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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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DOE OSTI2023

Canonical and noncanonical Hamiltonian operator inference

Here, a method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a straightforward linear solve given snapshot data and gray-box knowledge of the system Hamiltonian. Examples involving several hyperbolic partial differential equations show that the proposed method yields reduced models which, in addition to being accurate and stable with respect to the addition of basis modes, preserve conserved quantities well outside the range of their training data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Stress-constrained topology optimization of lattice-like structures using component-wise reduced order models

We report lattice-like structures can provide a combination of high stiffness with light weight that is useful in many applications, but a resolved finite element mesh of such structures results in a computationally expensive discretization. This computational expense may be particularly burdensome in many-query applications, such as optimization. We develop a stress-constrained topology optimization method for lattice-like structures that uses component-wise reduced order models as a cheap surrogate, providing accurate computation of stress fields while greatly reducing run time relative to a full order model. We demonstrate the ability of our method to produce large reductions in mass while respecting a constraint on the maximum stress in a pair of test problems. The ROM methodology provides a speedup of about 150x in forward solves compared to full order static condensation and provides a relative error of less than 5% in the relaxed stress.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Breaking Computational Barriers: Real-time Analysis and Optimization with Large-scale Nonlinear Models via Model Reduction

Model reduction for dynamical systems is a promising approach for reducing the computational cost of large-scale physics-based simulations to enable high-fidelity models to be used in many- query (e.g., Bayesian inference) and near-real-time (e.g., fast-turnaround simulation) contexts. While model reduction works well for specialized problems such as linear time-invariant systems, it is much more difficult to obtain accurate, stable, and efficient reduced-order models (ROMs) for systems with general nonlinearities. This report describes several advances that enable nonlinear reduced-order models (ROMs) to be deployed in a variety of time-critical settings. First, we present an error bound for the Gauss-Newton with Approximated Tensors (GNAT) nonlinear model reduction technique. This bound allows the state-space error for the GNAT method to be quantified when applied with the backward Euler time-integration scheme. Second, we present a methodology for preserving classical Lagrangian structure in nonlinear model reduction. This technique guarantees that important properties--such as energy conservation and symplectic time-evolution maps--are preserved when performing model reduction for models described by a Lagrangian formalism (e.g., molecular dynamics, structural dynamics). Third, we present a novel technique for decreasing the temporal complexity --defined as the number of Newton-like iterations performed over the course of the simulation--by exploiting time-domain data. Fourth, we describe a novel method for refining projection-based reduced-order models a posteriori using a goal-oriented framework similar to mesh-adaptive h -refinement in finite elements. The technique allows the ROM to generate arbitrarily accurate solutions, thereby providing the ROM with a 'failsafe' mechanism in the event of insufficient training data. Finally, we present the reduced-order model error surrogate (ROMES) method for statistically quantifying reduced- order-model errors. This enables ROMs to be rigorously incorporated in uncertainty-quantification settings, as the error model can be treated as a source of epistemic uncertainty. This work was completed as part of a Truman Fellowship appointment. We note that much additional work was performed as part of the Fellowship. One salient project is the development of the Trilinos-based model-reduction software module Razor , which is currently bundled with the Albany PDE code and currently allows nonlinear reduced-order models to be constructed for any application supported in Albany. Other important projects include the following: 1. ROMES-equipped ROMs for Bayesian inference: K. Carlberg, M. Drohmann, F. Lu (Lawrence Berkeley National Laboratory), M. Morzfeld (Lawrence Berkeley National Laboratory). 2. ROM-enabled Krylov-subspace recycling: K. Carlberg, V. Forstall (University of Maryland), P. Tsuji, R. Tuminaro. 3. A pseudo balanced POD method using only dual snapshots: K. Carlberg, M. Sarovar. 4. An analysis of discrete v. continuous optimality in nonlinear model reduction: K. Carlberg, M. Barone, H. Antil (George Mason University). Journal articles for these projects are in progress at the time of this writing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Analytical model for drag reduction on liquid-infused structured non-wetting surfaces

