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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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

High-Resolution, Rapid-Scan Dual-Doppler Retrievals of Vertical Velocity in a Simulated Supercell

Observation system simulation experiments are used to evaluate different dual-Doppler analysis (DDA) methods for retrieving vertical velocity w at grid spacings on the order of 100 m within a simulated tornadic supercell. Variational approaches with and without a vertical vorticity equation constraint are tested, along with a typical (traditional) method involving vertical integration of the mass conservation equation. The analyses employ emulated radar data from dual-Doppler placements 15, 30, and 45 km east of the mesocyclone, with volume scan intervals ranging from 10 to 150 s. The effect of near-surface data loss is examined by denying observations below 1 km in some of the analyses. At the longer radar ranges and when no data denial is imposed, the “traditional” method produces results similar to those of the variational method and is much less expensive to implement. However, at close range and/or with data denial, the variational method is much more accurate, confirming results from previous studies. The vorticity constraint shows the potential to improve the variational analysis substantially, reducing errors in the w retrieval by up to 30% for rapid-scan observations (≤30 s) at close range when the local vorticity tendency is estimated using spatially variable advection correction. However, the vorticity constraint also degrades the analysis for longer scan intervals, and the impact diminishes with increased range. Furthermore, analyses using 30-s data also frequently outperform analyses using 10-s data, suggesting a limit to the benefit of increasing the radar scan rate for variational DDA employing the vorticity constraint.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Cosmology meets cohomology

The cosmological polytope and bootstrap programs have revealed interesting connections between positive geometries, modern on-shell methods and bootstrap principles studied in the amplitudes community with the wavefunction of the Universe in toy models of FRW cosmologies. To compute these FRW correlators, one often faces integrals that are too difficult to evaluate by direct integration. Borrowing from the Feynman integral community, the method of (canonical) differential equations provides an efficient alternative for evaluating these integrals. Moreover, we further develop our geometric understanding of these integrals by describing the associated relative twisted cohomology. Leveraging recent progress in our understanding of relative twisted cohomology in the Feynman integral community, we give an algorithm to predict the basis size and simplify the computation of the differential equations satisfied by FRW correlators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Vibration-Based Sensor Design: A Grey-Box Approach

Knowledge of the internal structure of an object or device under investigation proceeds from the basic idea of constructing its dynamic behavioral relations governed by a set of differential/algebraic equations that characterize its response. These equations can be partial differential equations leading to finite element or finite difference relations requiring a complex numerical solution on a super computer or ordinary differential equations requiring sophisticated numerical integration techniques to obtain the desired solution. Discrete dynamic systems evolving from digitized data acquisition are typically captured by sampled-data (continuous-to-discrete) representations characterized by a set of difference equations specifying the underlying system dynamics. In any case, with a mathematical description in hand, Grey-Box modeling techniques have evolved, concerned with the estimation of model parameters embedded in a prescribed set of equations (the system) governing its behavior, while capturing the underlying physical phenomenology of the problem at hand.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Linear-Scaling Local Natural Orbital-Based Full Triples Treatment in Coupled-Cluster Theory

We present an efficient, asymptotically linear-scaling implementation of the canonically O(N 8 ) coupled-cluster method with singles, doubles, and full triples excitations (CCSDT) method. We apply the domain-based local pair natural orbital (DLPNO) approach for computing CCSDT amplitudes. Our method, called DLPNO–CCSDT, uses the converged coupled-cluster amplitudes from a preceding DLPNO–CCSD(T) computation as a starting point for the solution of the CCSDT equations in the local natural orbital basis. To simplify the working equations, we t1-dress our two-electron integrals and Fock matrices, allowing our equations to take on the form of CCDT. With appropriate parameters, our method can recover more than 99.99% of the total canonical CCSDT correlation energy. In addition, we demonstrate that our method consistently yields sub-kJ mol –1 errors in relative energies when compared to canonical CCSDT, and, likewise, when computing the difference between CCSDT and CCSD(T). Finally, to highlight the low scaling of our algorithm, we present timings on linear alkanes (up to 30 carbons and 730 basis functions) and water clusters (up to 131 water molecules and 3144 basis functions).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Parallel-In-Time Integration for Hyperbolic Problems (Final Report)

The work for the subcontract was situated in the area of parallel-in-time integration for advection-dominated and hyperbolic partial differential equations (PDEs). Parallel-in-time integration is an active area of research due to its ability to enable faster numerical simulations for applications throughout many areas of science. Over the past two decades, much progress has been made in this area; however, this progress has largely been limited to non-hyperbolic, diffusion-dominated PDEs. Given the ubiquity of numerical simulations of advection-dominated hyperbolic PDEs throughout the sciences, there is a strong need to develop efficient parallel-in-time techniques for hyperbolic problems, which was the main topic of this subcontract.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Cauchy-type integral method for solving the linearized one-dimensional Vlasov-Poisson equation

