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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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At least 1,171 records · Page 65
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Forward sensitivity analysis and mode dependent control for closure modeling of Galerkin systems

Model reduction by projection-based approaches is often associated with losing some of the important features that contribute towards the dynamics of the retained scales. As a result, a mismatch occurs between the predicted trajectories of the original system and the truncated one. We put forth a framework to apply a continuous time control signal in the latent space of the reduced order model (ROM) to account for the effect of truncation. We set the control input using parameterized models by following energy transfer principles. Our methodology relies on observing the system behavior in the physical space and using the projection operator to restrict the feedback signal into the latent space. Then, we leverage the forward sensitivity method (FSM) to derive relationships between the feedback and the desired mode-dependent control. We test the performance of the proposed approach using two test cases, corresponding to viscous Burgers and vortex merger problems at high Reynolds number. Results show that the ROM trajectory with the applied FSM control closely matches its target values in both the data-dense and data-sparse regimes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Lagrange-Remap strategy for multi-material fluid-solid simulations using compressive limiters

In the present work, the Lagrange-Remap strategy proposed in [1] is extended to multi-material fluid-solid simulations. Both hypo-elastic and hyper-elastic material models are considered to describe the mechanical behavior of the solids. In practice, the deviatoric stress tensor (for hypo-elastic materials) and the left Cauchy-Green tensor (for isotropic hyper-elastic materials) are remapped, while the use of compressive limiters effectively reduces numerical diffusion during the remapping step. The simplicity of this diffuse interface approach is emphasized in the context of multi-material fluid-solid simulations. A series of Lagrange-Remap test cases, involving both solids and fluids, are conducted and compared with reference Lagrangian simulations, demonstrating the robustness and accuracy of the overall numerical strategy.

Compressive limiters↗
DOE OSTI2019

Eulerian-Eulerian large eddy simulation of two-phase dilute bubbly flows

An efficient mathematical model is presented for conducting large eddy simulation (LES) of turbulent bubbly flows at low gas hold-ups. The mathematical model is based on the filtered multi-fluid equations derived by application of the component-weighted volume-averaging process of each phase. A two-fluid model is applied to the filtered set of equations, yielding a more computationally tractable set of filtered equations. The filtered equations are formulated in generalized curvilinear coordinates to simulate turbulent gas-liquid bubbly flows in complex geometries. The Germano model is used to account for sub-grid turbulent stresses. The gas and liquid momentum equations are discretized with the hybrid staggered/non-staggered method. The performance of the developed mathematical model is demonstrated by simulating the benchmark test case of a turbulent gas-liquid bubbly flow in a rectangular bubble column. The accuracy of the proposed method is assessed via comparison with the experimental data and other numerical results in the literature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

A new numerically stable sequential algorithm for coupled finite-strain elastoplastic geomechanics and flow

In this work, we propose a new numerically stable sequential implicit method for coupled flow and finite-strain multiplicative elastoplastic geomechanics. We find from stability analysis that the sequential method that solves the flow problem first by fixing the first Piola-Kirchhoff total stress, solving the geomechanics (solid deformation) problem at the next step, is unconditionally stable (contractive and B-stable). In this sense, this method named the fixed first Piola-Kirchhoff stress method is an extension of the fixed stress method in coupled flow and infinitesimal geomechanics. We also study the fixed second Piola-Kirchhoff stress method, comparing it with the fixed first Piola-Kirchhoff stress method, because the constitutive relations are formulated by the second Piola-Kirchhoff total stress, although fixing the second Piola-Kirchhoff total stress field does not provide theoretical unconditional stability. In space discretization, we use the finite element method for the geomechanics problem with the total Lagrangian approach, while employing the finite volume method for the flow problem. Geometrical nonlinearity from the total Lagrangian approach results in full-tensor permeability even if the initial permeability is isotropic. To consider the full-tensor permeability accurately, we employ the multipoint flux approximation in solving the flow problem. In time discretization, the backward Euler method is used. Then, we perform numerical experiments of the two fixed-stress sequential methods with various scenarios, and find superiority of their numerical stability. Specifically, the two fixed-stress sequential methods provide almost identical results for elasticity. For J2 plasticity, the two sequential methods yield slightly different numerical results although the trends of the results are similar. For the Drucker-Prager plasticity, we find that the results from the two methods are almost identical. For all the test cases, the two sequential methods are numerically stable.

