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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A Hybrid Lagrangian/Eulerian Collocated Velocity Advection and Projection Method for Fluid Simulation

Abstract We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. Our approach supports both particle‐based Lagrangian advection in very detailed regions of the flow and efficient Eulerian grid‐based advection in other regions of the flow. A novel Backward Semi‐Lagrangian method is derived to improve accuracy of grid based advection. Our approach utilizes the implicit formula associated with solutions of the inviscid Burgers’ equation. We solve this equation using Newton's method enabled by C 1 continuous grid interpolation. We enforce incompressibility over collocated, rather than staggered grids. Our projection technique is variational and designed for B‐spline interpolation over regular grids where multiquadratic interpolation is used for velocity and multilinear interpolation for pressure. Despite our use of regular grids, we extend the variational technique to allow for cut‐cell definition of irregular flow domains for both Dirichlet and free surface boundary conditions.

Gagniere, S.↗
DOE OSTI2021

Analysis of Three Types of Collocated Disdrometer Measurements at the ARM Southern Great Plains Observatory

To better provide U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) user facility’s disdrometer deployment strategy and support ARM precipitation-related projects, this study analyzes 18 months of drop size distribution (DSD) observations from six collocated disdrometers deployed at the ARM Southern Great Plains (SGP) site. Emphasis is placed on quantifying the uncertainties related to DSD and rainfall properties using different types of disdrometers and different pairing concepts. The instrument sampling errors are also discussed, which improves our understanding of instrument-specific impacts on rainfall measurements. The key findings are as follows: 1) All the disdrometers show consistent behaviors overall regarding accumulated precipitation, mean rainfall rate, DSD parameters, and radar reflectivity values; and 2) Strong agreement is shown between three disdrometer types in terms of their DSDs for mid-size drop range (D = 1 mm-4 mm). The two-dimensional video disdrometer performance meets expectations as the most accurate unit among all. The paired disdrometer shows a reduced statistical sampling error in terms of drop counts and other DSD properties. A concept of deploying two or more collocated disdrometers side by side is recommended for future ARM field campaigns.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Adaptive Sparse-Grid Stochastic Collocation Uncertainty Quantification Convergence for Multigroup Diffusion

Advanced methods in uncertainty quantification for numerical models in computational physics continue to gain acceptance in nuclear modeling. Previously, the efficiency of sparse-grid stochastic collocation in comparison with Monte Carlo for uncertainty quantification through convergence studies was demonstrated. An adaptive method for anisotropic sparse grid collocation and its convergence compared to previous efforts is considered. The physical system in consideration is a two-dimensional quarter-core reactor, consisting of 5 materials distributed in 121 regions. The two-group neutron diffusion criticality approximation is solved. Vacuum boundaries are applied on the top and right, and reflecting boundaries on the bottom and left. The material cross sections, neutron multiplication factors, and diffusion coefficients are potential sources of uncertainty. Uniformly-distributed uncertainty within 5% of the reference values is introduced for material properties. The distribution of the uncertain parameters make up the uncertainty space Γ included in R{sup N}, where N is the number of uncertain parameters. The input parameter uncertainties are independently distributed. As expected, the convergence of Monte Carlo on the benchmark as a function of computational solves is nearly linear and lethargic compared to the other methods. The static isotropic index set, in which each input dimension is treated with equal importance, converges much more efficiently than Monte Carlo, but lacks the benefit of emphasizing some dimensions over others. The anisotropic case is most efficient, where first-order sensitivity information was used to determine anisotropic weights for polynomials to use in the polynomial chaos expansion. Interestingly, the adaptive algorithm converges slightly less efficiently than the anisotropic case, while still performing better than the isotropic case. Because the adaptive case has to determine the importance of each input dimension, it occasionally predicts inaccurately and wastes computation solves compared to the more ideal anisotropic case. However, in circumstances when an ideal anisotropy is not understood a priori, the adaptive algorithm may be optimally efficient in representing the original model. Given the potential loss of efficiency when using a poorly-chosen anisotropic weighting, the adaptive algorithm may be an effective choice for initial uncertainty quantification in problems with a low-dimensionality input space. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Investigating Inherent Numerical Stabilization for the Moist, Compressible, Non‐Hydrostatic Euler Equations on Collocated Grids

