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NASA NTRS2021

Trend Detection of Atmospheric Time Series: Incorporating Appropriate Uncertainty Estimates and Handling Extreme Events

This paper is aimed at atmospheric scientists without formal training in statistical theory. Its goal is to, 1) provide a critical review of the rationale for trend analysis of the time series typically encountered in the field of atmospheric chemistry; 2) describe a range of trend-detection methods; and 3) demonstrate effective means of conveying the results to a general audience. Trend detections in atmospheric chemical composition data are often challenged by a variety of sources of uncertainty, which often behave differently to other environmental phenomena such as temperature, precipitation rate, or stream flow, and may require specific methods depending on the science questions to be addressed. Some sources of uncertainty can be explicitly included in the model specification, such as autocorrelation and seasonality, but some inherent uncertainties are difficult to quantify, such as data heterogeneity and measurement uncertainty due to the combined effect of short- and long-term natural variability, instrumental stability, and aggregation of data from sparse sampling frequency. Failure to account for these uncertainties might result in an inappropriate inference of the trends and their estimation errors. On the other hand, the variation in extreme events might be interesting for different scientific questions, for example, the frequency of extremely high surface ozone events and their relevance to human health. In this study we aim to, 1) review trend detection methods for addressing different levels of data complexity in different chemical species; 2) demonstrate that the incorporation of scientifically interpretable covariates can outperform pure numerical curve fitting techniques in terms of uncertainty reduction and improved predictability; 3) illustrate the study of trends based on extreme quantiles that can provide insight beyond standard mean or median based trend estimates; and 4) present an advanced method of quantifying regional trends based on the inter-site correlations of multi-site data. All demonstrations are based on time series of observed trace gases relevant to atmospheric chemistry, but the methods can be applied to other environmental data sets.

Trace gas↗

NASA NTRS2024

The CARMENES Search for Exoplanets Around M Dwarfs: Revisiting the GJ 581 Multi-Planetary System With New Doppler Measurements From CARMENES, HARPS, and HIRES

Context.GJ 581 is a nearby M dwarf known to host a packed multiple planet system composed of two super-Earths and a Neptune-mass planet. We present new orbital analyses of the GJ 581 system, utilizing recent radial velocity (RV) data obtained from the CARMENES spectrograph combined with newly reprocessed archival data from the HARPS and HIRES spectrographs. Aims.Our aim was to analyze the post-discovery spectroscopic data of GJ 581, which were obtained with CARMENES. In addition, we used publicly available HIRES and HARPS spectroscopic data to seek evidence of the known and disputed exoplanets in this system. We aimed to investigate the stellar activity of GJ 581 and update the planetary system’s orbital parameters using state-of-the-art numerical models and techniques. Methods.We performed a periodogram analysis of the available precise CARMENES, HIRES, and HARPS RVs and of stellar activity indicators. We conducted detailed orbital analyses by testing various orbital configurations consistent with the RV data. We studied the posterior probability distribution of the parameters fit to the data and we explored the long-term stability and overall orbital dynamics of the GJ 581 system. Results. We refined the orbital parameters of the GJ 581 system using the most precise and complete set of Doppler data available. Consistent with the existing literature, our analysis confirms that the system is unequivocally composed of only three planets detectable in the present data, dismissing the putative planet GJ 581 d as an artifact of stellar activity. Our N-body fit reveals that the system’s inclination is i=47.0+14.6−13.0deg, which implies that the planets could be up to 30% more massive than their previously reported minimum masses. Furthermore, we report that the GJ 581 system exhibits long-term stability, as indicated by the posterior probability distribution, characterized by secular dynamical interactions without the involvement of mean motion resonances.