58 GEOSCIENCES↗
DOE OSTI2020

Data-driven variational multiscale reduced order models

We propose a new data-driven reduced order model (ROM) framework that centers around the hierarchical structure of the variational multiscale (VMS) methodology and utilizes data to increase the ROM accuracy at a modest computational cost. The VMS methodology is a natural fit for the hierarchical structure of the ROM basis: In the first step, we use the ROM projection to separate the scales into three categories: (i) resolved large scales, (ii) resolved small scales, and (iii) unresolved scales. In the second step, we explicitly identify the VMS–ROM closure terms, i.e., the terms representing the interactions among the three types of scales. In the third step, we use available data to model the VMS–ROM closure terms. Thus, instead of phenomenological models used in VMS for standard numerical discretizations (e.g., eddy viscosity models), we utilize available data to construct new structural VMS–ROM closure models. Specifically, we build ROM operators (vectors, matrices, and tensors) that are closest to the true ROM closure terms evaluated with the available data. We test the new data-driven VMS–ROM in the numerical simulation of four test cases: (i) the 1D Burgers equation with viscosity coefficient v = 10 -3 ; (ii) a 2D flow past a circular cylinder at Reynolds numbers, Re = 100, Re = 500, and Re= 1000; (iii) the quasi-geostrophic equations at Reynolds number Re = 450 and Rossby number Ro = 0.0036; and (iv) a 2D flow over a backward facing step at Reynolds number Re = 1000. The numerical results show that the data-driven VMS–ROM is significantly more accurate than standard ROMs.

42 ENGINEERING↗
DOE OSTI2021

Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting

In this paper, we develop high-order nodal discontinuous Galerkin (DG) methods for hyperbolic conservation laws that satisfy invariant domain preserving properties using subcell flux corrections and convex limiting. These methods are based on a subcell flux corrected transport (FCT) methodology that involves blending a high-order target scheme with a robust, low-order invariant domain preserving method that is obtained using a graph viscosity technique. Furthermore, the new low-order discretizations are based on sparse stencils which do not increase with the polynomial degree of the high-order DG method. As a result, the accuracy of the low-order method does not degrade when used with high-order target methods. The method is applied to both scalar conservation laws, for which the discrete maximum principle is naturally enforced, and to systems of conservation laws such as the Euler equations, for which positivity of density and a minimum principle for specific entropy are enforced. Numerical results are presented on a number of benchmark test cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A compute-bound formulation of Galerkin model reduction for linear time-invariant dynamical systems

This work aims to advance computational methods for projection-based reduced-order models (ROMs) of linear time-invariant (LTI) dynamical systems. For such systems, current practice relies on ROM formulations expressing the state as a rank-1 tensor (i.e., a vector), leading to computational kernels that are memory bandwidth bound and, therefore, ill-suited for scalable performance on modern architectures. This weakness can be particularly limiting when tackling many-query studies, where one needs to run a large number of simulations. This work introduces a reformulation, called rank-2 Galerkin, of the Galerkin ROM for LTI dynamical systems which converts the nature of the ROM problem from memory bandwidth to compute bound. We present the details of the formulation and its implementation, and demonstrate its utility through numerical experiments using, as a test case, the simulation of elastic seismic shear waves in an axisymmetric domain. We quantify and analyze performance and scaling results for varying numbers of threads and problem sizes. In conclusion, we present an end-to-end demonstration of using the rank-2 Galerkin ROM for a Monte Carlo sampling study. We show that the rank-2 Galerkin ROM is one order of magnitude more efficient than the rank-1 Galerkin ROM (the current practice) and about 970 times more efficient than the full-order model, while maintaining accuracy in both the mean and statistics of the field.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

$\mathrm{IH}$-$\mathrm{GAN}$: A conditional generative model for implicit surface-based inverse design of cellular structures