This study investigates inherent numerical dissipation due to upwind fluxes and reconstruction strategies for collocated Finite-Volume integration of the Euler equations. Idealized supercell simulations are used without any explicit dissipation. Flux terms are split into: mass flux, pressure, and advected quantities. They are computed with the following upwind strategies: central, advectively upwind, and acoustically upwind. This is performed for third and ninth-order-accurate reconstructions with and without Weighted Essentially Non-Oscillatory limiting. Acoustic-only upwinding for pressure and mass flux terms and advective-only upwinding for advected quantities is the most flexible simplification found. It reduces data movement and computations. Assuming a constant speed of sound in acoustic upwinding gives similar results to using the true speed of sound. Dissipation from upwind adapts automatically to grid spacing, time step, reconstruction accuracy, and flow smoothness. While stability is maintained even at 21st-order spatial accuracy, there is a limit to the spatial order of accuracy for which upwinding alone can create a realizable solution in the conditions of this study. Convex combinations of upwind and central solutions for flux terms also reduced dissipation, but as the central proportion grows, solutions become physically unrealizable. The range of length scales of the kinetic energy spectra can be extended along k −5/3 to smaller spatial scales by reducing dissipation either with higher-order reconstructions or using convex combinations of upwind and central fluxes. However, not all extensions of the length scale range along k −5/3 exhibit physically realizable solutions, even though the spectra appear to be physical.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems

Previous work has demonstrated that propagating groups of samples, called ensembles, together through forward simulations can dramatically reduce the aggregate cost of sampling-based uncertainty propagation methods [E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam, SIAM J. Sci. Comput., 39 (2017), pp. C162--C193]. However, critical to the success of this approach when applied to challenging problems of scientific interest is the grouping of samples into ensembles to minimize the total computational work. For example, the total number of linear solver iterations for ensemble systems may be strongly influenced by which samples form the ensemble when applying iterative linear solvers to parameterized and stochastic linear systems. In this paper we explore sample grouping strategies for local adaptive stochastic collocation methods applied to PDEs with uncertain input data, in particular canonical anisotropic diffusion problems where the diffusion coefficient is modeled by truncated Karhunen--Loève expansions. Finally, we demonstrate that a measure of the total anisotropy of the diffusion coefficient is a good surrogate for the number of linear solver iterations for each sample and therefore provides a simple and effective metric for grouping samples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

An Evolve-Filter-Relax Stabilized Reduced Order Stochastic Collocation Method for the Time-Dependent Navier--Stokes Equations

In this paper, we propose a filter-based stabilization of reduced order models (ROMs) for uncertainty quantification (UQ) of the time-dependent Navier--Stokes equations in convection-dominated regimes. Here we propose a novel high-order ROM differential filter and use it in conjunction with an evolve-filter-relax (EFR) algorithm to attenuate the numerical oscillations of standard ROMs. We also examine how stochastic collocation methods can be combined with the EFR algorithm for efficient UQ of fluid flows. We test the new framework in the numerical simulation of a two-dimensional flow past a circular cylinder with a random viscosity that yields a random Reynolds number with mean Re = 100.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Microstructure-Sensitive Uncertainty Quantification for Crystal Plasticity Finite Element Constitutive Models Using Stochastic Collocation Methods