Liquid-infused structured non-wetting surfaces provide alternating no-slip and partial slip boundary conditions to the fluid flow, resulting in reduced friction at the interface. In this paper, an analytical model is developed for the evaluation of effective slip and, in turn, friction factor and drag reduction on liquid-infused structured non-wetting surfaces. By considering the entire range of anisotropy and heterogeneity of the surface structures as well as the full range of partial slip offered by the infusion liquid, the present model eliminates empirical fitting or correlations that are inherent in previous studies. Based on the effective slip length, drag reduction and skin friction coefficient values for Newtonian flow between two infinite parallel plates and flow in round tubes are presented. Extension of Moody charts for non-wetting surfaces and design maps of surface meso/micro/nano texturing for achieving desired drag reduction are presented for a broad range of engineering applications. The paper further presents independent validation of the model across experimental and computational data from the literature and brings together several previous studies in a unified manner.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Model Reduction for Compressible Cavity Simulations Towards Uncertainty Quantification of Structural Loading

This report summarizes FY16 progress towards enabling uncertainty quantification for compressible cavity simulations using model order reduction (MOR). The targeted application is the quantification of the captive-carry environment for the design and qualification of nuclear weapons systems. To accurately simulate this scenario, Large Eddy Simulations (LES) require very fine meshes and long run times, which lead to week-long runs even on parallel state-of-the-art super- computers. MOR can reduce substantially the CPU-time requirement for these simulations. We describe two approaches for model order reduction for nonlinear systems, which can yield significant speed-ups when combined with hyper-reduction: the Proper Orthogonal Decomposition (POD)/Galerkin approach and the POD/Least-Squares Petrov Galerkin (LSPG) approach. The implementation of these methods within the in-house compressible flow solver SPARC is discussed. Next, a method for stabilizing and enhancing low-dimensional reduced bases that was developed as a part of this project is detailed. This approach is based on a premise termed "minimal subspace rotation", and has the advantage of yielding ROMs that are more stable and accurate for long-time compressible cavity simulations. Numerical results for some laminar cavity problems aimed at gauging the viability of the proposed model reduction methodologies are presented and discussed.

42 ENGINEERING↗
DOE OSTI2024

Accelerating structural dynamics simulations with localised phenomena through matrix compression and projection‐based model order reduction

In this work, a novel approach is introduced for accelerating the solution of structural dynamics problems in the presence of localised phenomena, such as cracks. For this category of problems, conventional projection-based Model Order Reduction (MOR) methods are either limited with respect to the range of system configurations that can be represented or require frequent solutions of the Full Order Model (FOM) to update the low-dimensional spaces, in which solutions are represented. In the proposed approach, low-dimensional spaces, constructed for the healthy structure, are enriched with appropriately selected columns of the flexibility matrix of the system. It can be shown that these spaces contain the solution to the original problem for the static case, while their dimension is much smaller. In order to allow their online construction for arbitrary localised features, the full flexibility matrix of the system should be available. To this end, a hierarchical representation is used for the matrices involved, allowing to compute the flexibility matrix efficiently and with reduced memory requirements. The resulting method offers significant speedups, without sacrificing the flexibility and accuracy of the full order model. The performance and limitations of the approach are studied through a series of examples in structural dynamics.

fracture mechanics↗
DOE OSTI2018

Structure- and Physics-Preserving Reductions of Power Grid Models

The large size of multiscale, distribution and transmission, power grids hinders fast systemwide estimation and real-time control and optimization of operations. This paper studies graph reduction methods of power grids that are favorable for fast simulations and follow-up applications. While the classical Kron reduction has been successful in reduced order modeling of power grids with traditional, hierarchical design, the selection of reference nodes for the reduced model in a multiscale, distribution and transmission, network becomes ambiguous. In this work we extend the use of the iterative Kron reduction by utilizing the electric grid's graph topology for the selection of reference nodes, consistent with the design features of multiscale networks. Additionally, we propose further reductions by aggregation of coherent subnetworks of triangular meshes, based on the graph topology and network characteristics, in order to preserve currents and build another power-flow equivalent network. Our reductions are achieved through the use of iterative aggregation of subgraphs that include general tree structures, lines, and triangles. Important features of our reduction algorithms include that (i) the reductions are either equivalent to the Kron reduction or otherwise produce a power-flow equivalent network; (ii) due to the mentioned power-flow equivalence, the reduced network can model the dynamic of the swing equations for a lossless, inductive, steady state network; (iii) the algorithms efficiently utilize hash tables to store the sequential reduction steps. The third feature allows for easy reintroduction of detailed models into the reduced, conceptual network and makes the final reduced order model backward compatible with a sequence of intermediate, partially reduced networks with varying resolution---the ordered sequence of iterative reductions corresponds to a sequence of reduced order models. The performance of our graph reduction algorithms and features of the reduced grids are discussed on a real-word transmission and distribution grid. We produce visualizations of the reduced models through open source libraries and release our reduction algorithms with example code and toy data.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

