkanyi, Leslie R.↗
DOE OSTI2022

Failure Probability Constrained AC Optimal Power Flow

Despite cascading failures being the central cause of blackouts in power transmission systems, existing operational and planning decisions are made largely by ignoring their underlying cascade potential. This paper posits a reliability-aware AC Optimal Power Flow formulation that seeks to design a dispatch point which has a low operator-specified likelihood of triggering a cascade starting from any single component outage. By exploiting a recently developed analytical model of the probability of component failure, our Failure Probability-constrained ACOPF (FP-ACOPF) utilizes the system's expected first failure time as a smoothly tunable and interpretable signature of cascade risk. Here, we use techniques from bilevel optimization and numerical linear algebra to efficiently formulate and solve the FP-ACOPF using off-the-shelf solvers. Extensive simulations on the IEEE 118-bus case show that, when compared to the unconstrained and N-1 security-constrained ACOPF, our probability-constrained dispatch points can significantly lower the probabilities of long severe cascades and of large demand losses, while incurring only minor increases in total generation costs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Cosmology meets cohomology

The cosmological polytope and bootstrap programs have revealed interesting connections between positive geometries, modern on-shell methods and bootstrap principles studied in the amplitudes community with the wavefunction of the Universe in toy models of FRW cosmologies. To compute these FRW correlators, one often faces integrals that are too difficult to evaluate by direct integration. Borrowing from the Feynman integral community, the method of (canonical) differential equations provides an efficient alternative for evaluating these integrals. Moreover, we further develop our geometric understanding of these integrals by describing the associated relative twisted cohomology. Leveraging recent progress in our understanding of relative twisted cohomology in the Feynman integral community, we give an algorithm to predict the basis size and simplify the computation of the differential equations satisfied by FRW correlators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

hr-Adaptivity for nonconforming high-order meshes with the target matrix optimization paradigm

In this study, we present an \(hr\) -adaptivity framework for optimization of high-order meshes. This work extends the r -adaptivity method by Dobrev et al. (Comput Fluids, 2020), where we utilized the Target-Matrix Optimization Paradigm (TMOP) to minimize a functional that depends on each element’s current and target geometric parameters: element aspect-ratio , size , skew , and rotation . Since fixed mesh topology limits the ability to achieve the target size and aspect-ratio at each position, in this paper, we augment the r -adaptivity framework with nonconforming adaptive mesh refinement to further reduce the error with respect to the target geometric parameters. The proposed formulation, referred to as \(hr\) -adaptivity, introduces TMOP-based quality estimators to satisfy the aspect-ratio target via anisotropic refinements and size target via isotropic refinements in each element of the mesh. The methodology presented is purely algebraic, extends to both simplices and hexahedra/quadrilaterals of any order, and supports nonconforming isotropic and anisotropic refinements in 2D and 3D. Using a problem with a known exact solution, we demonstrate the effectiveness of \(hr\) -adaptivity over both r - and \(h\) -adaptivity in obtaining similar accuracy in the solution with significantly fewer mesh nodes. We also present several examples that show that \(hr\) -adaptivity can help satisfy geometric targets even when \(r\) -adaptivity fails to do so, due to the topology of the initial mesh.

42 ENGINEERING↗