Variable-density cellular structures can overcome connectivity and manufacturability issues of topologically optimized structures, particularly those represented as discrete density maps. However, the optimization of such cellular structures is challenging due to the multiscale design problem. Past work addressing this problem generally either only optimizes the volume fraction of single-type unit cells but ignoring the effects of unit cell geometry on properties, or considers the geometry–property relation but builds this relation via heuristics. In contrast, we propose a simple yet more principled way to accurately model the property to geometry mapping using a conditional deep generative model, named Inverse Homogenization Generative Adversarial Network (IH-GAN). It learns the conditional distribution of unit cell geometries given properties and can realize the one-to-many mapping from properties to geometries. Here we further reduce the complexity of IH-GAN by using the implicit function parameterization to represent unit cell geometries. Results show that our method can 1) generate various unit cells that satisfy given material properties with high accuracy (R 2 -scores between target properties and properties of generated unit cells >98%) and 2) improve the optimized structural performance over the conventional variable-density single-type structure. In the minimum compliance example, our IH-GAN generated structure achieves a 79.7% reduction in concentrated stress and an extra 3.03% reduction in displacement. In the target deformation examples, our IH-GAN generated structure reduces the target matching error by 86.4% and 79.6% for two test cases, respectively. We also demonstrated that the connectivity issue for multi-type unit cells can be solved by transition layer blending.

42 ENGINEERING↗
DOE OSTI2025

Non-intrusive reduced-order modeling for dynamical systems with spatially localized features

This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced and full-order non-intrusive modeling, namely Operator Inference (OpInf) and sparse Full-Order Model (sFOM) inference. We decompose the domain into two complementary subdomains that exhibit fast and slow singular value decay. The dynamics of the subdomain exhibiting slow singular value decay are learned with sFOM while the dynamics with intrinsically low dimensionality on the complementary subdomain are learned with OpInf. The resulting, coupled OpInf-sFOM formulation leverages the computational efficiency of OpInf and the high resolution of sFOM, and thus enables fast non-intrusive predictions for conditions beyond those sampled in the training data set. A novel regularization technique with a closed-form solution based on the Gershgorin disk theorem is introduced to promote stable sFOM and OpInf models. We also provide a data-driven indicator for subdomain selection and ensure solution smoothness over the interface via a post-processing interpolation step. We evaluate the efficiency of the approach in terms of offline and online speedup through a quantitative, parametric computational cost analysis. We demonstrate the coupled OpInf-sFOM formulation for two test cases: a one-dimensional Burgers’ model for which accurate predictions beyond the span of the training snapshots are presented, and a two-dimensional parametric model for the Pine Island Glacier ice thickness dynamics, for which the OpInf-sFOM model achieves an average prediction error on the order of 1% with an online speedup factor of approximately 8$\times$ compared to the numerical simulation.

42 ENGINEERING↗
DOE OSTI2025

A comparative study of calibration techniques for finite strain elastoplasticity: Numerically-exact sensitivities for FEMU and VFM

Accurate identification of material parameters is crucial for predictive modeling in computational mechanics. Here, the two primary approaches in the experimental mechanics community for calibration from full-field digital image correlation data are known as finite element model updating (FEMU) and the virtual fields method (VFM). In VFM, the objective function is a squared mismatch between internal and external virtual work or power. In FEMU, the objective function quantifies the weighted mismatch between model predictions and corresponding experimentally measured quantities of interest. It is minimized by iteratively updating the parameters of an FE model. While FEMU is seen as more flexible, VFM is commonly used instead of FEMU due to its considerably greater computational expense. However, comparisons between the two methods usually involve approximations of gradients or sensitivities with finite difference schemes, thereby making direct assessments difficult. Hence, in this study, we compare VFM and FEMU in the context of numerically-exact sensitivities obtained through local sensitivity analyses and the application of automatic differentiation software. To this end, we conduct a series of test cases to assess both methods under practical challenges using a finite strain elastoplasticity model.

Automatic differentiation↗
DOE OSTI2016

An a priori DNS study of the shadow-position mixing model

In this study, the modeling of mixing by molecular diffusion is a central aspect for transported probability density function (tPDF) methods. In this paper, the newly-proposed shadow position mixing model (SPMM) is examined, using a DNS database for a temporally evolving di-methyl ether slot jet flame. Two methods that invoke different levels of approximation are proposed to extract the shadow displacement (equivalent to shadow position) from the DNS database. An approach for a priori analysis of the mixing-model performance is developed. The shadow displacement is highly correlated with both mixture fraction and velocity, and the peak correlation coefficient of the shadow displacement and mixture fraction is higher than that of the shadow displacement and velocity. This suggests that the composition-space localness is reasonably well enforced by the model, with appropriate choices of model constants. The conditional diffusion of mixture fraction and major species from DNS and from SPMM are then compared, using mixing rates that are derived by matching the mixture fraction scalar dissipation rates. Good qualitative agreement is found, for the prediction of the locations of zero and maximum/minimum conditional diffusion locations for mixture fraction and individual species. Similar comparisons are performed for DNS and the IECM (interaction by exchange with the conditional mean) model. The agreement between SPMM and DNS is better than that between IECM and DNS, in terms of conditional diffusion iso-contour similarities and global normalized residual levels. It is found that a suitable value for the model constant c that controls the mixing frequency can be derived using the local normalized scalar variance, and that the model constant a controls the localness of the model. A higher-Reynolds-number test case is anticipated to be more appropriate to evaluate the mixing models, and stand-alone transported PDF simulations are required to more fully enforce localness and to assess model performance.

