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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

Application of Exactly Linearized Error Transport Equations to AIAA CFD Prediction Workshops

The computational fluid dynamics (CFD) prediction workshops sponsored by the AIAA have created invaluable opportunities in which to discuss the predictive capabilities of CFD in areas in which it has struggled, e.g., cruise drag, high-lift, and sonic boom pre diction. While there are many factors that contribute to disagreement between simulated and experimental results, such as modeling or discretization error, quantifying the errors contained in a simulation is important for those who make decisions based on the computational results. The linearized error transport equations (ETE) combined with a truncation error estimate is a method to quantify one source of errors. The ETE are implemented with a complex-step method to provide an exact linearization with minimal source code modifications to CFD and multidisciplinary analysis methods. The equivalency of adjoint and linearized ETE functional error correction is demonstrated. Uniformly refined grids from a series of AIAA prediction workshops demonstrate the utility of ETE for multidisciplinary analysis with a connection between estimated discretization error and (resolved or under-resolved) flow features.

Derlaga, Joseph M.↗
NASA NTRS2015

Aerodynamic Shape Optimization Benchmarks with Error Control and Automatic Parameterization

Results are presented for four optimization benchmark problems posed by the AIAA Aerodynamic Design Optimization Discussion Group. The benchmarks are intended to exercise optimization frameworks on representative airfoil and wing design problems. All problems involve drag minimization subject to geometric and aerodynamic constraints. Our design approach involves two forms of adaptation. First, the shape parameterization is gradually and automatically enriched from an initially coarse search space. Second, adjoint solutions are used to drive adaptive mesh refinement to control discretization error. The error threshold is tailored so that the nest meshes, with the greatest accuracy, are used only when nearing the optimum. On the inviscid airfoil design problem, while reducing the drag by a factor of 10, we show how the combination of progressive parameterization and tiered discretization error control can dramatically accelerate the optimization. On the viscous airfoil design problem, we use inviscid analysis-driven optimization to reduce the total drag by a factor of two. Next, we improve the span efficiency factor of a wing by performing twist optimization. Finally, we optimize the Common Research Model wing, managing to hold drag roughly fixed, while targeting an initially-violated pitching moment constraint. Our approach aims to introduce greater complexity and accuracy only when necessary to improve the design, and also support a greater degree of automation.

Anderson, George R.↗
NASA NTRS2019

Adjoint-Based Mesh Adaptation and Shape Optimization for Simulations with Propulsion

Objectives: Reliable evaluation of mass flow rates through permeable boundaries - Estimate and control discretization error- Consider both computational domain outflow and inflow- Applicable to simulating propulsion-system effects, as well as secondary flow paths - Explore feasibility of handling more general outputs at domain boundaries. Design optimization subject to mass-flow-rate constraints - Improve aerodynamic performance and reduce noise due to sonic boom - Control discretization error in design space to improve confidence in final designs.

Nemec, Marian↗
DOE OSTI2025

Addendum: Unified framework for open quantum dynamics with memory

This Addendum presents a detailed analysis of the discretization error in time-integration and time-derivative that appear in the Nakajima-Zwanzig equation. This was brought to our attention by Makri et al. [arXiv:2410.08239]. Our analysis in the Addendum shows that the relationship derived in our earlier work [Nat. Commun. 15, 8087 (2024)] is valid within the choice of discretization and is not contaminated by the discretization error.

Science & Technology - Other Topics↗
DOE OSTI2020

DPM: A deep learning PDE augmentation method with application to large-eddy simulation

A framework is introduced that leverages known physics to reduce overfitting in machine learning for scientific applications. The partial differential equation (PDE) that expresses the physics is augmented with a neural network that uses available data to learn a description of the corresponding unknown or unrepresented physics. Training within this combined system corrects for missing, unknown, or erroneously represented physics, including discretization errors associated with the PDE's numerical solution. For optimization of the network within the PDE, an adjoint PDE is solved to provide high-dimensional gradients, and a stochastic adjoint method (SAM) further accelerates training. Additionally, the approach is demonstrated for large-eddy simulation (LES) of turbulence. High-fidelity direct numerical simulations (DNS) of decaying isotropic turbulence provide the training data used to learn sub-filter-scale closures for the filtered Navier–Stokes equations. Out-of-sample comparisons show that the deep learning PDE method outperforms widely-used models, even for filter sizes so large that they become qualitatively incorrect. It also significantly outperforms the same neural network when a priori trained based on simple data mismatch, not accounting for the full PDE. Measures of discretization errors, which are well-known to be consequential in LES, point to the importance of the unified training formulation's design, which without modification corrects for them. For comparable accuracy, simulation runtime is significantly reduced. A relaxation of the typical discrete enforcement of the divergence-free constraint in the solver is also successful, instead allowing the DPM to approximately enforce incompressibility physics. Since the training loss function is not restricted to correspond directly to the closure to be learned, training can incorporate diverse data, including experimental data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Electron-Proton Scattering Event Generation using Structured Tokenization