On modeling subgrid-scale macro-structures in narrow twisted channels

Porosity-based subgrid topography models often fail to capture the effects of subgrid-scale topographic features in the interior of coarse grid cells. Existing approaches that modify bottom roughness or a drag coefficient are inadequate for macro-structures (large emergent or submerged obstacles) in subgrid-scale narrow twisted channels. Such structures partially block the cross-sectional area and provide enhanced topographic dissipation – effects that are not well represented by a drag coefficient that scales on a coarse-grid cell-averaged velocity and the cell volume. The relative alignment between mesh and flow further complicates this problem as it makes the subgrid model sensitive to mesh design. In the present study, three new approaches for simulating subgrid-scale macro-structures in narrow channels are proposed. The interior partial-blocking effect of structures is modeled as reduction of grid face-area. The sheltering of flow volumes around obstacles, which leads to topographic dissipation, is modeled by reducing the cell volume in the momentum equation (only). A mesh-shift procedure is designed to optimize mesh alignment for identifiable subgrid features. Combining the three subgrid methods improves the approximation of surface elevation and in-channel flow rate with a coarse-grid model. Tests are conducted for channelized flow using both synthetic domains and real marsh topography. Finally, the new methods reduce the overall mesh dependency of the subgrid model and provides stronger physical connection between effects of macro-structures and their geometry at coarse grid scales.

42 ENGINEERING↗
DOE OSTI2021

Modeling and simulation of earthquake soil structure interaction excited by inclined seismic waves

Presented is an application of wave potential formulation (WPF) together with domain reduction method (DRM) to modeling earthquake soil structure interaction (ESSI) behavior in horizontally layered ground under inclined incident seismic waves. Wave potential formulation is used to develop a spatially varying, inclined seismic wave field from incident Primary (P) and Secondary (S) waves that propagate through layered ground. Developed seismic wave field is then used to develop effective forces for Domain Reduction Method that are then used for analyzing ESSI response of a soil structure system. Developed methodology, called WPF-DRM, is verified using analytic solution for a free field response of layered ground subjected to inclined incident waves. Developed WPF-DRM methodology is illustrated through analysis of an ESSI response of a deeply embedded structure, a small modular reactor (SMR) subjected to incident S wave polarized in vertical plane (SV) with variation in inclinations and frequencies. Presented example highlights the influences of incident wave inclination and frequency on ESSI response of analyzed SMR.

58 GEOSCIENCES↗
DOE OSTI2024

Accelerating uncertainty quantification in incremental dynamic analysis using dimension reduction-based surrogate modeling

We propose a surrogate modeling framework based on dimension reduction to facilitate the quantification of seismic risk of structural systems in performance-based earthquake engineering. The framework adopts incremental dynamic analysis (IDA) for addressing hazard variability, and promotes significant computational efficiency improvement for propagating epistemic uncertainties associated with the structural models. It utilizes both linear and nonlinear dimension reduction approaches, equipped with inverse mappings, to learn a functional between the input parameter space (e.g., the epistemic uncertainties of the structure) to the high-dimensional output space created through the IDA implementation across different ground motions and seismic intensity levels. Polynomial chaos expansion is adopted as the surrogate model to learn this functional in the reduced space. A nine-story steel moment-resisting frame with uncertain structural properties is used as a testbed. Furthermore, we select the seismic fragility curves as a measure of the structure’s seismic performance, since it provides an estimate of the probability of entering specified damage states for given levels of ground shaking.