Satellites↗

NASA NTRSDate not supplied

Turbulence Modeling near Gas-Liquid Interfaces for Cryogenic Fluid Management

In cryogenic fluid management (CFM), gas-liquid interface turbulence transport (ITT) heavily influences crucial design parameters of spaceflight missions. ITT and phase change processes require length-scales and time-scales that are around 4-8 orders of magnitude smaller than the scales of CFM operations in spaceflights. A sharp interface method based parsimonious yet elegant turbulence modeling approach was developed from experimental observations and high-fidelity numerical studies. The technique was validated using flight-scale CFM tests.

cryogenic fluid management↗

DOE OSTI2023

Exploring the Dynamics of Transverse Inter-planar Coupling in the Superconducting Section of the PIP-II LINAC

This study investigates the crucial role that an accurate understanding of inter-planar coupling in the transverse plane plays in regulating charged particle dynamics in a high intensity linear accelerator and minimizing foil/septum impacts during injection from the linac to a ring. We performed an in-depth analysis for the emergence and evolution of trans verse inter-planar coupling through multiple active lattice elements, taking into account space charge and field nonlinearities in the superconducting section of the PIP-II linac. The article compares various analytical, numerical, and experimental techniques for measuring transverse coupling using beam and lattice matrices and provides insight into effective strategies for its mitigation prior to ring injection.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

A Review of Lattice-Boltzmann Models Coupled with Geochemical Modeling Applied for Simulation of Advanced Waterflooding and Enhanced Oil Recovery Processes

To maintain economic profit and improve the oil production efficiency after the primary and secondary production phase, advanced waterflooding techniques such as low salinity waterflooding in carbonate reservoirs have been investigated in numerical simulations, laboratory experiments, and field pilot tests. Multiple underlying mechanisms have been proposed based on these studies, and they are still under debate. Various numerical modeling approaches are introduced, but there exists a lack of a pore-scale comprehensive modeling scheme to fully understand the processes. Lattice-Boltzmann method (LBM) is a type of numerical fluid flow modeling technique that shows capabilities and flexibilities in modeling pore-scale fluid flow to integrate physical–chemical processes within complex structures. The intrinsic feature of LBM makes it a promising framework for simulating advanced waterflooding due to its flexibility, accuracy, and parallel efficiency. LBM works either by itself for solving reactive transport problems or by coupling with a third-party reaction solver. This review mainly introduces the LBM fluid flow and reactive transport capabilities and the concept and modeling approaches to simulate advanced waterflooding techniques. Meanwhile, an evaluation of the coupled LBM models for enhanced oil recovery (EOR) simulations is discussed with future research challenges and directions concluded.

02 PETROLEUM↗

NASA NTRS1987

Viscous shock-layer analysis of hypersonic flows over long slender bodies

Numerical solutions from the time-steady viscous shock-layer equations are presented for the hypersonic laminar and turbulent flow of a perfect gas over long slender bodies. These results are obtained from a spatial-marching implicit finite-difference technique. Detailed comparisons have been made with other predictions and experimental data to assess the accuracy of the present numerical technique, especially for slender-body flows. Results from the present method show that coupling the normal momentum and continuity equations and the use of the Vigneron pressure condition in the subsonic nose region give quite accurate and stable results. These results compare (with some exceptions) favorably with those obtained using PNS and other VSL methods.

Gupta, R. N.↗

NASA NTRS1986

Optical technique to characterize heavy rain

A technique to measure the size and velocity of raindrops is presented and experimental and numerical results discussed. The technique bases the droplet size on the absolute intensity of the light scattered when the droplets cross a laser-based probe volume. The velocity is obtained from the Doppler frequency. A size range of 0.1 mm to 9 mm was covered with overlapping ranges. Experiments were conducted with simulated rain sprays except that the local LWC was much larger than the values encountered in natural rain. The accuracy of the size measurement was not strongly affected by spray interference, but it showed a clear dependence with the droplet shape. A simple numerical model based on the light reflected from ellipsoids attempts to explain the relationship between droplet shape and absolute scattered light.