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

A general probabilistic approach for the quantitative assessment of LES combustion models

The Wasserstein metric is introduced as a probabilistic method to enable quantitative evaluations of LES combustion models. The Wasserstein metric can directly be evaluated from scatter data or statistical results through probabilistic reconstruction. The method is derived and generalized for turbulent reacting flows, and applied to validation tests involving a piloted turbulent jet flame with inhomogeneous inlets. It is shown that the Wasserstein metric is an effective validation tool that extends to multiple scalar quantities, providing an objective and quantitative evaluation of model deficiencies and boundary conditions on the simulation accuracy. Several test cases are considered, beginning with a comparison of mixture-fraction results, and the subsequent extension to reactive scalars, including temperature and species mass fractions of CO and CO2. To demonstrate the versatility of the proposed method in application to multiple datasets, the Wasserstein metric is applied to a series of different simulations that were contributed to the TNF-workshop. Analysis of the results allows to identify competing contributions to model deviations, arising from uncertainties in the boundary conditions and model deficiencies. These applications demonstrate that the Wasserstein metric constitutes an easily applicable mathematical tool that reduce multiscalar combustion data and large datasets into a scalar-valued quantitative measure.

42 ENGINEERING↗
DOE OSTI2021

Preheating and premixing effects on NO x emissions in a high-pressure axially staged combustor

NO x emissions remain a primary concern for modern and future gas turbines, particularly as we progress towards a net-zero carbon future. It is critical to identify novel strategies to mitigate environmental pollutants for both modern turbines operated on natural gas and future turbines projected to use carbon-free fuels (such as hydrogen). In the current study, NO x emissions of a reacting methane-air jet in a vitiated crossflow are experimentally investigated in a model axially staged combustor at 5 atm. The combustion products from the main stage combustor flow into the axial stage at temperatures ranging from 1580 to 1650 °C. The axial stage contains a reacting jet in crossflow, which provides an overall temperature rise ranging from 50 to 220 °C to generate exit temperatures similar to gas turbine engines. The focus of this paper is to explore the effects of flame liftoff and ignition timescales on the NO x contribution of this secondary jet. This is done by varying the premixed level and preheat temperature of the axial jet. The effects are explored at different momentum flux ratios (J), jet equivalence ratios (φ jet ), exit temperatures (T exit ), and main stage (headend) temperatures (T HE ). High-speed CH* chemiluminescence imaging is employed for each test case to determine the flame stabilization point. For a given temperature rise and combustor exit temperature, an increase in ignition delay was observed with a decrease in jet temperature. This provided a NO x benefit, particularly for jets that are injected at or close to an ignitable mixture fraction. Similarly, the coaxial injector caused a significant ignition delay compared to the fully premixed injector; this also led to a NO x benefit. Overall, the results show that a thermally driven delay in the axial stage provides a greater NO x reduction than a mixing delay.

03 NATURAL GAS↗
DOE OSTI2023

A projection-based analytical Jacobian framework for chemical kinetics applications

A major challenge in simulating complex combustion systems with detailed chemical kinetic models is the cost of integrating the chemical source terms, often done using stiff ODE solvers that require frequent Jacobian evaluations. Using analytically derived Jacobian matrices instead of divided-difference-based numerical Jacobian approximations can significantly reduce the associated computational cost. However, ambiguities arise in the formulation of analytical Jacobians because the chemical state of the system, or state vector, can be expressed in multiple ways, involving variables that are typically not independent from one another. Here, in this work, the consequences of those ambiguities on practical calculations are characterized in detail, and a generalized, projection-based framework is proposed as a mitigation strategy. Performances are assessed in a series of test cases involving a variety of configurations and numerical solution approaches. Results show that with proper treatment, commonly used analytical Jacobian formulations can be considered as equivalent for practical purposes, thereby alleviating concerns that the state vector chosen to express the governing equations and corresponding analytical Jacobian may significantly impact the accuracy of the simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Time-dependent-bases with local CUR decomposition method for accelerating turbulent combustion simulations