Recent work such as Omnijet-$\alpha$ has demonstrated that effective tokenization combined with transformer-based architectures can produce effective foundation models for jet physics. While tokenization may help models capture generalizable event characteristics, it also introduces discretization errors that may compromise the precision required for downstream physics analyses. As the number and complexity of the particle features grow, these errors are likely to grow proportionally. In this study, we investigate new tokenization strategies to improve the application of generative transformer models to \textsc{Pythia8} simulations of electron-proton scattering at the Electron-Ion Collider. Specifically, we propose a feature-based structured tokenization approach that utilizes multiple tokens per particle, improving expressivity, while reducing the total number of unique tokens needed. We evaluate this method against grid-based binning, K-means clustering, and vector-quantized variational auto-encoders on the event simulations. Our results show that feature-based structured tokenization reduces discretization error, leading to more accurate generative modeling of particle-level events.

Goldenberg, Steven [Thomas Jefferson National Acce↗
DOE OSTI2025

Electron-Proton Scattering Event Generation using Structured Tokenization

Recent work such as Omnijet-$\alpha$ has demonstrated that effective tokenization combined with transformer-based architectures can produce effective foundation models for jet physics. While tokenization may help models capture generalizable event characteristics, it also introduces discretization errors that may compromise the precision required for downstream physics analyses. As the number and complexity of the particle features grow, these errors are likely to grow proportionally. In this study, we investigate new tokenization strategies to improve the application of generative transformer models to \textsc{Pythia8} simulations of electron-proton scattering at the Electron-Ion Collider. Specifically, we propose a feature-based structured tokenization approach that utilizes multiple tokens per particle, improving expressivity, while reducing the total number of unique tokens needed. We evaluate this method against grid-based binning, K-means clustering, and vector-quantized variational auto-encoders on the event simulations. Our results show that feature-based structured tokenization reduces discretization error, leading to more accurate generative modeling of particle-level events.

Goldenberg, Steven [Thomas Jefferson National Acce↗
DOE OSTI2022

Quantum simulation of real-space dynamics

Quantum simulation is a prominent application of quantum computers. While there is extensive previous work on simulating finite-dimensional systems, less is known about quantum algorithms for real-space dynamics. We conduct a systematic study of such algorithms. In particular, we show that the dynamics of a d-dimensional Schrödinger equation with η particles can be simulated with gate complexity O ~ (ηdFpoly(log(g'/ϵ))), where ϵ is the discretization error, g' controls the higher-order derivatives of the wave function, and F measures the time-integrated strength of the potential. Compared to the best previous results, this exponentially improves the dependence on ϵ and g' from poly(g'/ϵ) to poly(log(g'/ϵ)) and polynomially improves the dependence on T and d, while maintaining best known performance with respect to η. For the case of Coulomb interactions, we give an algorithm using η 3 (d + η)Tpoly(log(ηdTg'/(Δϵ)))/Δ one- and two-qubit gates, and another using η 3 (4d) d/2 Tpoly(log(ηdTg'/(Δϵ)))/Δ one- and two-qubit gates and QRAM operations, where T is the evolution time and the parameter Δ regulates the unbounded Coulomb interaction. We give applications to several computational problems, including faster real-space simulation of quantum chemistry, rigorous analysis of discretization error for simulation of a uniform electron gas, and a quadratic improvement to a quantum algorithm for escaping saddle points in nonconvex optimization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Calibr8 v.1.0

Calibr8 provides an application to rapidly prototype and perform material model calibration for complex plasticity models using advanced adjoint or forward sensitivity analyses for execution on massively parallel machines. These techniques can be orders of magnitude faster than traditional finite difference approaches for material model calibration. The underlying technology used in Calibr8 is automatic differentiation, which allows for the rapid implementation and testing of new plasticity models within its framework. Additionally, Calibr8 can perform adjoint-based error estimation to approximate discretization errors for user-implemented plasticity models. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. SAND2021-10630 O