Hess, C. F.↗

NASA NTRS2021

Solving Two-Equation Turbulence Models With a Perspective on Solving Transport Equations

There are three principal objectives of this report. The first objective is to investigate frequently used two-equation models when solving the RANS equations. In this study, we consider the 2006Wilcox and the 2003 Menter Shear Stress Transport (SST) models. Also, a simple change of the Wilcox model is introduced to improve computational predictions for transonic flows. Computations for flows over two different airfoils are examined to compare these turbulence models. Effects on modeling the physics of each flow due to variations in the models, such as using either strainrate or vorticity in the turbulence production term, are considered and discussed. The second objective of this report is to not only explore but also evaluate the performance of the solution algorithm for the mean flow and the transport equations. The RANS and turbulence modeling equations aresolved in a weakly coupled manner with a diagonal implicit Runge-Kutta (DIRK) solution algorithm. Throughout this report, emphasis is given to reducing the residuals to machine zero in all flow calculations, so as to eliminate the error due to numerical integration of the discrete governing equations. The final objective is to provide a perspective on solving transport equations for turbulence modeling. Aspects of solving such stiff systems of equations, as well as various numerical difficulties and possible techniques to overcome them, are considered. Discussion is also provided concerning what is called ’numerical compatibility’, which is an essential requirement when designing a solution algorithm for solving transport equations.

turbulence modeling↗

NASA NTRS1985

Errors in reduction methods

A mathematical basis is given for comparing the relative merits of various techniques used to reduce the order of large linear and nonlinear dynamics problems during their numerical integration. In such techniques as Guyan-Irons, path derivatives, selected eigenvectors, Ritz vectors, etc., the nth order initial value problem of /y(dot) = f(y) for t greater than 0, y(0) given/ is typically reduced to the mth order (m is much less than n) problem of /z(dot) = g(z) for t greater than 0, z(0) given/ by the transformation y = Pz where P changes from technique to technique. This paper gives an explicit approximate expression for the reduction error e-i in terms of P and the Jacobian of f. It is shown that: (a) reduction techniques are more accurate when the time rate of change of the response y is relatively small; (b) the change in response between two successive stations contributes to the errors at future stations after the change in response is transformed by a filtering matrix H, defined in terms of P; (c) the error committed at a station propagates to future stations by a mixing and scaling matrix G, defined in terms of P, Jacobian and of f, and time increment h. The paper discusses the conditions under which the reduction errors may be minimized and gives guidelines for selecting the reduction basis vector, i.e., the columns of P.

Utku, S.↗

DOE OSTI2026

Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits

Time-dependent electromagnetic drives are fundamental for controlling complex quantum systems, including superconducting Josephson circuits. In these devices, accurate time-dependent Hamiltonian models are imperative for predicting their dynamics and designing high-fidelity quantum operations. Existing numerical methods, such as black-box quantization (BBQ) and energy-participation ratio (EPR), excel at modeling the static Hamiltonians of Josephson circuits. However, these techniques do not fully capture the behavior of driven circuits stimulated by external microwave drives, nor do they include a generalized approach to account for the inevitable noise and dissipation that enter through microwave ports. Here, we introduce numerical techniques that leverage classical microwave simulations, efficiently executable in finite-element solvers, to obtain the time-dependent Hamiltonian of microwave-driven superconducting circuits with arbitrary geometries under charge, flux, or mixed electromagnetic modulation. Importantly, our techniques do not rely on a lumped-element description of the superconducting circuit, in contrast to previous approaches to tackling this problem. We demonstrate the versatility of our approach by characterizing the driven properties of realistic circuit devices in complex electromagnetic environments, including coherent dynamics due to charge and flux modulation, as well as drive-induced relaxation and dephasing. Our techniques offer a powerful toolbox for optimizing circuit designs and advancing practical applications in superconducting quantum computing.