Uncertainty quantification (UQ) plays a major role in verification and validation for computational engineering models and simulations, and establishes trust in the predictive capability of computational models. In the materials science and engineering context, where the process-structure-property-performance linkage is well known to be the only road mapping from manufacturing to engineering performance, numerous integrated computational materials engineering (ICME) models have been developed across a wide spectrum of length-scales and time-scales to relieve the burden of resource-intensive experiments. Within the structure-property linkage, crystal plasticity finite element method (CPFEM) models have been widely used since they are one of a few ICME toolboxes that allows numerical predictions, providing the bridge from microstructure to materials properties and performances. Several constitutive models have been proposed in the last few decades to capture the mechanics and plasticity behavior of materials. While some UQ studies have been performed, the robustness and uncertainty of these constitutive models have not been rigorously established. In this work, we apply a stochastic collocation (SC) method, which is mathematically rigorous and has been widely used in the field of UQ, to quantify the uncertainty of three most commonly used constitutive models in CPFEM, namely phenomenological models (with and without twinning), and dislocation-density-based constitutive models, for three different types of crystal structures, namely face-centered cubic (fcc) copper (Cu), body-centered cubic (bcc) tungsten (W), and hexagonal close packing (hcp) magnesium (Mg). Our numerical results not only quantify the uncertainty of these constitutive models in stress-strain curve, but also analyze the global sensitivity of the underlying constitutive parameters with respect to the initial yield behavior, which may be helpful for robust constitutive model calibration works in the future.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Numerical solution of linear and nonlinear hyperbolic telegraph type equations with variable coefficients using shifted Jacobi collocation method

The telegraph equation is one of the important equations of mathematical physics. In this work, a spectral collocation scheme is proposed for the numerical solutions of one- and two-dimensional linear telegraph equations and telegraph equations with nonlinear forcing term. The homogeneous initial and boundary conditions are satisfied exactly by expanding the unknown variable using polynomial bases of functions which are built upon the Jacobi polynomials. The suggested scheme is successfully developed for the aforementioned problem with nonhomogeneous data. Extensive numerical experiments are presented to verify the efficiency of the proposed scheme.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A Müntz wavelets collocation method for solving fractional differential equations

In this paper, we introduce a new set of wavelets, namely Müntz wavelets. These wavelets are defined based on Müntz Legendre polynomials which have the property of orthogonality. We stabilize the wavelet coefficients by utilizing Jacobi polynomials to construct the modified Müntz wavelets. Next, we present a collocation scheme based on Müntz wavelets for solving fractional differential equations. The fractional derivative is described in the Caputo sense. Some error estimates are given and numerical examples are included to demonstrate the applicability and accuracy of the proposed method. This includes the elastic-dissipative mathematical model of linear mechanical devices known as Boltzman operator.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Parallel adaptive wavelet collocation method for PDEs

A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by developing an asynchronous parallel wavelet transform, which allows one to perform parallel wavelet transform and derivative calculations with only one data synchronization at the highest level of resolution. The data are stored using tree-like structure with tree roots starting at a priori defined level of resolution. Both static and dynamic domain partitioning approaches are developed. For the dynamic domain partitioning, trees are considered to be the minimum quanta of data to be migrated between the processes. This allows fully automated and efficient handling of non-simply connected partitioning of a computational domain. Dynamic load balancing is achieved via domain repartitioning during the grid adaptation step and reassigning trees to the appropriate processes to ensure approximately the same number of grid points on each process. The parallel efficiency of the approach is discussed based on parallel adaptive wavelet-based Coherent Vortex Simulations of homogeneous turbulence with linear forcing at effective non-adaptive resolutions up to 2048{sup 3} using as many as 2048 CPU cores.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Simplex-stochastic collocation method with improved scalability

The Simplex-Stochastic Collocation (SSC) method is a robust tool used to propagate uncertain input distributions through a computer code. However, it becomes prohibitively expensive for problems with dimensions higher than 5. The main purpose of this paper is to identify bottlenecks, and to improve upon this bad scalability. In order to do so, we propose an alternative interpolation stencil technique based upon the Set-Covering problem, and we integrate the SSC method in the High-Dimensional Model-Reduction framework. In addition, we address the issue of ill-conditioned sample matrices, and we present an analytical map to facilitate uniformly-distributed simplex sampling.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems

The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method. Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.