Here, this study presents a novel reduced-order modeling framework, Time-Dependent Bases with Local CUR decomposition (TDB-L-CUR), designed to efficiently and accurately approximate the species transport equations in reacting flow simulations. The method extends the existing TDB-CUR approach for chemically reacting flows (Jung et al. Comput. Methods Appl. Mech. Engrg. 437 (2025) 117758), which leverages matrix decomposition techniques to form a global-in-space, time-dependent low-dimensional manifold. While TDB-CUR performs well in homogeneous systems, it may be less well-suited to spatially heterogeneous systems such as turbulent flames, where higher-rank approximations are typically required. The proposed TDB-L-CUR framework introduces two methodological extensions to the baseline approach. First, it applies unsupervised clustering to partition the physical domain into distinct regions, enabling spatially localized manifold construction, thereby reducing the rank required for the reduced-order representation. Second, it incorporates a computational singular perturbation (CSP)-based scheme for identifying and penalizing fast species, allowing for spatio-temporally adaptive mitigation of chemical stiffness. The proposed framework is validated on a hierarchy of test cases, including a one-dimensional premixed flame, a two-dimensional nonpremixed ignition case with vortex interaction, and a three-dimensional turbulent premixed flame. TDB-L-CUR significantly improves accuracy over TDB-CUR while further reducing computational cost. The fully on-the-fly formulation of TDB-L-CUR (i.e., requiring no offline training or prior knowledge) makes it a robust and scalable tool for reduced-order modeling of reactive flows.

Local manifold↗
DOE OSTI2021

Non-orthogonal computational grids for studying dislocation motion in phase field approaches

In this work, new non-orthogonal computational grids are implemented into a phase field model called Phase Field Dislocation Dynamics (PFDD). We demonstrate that the new non-orthogonal grid can accommodate multiple slip planes in either the face centered cubic (FCC) or body centered cubic (BCC) crystallographic systems. Here, we show that they avoid numerical errors induced when modeling glide on inclined slip planes in an orthogonal grid. The Gibbs effect that arises in the orthogonal or rotated orthogonal grids is substantially diminished when a non-orthogonal grid is employed. A few test cases demonstrate the effectiveness of using non-orthogonal grids in solving systems with multiple non-planar slip systems.

36 MATERIALS SCIENCE↗
DOE OSTI2018

A multitree approach for global solution of ACOPF problems using piecewise outer approximations

Electricity markets rely on the rapid solution of the optimal power flow (OPF) problem to determine generator power levels and set nodal prices. Traditionally, the OPF problem has been formulated using linearized, approximate models, ignoring nonlinear alternating current (AC) physics. These approaches do not guarantee global optimality or even feasibility in the real ACOPF problem. We introduce an outer-approximation approach to solve the ACOPF problem to global optimality based on alternating solution of upper- and lower-bounding problems. The lower-bounding problem is a piecewise relaxation based on strong second-order cone relaxations of the ACOPF, and these piecewise relaxations are selectively refined at each major iteration through increased variable domain partitioning. Our approach is able to efficiently solve all but one of the test cases considered to an optimality gap below 0.1%. This approach opens the door for global solution of MINLP problems with AC power flow equations.

42 ENGINEERING↗
DOE OSTI2017

A framework for modeling and optimizing dynamic systems under uncertainty

Algebraic modeling languages (AMLs) have drastically simplified the implementation of algebraic optimization problems. However, there are still many classes of optimization problems that are not easily represented in most AMLs. These classes of problems are typically reformulated before implementation, which requires significant effort and time from the modeler and obscures the original problem structure or context. In this work we demonstrate how the Pyomo AML can be used to represent complex optimization problems using high-level modeling constructs. We focus on the operation of dynamic systems under uncertainty and demonstrate the combination of Pyomo extensions for dynamic optimization and stochastic programming. We use a dynamic semibatch reactor model and a large-scale bubbling fluidized bed adsorber model as test cases.

97 MATHEMATICS AND COMPUTING↗