Lu, Yao [Yale U.; Yale U. (main); Fermilab] (ORCID↗

NASA NTRS1992

Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems. Task 4: Advanced fan section aerodynamic analysis

The purpose of this study is the development of a three-dimensional Euler/Navier-Stokes flow analysis for fan section/engine geometries containing multiple blade rows and multiple spanwise flow splitters. An existing procedure developed by Dr. J. J. Adamczyk and associates and the NASA Lewis Research Center was modified to accept multiple spanwise splitter geometries and simulate engine core conditions. The procedure was also modified to allow coarse parallelization of the solution algorithm. This document is a final report outlining the development and techniques used in the procedure. The numerical solution is based upon a finite volume technique with a four stage Runge-Kutta time marching procedure. Numerical dissipation is used to gain solution stability but is reduced in viscous dominated flow regions. Local time stepping and implicit residual smoothing are used to increase the rate of convergence. Multiple blade row solutions are based upon the average-passage system of equations. The numerical solutions are performed on an H-type grid system, with meshes being generated by the system (TIGG3D) developed earlier under this contract. The grid generation scheme meets the average-passage requirement of maintaining a common axisymmetric mesh for each blade row grid. The analysis was run on several geometry configurations ranging from one to five blade rows and from one to four radial flow splitters. Pure internal flow solutions were obtained as well as solutions with flow about the cowl/nacelle and various engine core flow conditions. The efficiency of the solution procedure was shown to be the same as the original analysis.

Crook, Andrew J.↗

NASA NTRS1983

Parameter identification in continuum models

Approximation techniques for use in numerical schemes for estimating spatially varying coefficients in continuum models such as those for Euler-Bernoulli beams are discussed. The techniques are based on quintic spline state approximations and cubic spline parameter approximations. Both theoretical and numerical results are presented.

Banks, H. T.↗

NASA NTRS1983

Parameter identification in continuum models

Banks, H. T.↗

NASA NTRS1974

Approximate techniques of structural reanalysis

A study is made of two approximate techniques for structural reanalysis. These include Taylor series expansions for response variables in terms of design variables and the reduced-basis method. In addition, modifications to these techniques are proposed to overcome some of their major drawbacks. The modifications include a rational approach to the selection of the reduced-basis vectors and the use of Taylor series approximation in an iterative process. For the reduced basis a normalized set of vectors is chosen which consists of the original analyzed design and the first-order sensitivity analysis vectors. The use of the Taylor series approximation as a first (initial) estimate in an iterative process, can lead to significant improvements in accuracy, even with one iteration cycle. Therefore, the range of applicability of the reanalysis technique can be extended. Numerical examples are presented which demonstrate the gain in accuracy obtained by using the proposed modification techniques, for a wide range of variations in the design variables.

Noor, A. K.↗

NASA NTRS1989

An improved, robust, axial line singularity method for bodies of revolution

The failures encountered in attempts to increase the range of applicability of the axial line singularity method for representing incompressible, inviscid flow about an inclined and slender body-of-revolution are presently noted to be common to all efforts to solve Fredholm equations of the first kind. It is shown that a previously developed smoothing technique yields a robust method for numerical solution of the governing equations; this technique is easily retrofitted to existing codes, and allows the number of circularities to be increased until the most accurate line singularity solution is obtained.

Hemsch, Michael J.↗

NASA NTRS1987

A survey of nested grid techniques and their potential for use within the MASS weather prediction model

A survey of various one- and two-way interactive nested grid techniques used in hydrostatic numerical weather prediction models is presented and the advantages and disadvantages of each method are discussed. The techniques for specifying the lateral boundary conditions for each nested grid scheme are described in detail. Averaging and interpolation techniques used when applying the coarse mesh grid (CMG) and fine mesh grid (FMG) interface conditions during two-way nesting are discussed separately. The survey shows that errors are commonly generated at the boundary between the CMG and FMG due to boundary formulation or specification discrepancies. Methods used to control this noise include application of smoothers, enhanced diffusion, or damping-type time integration schemes to model variables. The results from this survey provide the information needed to decide which one-way and two-way nested grid schemes merit future testing with the Mesoscale Atmospheric Simulation System (MASS) model. An analytically specified baroclinic wave will be used to conduct systematic tests of the chosen schemes since this will allow for objective determination of the interfacial noise in the kind of meteorological setting for which MASS is designed. Sample diagnostic plots from initial tests using the analytic wave are presented to illustrate how the model-generated noise is ascertained. These plots will be used to compare the accuracy of the various nesting schemes when incorporated into the MASS model.