42 ENGINEERING↗
DOE OSTI2020

High Dynamic Range AFM Cantilever With a Collocated Piezoelectric Actuator-Sensor Pair

We present a novel approach to fundamentally eliminate electrical feedthrough (cross-talk) signal in self-sensing piezoelectric microcantilevers, used in dynamic mode atomic force microscopy (AFM). The probe is an Si microcantilever on which a two-layer piezoelectric stack transducer is microfabricated. The top transducer in the stack functions as an actuator, while the bottom transducer is used as a deflection sensor. This arrangement leads to a collocated actuator-sensor pair that co-exist on the same surface area. We report experimental results that establish the sensor's ability to capture the full dynamic range of the cantilever with minimal feedthrough from the actuator.

42 ENGINEERING↗
DOE OSTI2020

Solving Eco-Driving Problems Using Indirect Collocation Method and Smooth Representation

Here, we discuss the eco-driving problem, considering both electric and conventional powertrains, and presents a pathway to solving it numerically using an indirect collocation method. Despite the low-order system dynamics, the piecewise fuel/efficiency map, gear shifting, and real-world traffic/road situations bring system discontinuities/switchings and pure state constraints into the problem formulation, which make the problem highly nonlinear and nontrivial to solve. This letter introduces smooth approximations to convert the original problem to an unconstrained (and penalized) smooth boundary-value problem. This approach eliminates the discussion of the switching structure and leads to a lightweight Newton-method-based solution procedure.

42 ENGINEERING↗
DOE OSTI2019

Adaptive multi-index collocation for uncertainty quantification and sensitivity analysis

In this paper, we present an adaptive algorithm to construct response surface approximations of high-fidelity models using a hierarchy of lower fidelity models. Our algorithm is based on multiindex stochastic collocation and automatically balances physical discretization error and response surface error to construct an approximation of model outputs. This surrogate can be used for uncertainty quantification (UQ) and sensitivity analysis (SA) at a fraction of the cost of a purely high-fidelity approach. We demonstrate the effectiveness of our algorithm on a canonical test problem from the UQ literature and a complex multi-physics model that simulates the performance of an integrated nozzle for an unmanned aerospace vehicle. We find that when the input-output response is sufficiently smooth our algorithm produces approximations that can be up to orders of magnitude more accurate than single fidelity approximations for a fixed computational budget.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Application of Ocean Thermal Energy Conversion (OTEC) Systems for Powering Safety Monitoring Systems of Offshore Oil and Gas Operations, OESI 2.0 M-1 T-1-P1.1 – Objective 3 Report: Collocation of OTEC with Offshore Oil and Gas Activities

This report is a component of a comprehensive research initiative aimed at evaluating the technoeconomic feasibility of deploying Ocean Thermal Energy Conversion (OTEC) systems to power safety monitoring systems for offshore oil and gas operations in the Gulf of America (GOA). The overarching study has three primary objectives: summarizing existing oil and gas equipment monitoring systems, modeling OTEC as a renewable marine energy source, and exploring the collocation of OTEC power sources with offshore oil and gas activities to offset power demand. This report specifically addresses Objective 3, focusing on the integration of OTEC systems with floating oil and gas facilities.

02 PETROLEUM↗
DOE OSTI2018

Ice particle production in mid-level stratiform mixed-phase clouds observed with collocated A-Train measurements

Abstract. Collocated A-Train CloudSat radar and CALIPSO lidar measurements between 2006 and 2010 are analyzed to study primary ice particle production characteristics in mid-level stratiform mixed-phase clouds on a global scale. For similar clouds in terms of cloud top temperature and liquid water path, Northern Hemisphere latitude bands have layer-maximum radar reflectivity (ZL) that is ∼ 1 to 8 dBZ larger than their counterparts in the Southern Hemisphere. The systematically larger ZL under similar cloud conditions suggests larger ice number concentrations in mid-level stratiform mixed-phase clouds over the Northern Hemisphere, which is possibly related to higher background aerosol loadings. Furthermore, we show that springtime northern mid- and high latitudes have ZL that is larger by up to 6 dBZ (a factor of 4 higher ice number concentration) than other seasons, which might be related to more dust events that provide effective ice nucleating particles. Our study suggests that aerosol-dependent ice number concentration parameterizations are required in climate models to improve mixed-phase cloud simulations, especially over the Northern Hemisphere.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Identifying a regional aerosol baseline in the eastern North Atlantic using collocated measurements and a mathematical algorithm to mask high-submicron-number-concentration aerosol events