Granzow, BrianN.↗
DOE OSTI2022

Validation of URANS and STRUCT-ε turbulence models for stratified sodium flow

Simulations of a transient stratified sodium experiment are carried out using a classic unsteady RANS model and the second-generation URANS model, STRUCT-ε. Turbulence modeling challenges and their implications to stratified flow prediction are discussed in the context of other sources of error. Input errors are discussed and addressed; discretization error is calculated to be less than 5% of the inlet velocity, for 80% of the domain; and remaining errors in temperature distributions are attributed to the turbulence model. Qualitative flow features from the simulations are presented and discussed. Compared to the experiment, the STRUCT-ε turbulence model provides a more physically accurate prediction of temperature and momentum mixing in key regions of the domain. Quantitative measures such as the L 2 norm of the temperature discrepancy demonstrate the improved performance of the STRUCT-ε approach. In conclusion, the magnitude of the temperature fluctuations is very well-predicted by the STRUCT-ε, while URANS overpredicts them by approximately 50%.

42 ENGINEERING↗
NASA NTRS2008

Towards Verification of Unstructured-Grid Solvers

New methodology for verification of computational methods using unstructured grids is presented. The discretization order properties are studied in computational windows, easily constructed within a collection of grids or a single grid. The windows can be adjusted to isolate the interior discretization, the boundary discretization, or singularities. A major component of the methodology is the downscaling test, introduced previously for studying the convergence rates of truncation and discretization errors of finite-volume discretization schemes on general unstructured grids. Demonstrations of the method are shown, including a comparative accuracy assessment of commonly-used schemes on general mixed grids and the identification of local accuracy deterioration at intersections of tangency and inflow/outflow boundaries. Recommendations for the use of the methodology in large-scale computational simulations are given.

Thomas, James L.↗
NASA NTRS2008

Towards Verification of Unstructured-Grid Solvers

New methodology for verification of finite-volume computational methods using unstructured grids is presented. The discretization order properties are studied in computational windows, easily constructed within a collection of grids or a single grid. Tests are performed within each window and address a combination of problem-, solution-, and discretization/grid-related features affecting discretization error convergence. The windows can be adjusted to isolate particular elements of the computational scheme, such as the interior discretization, the boundary discretization, or singularities. Studies can use traditional grid-refinement computations within a fixed window or downscaling, a recently-introduced technique in which computations are made within windows contracting toward a focal point of interest. Grids within the windows are constrained to be consistently refined, allowing a meaningful assessment of asymptotic error convergence on unstructured grids. Demonstrations of the method are shown, including a comparative accuracy assessment of commonly-used schemes on general mixed grids and the identification of local accuracy deterioration at boundary intersections. Recommendations to enable attainment of design-order discretization errors for large-scale computational simulations are given.

Thomas, James L.↗
DOE OSTI2026

Optimal binning of correlated measurements

Experimental measurements are commonly represented on a discrete grid, requiring a balance between granularity and statistical noise. Two strategies have traditionally been used to improve such representations: selecting an appropriate bin width to control discretization error and applying kernel-based smoothing to suppress fluctuations. Despite their shared goal, these approaches have largely developed independently, without a unified statistical description of how discretization and correlation jointly determine measurement precision. Here, we extend the discussion of optimal interval averaging to a correlation-aware setting by Gaussian process regression, which explicitly accounts for correlations among neighboring bins. Starting from first principles, we derive the mean-squared error of discretized measurements and obtain closed-form asymptotic expressions for the optimal bin width and correlation length. When recast in reduced variables, the theory reveals distinct universal scaling laws governing the error in the correlation-free and correlation-controlled regimes. Characterized by intrinsically smooth intensity profiles and counting-based statistics, neutron scattering measurements are well suited for demonstrating the enhanced error contraction enabled by inter-bin correlations. We show that such improvement is achievable over the experimentally accessible Q-range and across multiple instruments and material systems. These results show that explicitly accounting for correlations systematically reshapes the limits of precision in discretized, noise-limited measurements. More broadly, the framework provides a transferable statistical foundation for optimizing data representation, inference, and experimental design across the physical and data sciences.