Koch, Steven E.↗

NASA NTRS1993

Towards a generalized computational fluid dynamics technique for all Mach numbers

Currently there exists no single unified approach for efficiently and accurately solving computational fluid dynamics (CFD) problems across the Mach number regime, from truly low speed incompressible flows to hypersonic speeds. There are several CFD codes that have evolved into sophisticated prediction tools with a wide variety of features including multiblock capabilities, generalized chemistry and thermodynamics models among other features. However, as these codes evolve, the demand placed on the end user also increases simply because of the myriad of features that are incorporated into these codes. In order for a user to be able to solve a wide range of problems, several codes may be needed requiring the user to be familiar with the intricacies of each code and their rather complicated input files. Moreover, the cost of training users and maintaining several codes becomes prohibitive. The objective of the current work is to extend the compressible, characteristic-based, thermochemical nonequilibrium Navier-Stokes code GASP to very low speed flows and simultaneously improve convergence at all speeds. Before this work began, the practical speed range of GASP was Mach numbers on the order of 0.1 and higher. In addition, a number of new techniques have been developed for more accurate physical and numerical modeling. The primary focus has been on the development of optimal preconditioning techniques for the Euler and the Navier-Stokes equations with general finite-rate chemistry models and both equilibrium and nonequilibrium thermodynamics models. We began with the work of Van Leer, Lee, and Roe for inviscid, one-dimensional perfect gases and extended their approach to include three-dimensional reacting flows. The basic steps required to accomplish this task were a transformation to stream-aligned coordinates, the formulation of the preconditioning matrix, incorporation into both explicit and implicit temporal integration schemes, and modification of the numerical flux formulae. In addition, we improved the convergence rate of the implicit time integration schemes in GASP through the use of inner iteration strategies and the use of the GMRES (General Minimized Resisual) which belongs to the class of algorithms referred to as Krylov subspace iteration. Finally, we significantly improved the practical utility of GASP through the addition of mesh sequencing, a technique in which computations begin on a coarse grid and get interpolated onto successively finer grids. The fluid dynamic problems of interest to the propulsion community involve complex flow physics spanning different velocity regimes and possibly involving chemical reactions. This class of problems results in widely disparate time scales causing numerical stiffness. Even in the absence of chemical reactions, eigenvalue stiffness manifests itself at transonic and very low speed flows which can be quantified by the large condition number of the system and evidenced by slow convergence rates. This results in the need for thorough numerical analysis and subsequent implementation of sophisticated numerical techniques for these difficult yet practical problems. As a result of this work, we have been able to extend the range of applicability of compressible codes to very low speed inviscid flows (M = .001) and reacting flows.

Walters, R. W.↗

NASA NTRS1975

A two parameter survey of periodic orbits in the restricted problem of three bodies

Within the context of the restricted problem of three bodies the effects caused by varying the mass ratio of the primaries and the eccentricity of their orbits, upon periodic orbits of the infinitesimal mass which are numerical continuations of circular orbits in the ordinary problem of two bodies are shown. A recursive power series technique is used to numerically integrate the equations of motion as well as the first variational equations in order to generate a two parameter family of perodic orbits and identify the linear stability characteristics. Seven such families are investigated with equally spaced mass ratios from 0.0 to 1.0 and eccentricities of the orbits of the primaries in a range 0.0 to 0.6. Stable orbits are associated with large distances of the infinitesimal mass from the perturbing primary, nearly circular motion of the primaries, and small mass ratios of the primaries. Unstable orbits for the infinitesimal mass are associated with small distances from the perturbing primary, highly elliptic orbits of the primaries and large mass ratios.

Shelus, P. J.↗