Abstract. High-time-resolution measurements of in situ aerosol and cloud properties provide the ability to study regional atmospheric processes that occur on timescales of minutes to hours. However, one limitation to this approach is that continuous measurements often include periods when the data collected are not representative of the regional aerosol. Even at remote locations, submicron aerosols are pervasive in the ambient atmosphere with many sources. Therefore, periods dominated by local aerosol should be identified before conducting subsequent analyses to understand aerosol regional processes and aerosol–cloud interactions. Here, we present a novel method to validate the identification of regional baseline aerosol data by applying a mathematical algorithm to the data collected at the U.S. Department of Energy's (DOE) Atmospheric Radiation Measurement (ARM) user facility in the eastern North Atlantic (ENA). The ENA central facility (C1) includes an aerosol observing system (AOS) for the measurement of aerosol physical, optical, and chemical properties at time resolutions from seconds to minutes. A second temporary supplementary facility (S1), located ∼0.75 km from C1, was deployed for ∼1 year during the Aerosol and Cloud Experiments (ACE-ENA) campaign in 2017. First, we investigate the local aerosol at both locations. We associate periods of high submicron number concentration (Ntot) in the fine-mode condensation particle counter (CPC) and size distributions from the Ultra-High Sensitivity Aerosol Spectrometer (UHSAS) as a function of wind direction using a meteorology sensor with local sources. Elevated concentrations of Aitken-mode (< 100 nm diameter) particles were observed in correspondence with the wind directions associated with airport operations. At ENA, the Graciosa Airport and its associated activities were found to be the main sources of high-concentration aerosol events at ENA, causing peaks in 1 min Ntot that exceeded 8000 and 10 000 cm−3 at C1, in summer and winter, respectively, and 5000 cm−3 at S1 in summer. Periods with high Ntot not associated with these wind directions were also observed. As a result, the diverse local sources at ENA yielded a poor relationship between Ntot measurements collected at C1 and S1 (R2=0.03 with a slope =0.05±0.001). As a first approach to mask these events, the time periods when the wind direction was associated with the airport operations (west to northwest and southeast to south at C1 and east to south at S1) were applied. The meteorological masks removed 38.9 % of the data at C1 and 43.4 % at S1, and they did not significantly improve the relationship between the two sites (R2=0.18 with a slope =0.06±0.001). Due to the complexity of high-Ntot events observed at ENA, we develop and validate a mathematical ENA Aerosol Mask (ENA-AM) to identify high-Ntot events using 1 min resolution data from the AOS CPC at C1 and S1. After its parameterization and application, ENA-AM generated a high correlation between Ntot in the summer at C1 and S1 (R2=0.87 with a slope =0.84±0.001). We identified the regional baseline at ENA to be 428±228 cm−3 in the summer and 346±223 cm−3 in the winter. Lastly, we compared masked measurements from the AOS with the ARM Aerial Facility (AAF) during flights over C1 in the summer to understand submicron aerosol vertical mixing over C1. The high correlation (R2=0.71 with a slope of 1.04±0.01) observed between C1 and the AAF Ntot collected within an area of 10 km surrounding ENA and at altitudes < 500 m indicated that the submicron aerosol at ENA was well mixed within the first 500 m of the marine boundary layer during the month of July during ACE-ENA. Our novel method for determining a regional aerosol baseline at ENA can be applied to other time periods and at other locations with validation by a secondary site or additional collocated measurements.

54 ENVIRONMENTAL SCIENCES↗