Tung, Chi-Huan [ORNL] (ORCID:0000000221972074)↗
DOE OSTI2023

Non-singlet quark helicity $\mathrm{PDF}$s of the nucleon from pseudo-distributions

The non-singlet helicity quark parton distribution functions (PDFs) of the nucleon are determined from lattice QCD, by jointly leveraging pseudo-distributions and the distillation spatial smearing paradigm. A Lorentz decomposition of appropriately isolated space-like matrix elements reveals pseudo-distributions that contain information on the leading-twist helicity PDFs, as well as an invariant amplitude that induces an additional z 2 contamination of the leading-twist signal. An analysis of the short-distance behavior of the space-like matrix elements using matching coefficients computed to next-to-leading order (NLO) exposes the desired PDF up to this additional z 2 contamination. Due to the non-conservation of the axial current, we elect to isolate the helicity PDFs normalized by the nucleon axial charge at the same scale μ 2 . The leading-twist helicity PDFs as well as several sources of systematic error, including higher-twist effects, discretization errors, and the aforementioned z 2 contaminating amplitude are jointly determined by characterizing the computed pseudo-distribution in a basis of Jacobi polynomials. The Akaike Information Criterion is exploited to effectively average over distinct model parameterizations and cuts on the pseudo-distribution. Encouraging agreement is observed with recent global analyses of each non-singlet quark helicity PDF, notably a rather small non-singlet anti-quark helicity PDF for all quark momentum fractions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1985

A factored implicit scheme for numerical weather prediction

An implicit method is proposed to factor the nonlinear partial differential equations governing fast and slow modes of dynamic motion in numerical weather prediction schemes. The method permits separate factorization of the slow and fast modes of the implicit operator. A simple two-dimensional version of the system of three-dimensional equations governing atmospheric dynamics over shallow water was analyzed to assess the accuracy of the proposed method. It is shown that the method has a small error which is comparable to other discretization errors in the overall scheme.

Augenbaum, J. M.↗
NASA NTRS2012

Reynolds-Averaged Turbulence Model Assessment for a Highly Back-Pressured Isolator Flowfield

The use of computational fluid dynamics in scramjet engine component development is widespread in the existing literature. Unfortunately, the quantification of model-form uncertainties is rarely addressed with anything other than sensitivity studies, requiring that the computational results be intimately tied to and calibrated against existing test data. This practice must be replaced with a formal uncertainty quantification process for computational fluid dynamics to play an expanded role in the system design, development, and flight certification process. Due to ground test facility limitations, this expanded role is believed to be a requirement by some in the test and evaluation community if scramjet engines are to be given serious consideration as a viable propulsion device. An effort has been initiated at the NASA Langley Research Center to validate several turbulence closure models used for Reynolds-averaged simulations of scramjet isolator flows. The turbulence models considered were the Menter BSL, Menter SST, Wilcox 1998, Wilcox 2006, and the Gatski-Speziale explicit algebraic Reynolds stress models. The simulations were carried out using the VULCAN computational fluid dynamics package developed at the NASA Langley Research Center. A procedure to quantify the numerical errors was developed to account for discretization errors in the validation process. This procedure utilized the grid convergence index defined by Roache as a bounding estimate for the numerical error. The validation data was collected from a mechanically back-pressured constant area (1 2 inch) isolator model with an isolator entrance Mach number of 2.5. As expected, the model-form uncertainty was substantial for the shock-dominated, massively separated flowfield within the isolator as evidenced by a 6 duct height variation in shock train length depending on the turbulence model employed. Generally speaking, the turbulence models that did not include an explicit stress limiter more closely matched the measured surface pressures. This observation is somewhat surprising, given that stress-limiting models have generally been developed to better predict shock-separated flows. All of the models considered also failed to properly predict the shape and extent of the separated flow region caused by the shock boundary layer interactions. However, the best performing models were able to predict the isolator shock train length (an important metric for isolator operability margin) to within 1 isolator duct height.

Baurle, Robert A.↗
NASA NTRSDate not supplied

Uncertainty Estimates for Sonic-Boom Pressure Signatures and Loudness Carpets

A non-intrusive uncertainty quantification method is applied to computational analysis of supersonic, low-boom aircraft. The mean and standard deviation statistics of the pressure waveforms and loudness metrics are evaluated through use of numerical quadrature. The probability density function (p.d.f.) of these outputs is evaluated via kernel density estimation. The simulations use an inviscid, embedded-boundary Cartesian-mesh flow solver in the nearfield combined with an augmented Burgers’ equation solver for propagation in the farfield. The results show that the p.d.f. of the waveform is bimodal at shocks, which makes the mean and standard deviation statistics inappropriate. Despite this limitation, we show that the moment statistics can provide effective assessment of discrepancies when comparing with experimental data. This is demonstrated by presenting uncertainty analysis of a wind-tunnel test and showing that we significantly improve the predictions when we include the test uncertainties in the simulation. Normal distributions are obtained for the ground signature and loudness metrics, which is primarily due to the careful shaping of the low-boom waveform. Separation of variables and error control are used to reduce computational cost. We demonstrate that this is an efficient approach in the sense of balancing numerical errors in the statistics quadrature with discretization errors in the solvers.

ARMD↗