42 ENGINEERING↗
DOE OSTI2023

A small-box approach to the local crystal structure of Y 3 NbO 7

The local crystal structure of Y 3 NbO 7 was probed using neutron total scattering. Five different structural models were fit to the experimental pair distribution function of this material up to 15 Å. Fits of defect fluorite (Fm$\overline{3}$m), pyrochlore (Fd$\overline{3}$m), and orthorhombic C weberite models (C222 1 ) were attempted based on prior structural investigations of Y 3 NbO 7 and related fluorite-based materials. Orthorhombic P weberite (P222 1 ) and monoclinic weberite models (P112 1 ) were derived via symmetry reduction of the orthorhombic C weberite structure. All models except monoclinic weberite failed to reproduce the experimental pair distribution function. Misfits were clearly visible for peaks arising from atom pairs within the first coordination shell (defect fluorite and pyrochlore) and beyond (orthorhombic C and P weberite). By contrast, monoclinic weberite (γ ≈ 91.8°) provided an excellent fit, with no major misfits observed. This unit cell features distorted YO 8 dodecahedra, YO 7 monocapped octahedra, and NbO 6 octahedra as building blocks. Comparison between the topologies of the cationic and anionic substructures in monoclinic weberite and its parent orthorhombic C structure revealed displacements of the metal atoms along the [100] direction and a less compact spatial distribution of oxygen atoms along the a axis. In conclusion, the monoclinic weberite model presented herein may serve as a starting point to revisit structural modeling of fluorite-based materials with challenging local structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

A Dicationic fac -Re(bpy)(CO) 3 Cl for CO 2 Electroreduction at a Reduced Overpotential

Here, a dicationic Re bipyridine-type complex, fac-Re(6,6'-(2-((trimethylammonio)-methyl)phenyl)-2,2'-bipyridine)(CO) 3 Cl hexafluorophosphate (1 2+ ), has been synthesized and its electrochemical behavior under Ar and CO 2 has been investigated. The presence of pendent tetra-alkylammonium cations induces an anodic shift in the electrocatalytic potential for CO 2 reduction relative to structurally similar model complexes. The electrochemical mechanisms in anhydrous CH 3 CN and in the presence of weak acids (water or trifluoroethanol) have been analyzed using cyclic voltammetry assisted by infrared spectroelectrochemistry and theoretical calculations. The dication enables catalysis at a diminished potential through coulombic stabilization of the doubly reduced pentacoordinate species, its CO 2 adduct, the hydroxide anion, and the conjugate base formed during acid-assisted C-OH bond cleavage of the metallocarboxylic acid to the metallocarbonyl and H 2 O. The major reduction product is CO, but in the presence of trifluoroethanol, formate is also produced with 14% Faradaic efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method used to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.

42 ENGINEERING↗
DOE OSTI2022

Stabilization of Cu 2 O through Site-Selective Formation of a Co 1 Cu Hybrid Single-Atom Catalyst

Single-atom catalysts (SACs) consist of a low coverage of isolated metal atoms dispersed on a metal substrate, called single-atom alloys (SAAs), or alternatively single metal atoms coordinated to oxygen atoms on an oxide support. We present the synthesis of a new type of Co 1 Cu SAC centers on a Cu 2 O(111) support by means of a site-selective atomic layer deposition technique. Isolated metallic Co atoms selectively coordinate to the native oxygen vacancy sites (Cu sites) of the reconstructed Cu 2 O(111) surface, forming a Co 1 Cu SAA with no direct Co–O x bonds. The centers, here referred to as Co 1 Cu hybrid SACs, are found to stabilize the active Cu + sites of the low-cost Cu 2 O catalyst that otherwise is prone to deactivation under reaction conditions. The stability of the Cu 2 O(111) surface was investigated by synchrotron radiation-based ambient-pressure X-ray photoelectron spectroscopy under reducing CO environment. The structure and reduction reaction are modeled by density functional theory calculations, in good agreement with experimental results.

36 MATERIALS SCIENCE↗