Here, we present a method for solving the linearized Vlasov-Poisson equation, based on analyticity properties of the equilibrium and initial condition through Cauchy-type integrals, that produces algebraic expressions for the distribution and field, i.e., the solution is expressed without integrals. Standard extant approaches involve deformations of the Bromwich contour that give erroneous results for certain physically reasonable configurations or eigenfunction expansions that are misleading as to the temporal structure of the solution. Our method is more transparent, lacks these defects, and predicts previously unrecognized behavior.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Analytic quasi-steady evolution of marginally unstable kinetic plasma instabilities in the presence of drag and scattering

The 1D bump-on-tail problem is studied in order to determine the influence of drag on quasi-steady solutions near marginal stability (1-γ d /γ L << 1) when effective collisions are much larger than the instability growth rate (ν>>γ). In this common tokamak regime, it is rigorously shown that the paradigmatic Berk–Breizman cubic equation for the nonlinear mode evolution reduces to a much simpler differential equation, dubbed the time-local cubic equation, which can be solved directly. It is found that in addition to increasing the saturation amplitude, drag introduces a shift in the apparent oscillation frequency by modulating the saturated wave envelope. Furthermore, excellent agreement is found between the analytic solution for the mode evolution and both the numerically integrated Berk–Breizman cubic equation and fully nonlinear 1D Vlasov simulations. Experimentally isolating the contribution of drag to the saturated mode amplitude for verification purposes is explored but complicated by the reality that the amount of drag cannot be varied independently of other key parameters in realistic scenarios. While the influence of drag is modest when the ratio of effective drag to effective scattering α/ν is very small, it can become substantial when α/ν ≳ 0.5, suggesting that drag should be accounted for in quantitative models of fast-ion-driven instabilities in fusion plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Estimating physics models and quantifying their uncertainty using optimization with a Bayesian objective function

This paper reports a verification study for a method that fits functions to sets of data from several experiments simultaneously. The method finds a maximum a posteriori probability (MAP) estimate of a function subject to constraints (e. g., convexity in the study), uncertainty about the estimate, and a quantitative characterization of how data from each experiment constrains that uncertainty. While the present work focuses on a model of the Equation Of State (EOS) of gasses produced by detonating a high explosive, the method can be applied to a wide range of physics processes with either parametric or semi-parametric models. As a verification exercise, a reference EOS is used and artificial experimental data sets are created using numerical integration of ordinary differential equations and pseudo-random noise. The method yields an estimate of the EOS that is close to the reference, and identifies how each experiment most constrains the result.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A High-Order Eulerian–Lagrangian Runge–Kutta Finite Volume (EL–RK–FV) Method for Scalar Nonlinear Conservation Laws

Abstract We present a class of high-order Eulerian–Lagrangian Runge–Kutta finite volume methods that can numerically solve Burgers’ equation with shock formations, which could be extended to general scalar conservation laws. Eulerian–Lagrangian (EL) and semi-Lagrangian (SL) methods have recently seen increased development and have become a staple for allowing large time-stepping sizes. Yet, maintaining relatively large time-stepping sizes post shock formation remains quite challenging. Our proposed scheme integrates the partial differential equation on a space-time region partitioned by linear approximations to the characteristics determined by the Rankine–Hugoniot jump condition. We trace the characteristics forward in time and present a merging procedure for the mesh cells to handle intersecting characteristics due to shocks. Following this partitioning, we write the equation in a time-differential form and evolve with Runge–Kutta methods in a method-of-lines fashion. High-resolution methods such as ENO and WENO-AO schemes are used for spatial reconstruction. Extension to higher dimensions is done via dimensional splitting. Numerical experiments demonstrate our scheme’s high-order accuracy and ability to sharply capture post-shock solutions with large time-stepping sizes.

Chen, Jiajie↗
DOE OSTI2023

Expanded verification and validation studies of hypersonic aerodynamics with multiple physics-fidelity models

Hypersonic aerothermodynamics is an important domain of modern multiphysics simulation. The Multi-Fidelity Toolkit is a simulation tool being developed at Sandia National Laboratories to predict aerodynamic properties for compressible flows from a range of physics fidelities and computational speeds. These models include the Reynolds-averaged Navier–Stokes (RANS) equations, the Euler equations with momentum-energy integral technique (MEIT), and modified Newtonian aerodynamics with flat-plate boundary layer (MNA+FPBL) equations, and they can be invoked independently or coupled with hierarchical Kriging to interpolate between high-fidelity simulations using lower-fidelity data. However, as with any new simulation capability, verification and validation are necessary to gather credibility evidence. This work describes formal code- and solution-verification activities, as well as model validation with uncertainty considerations. Code verification activities on the MNA+FPBL model build on previous work by focusing on the viscous portion of the model. Viscous quantities of interest are compared against those from an analytical solution for flat-plate, inclined-plate, and cone geometries. The code verification methodology for the MEIT model is also presented. Test setup and results of code verification tests on the laminar and turbulent models within MEIT are shown. Solution-verification activities include grid-refinement studies on simulations that model the HIFiRE-1 wind tunnel experiments. These experiments are used for validation of all model fidelities. A thorough validation comparison with prediction error and uncertainty is also presented. Three additional HIFiRE-1 experimental runs are simulated in this study, and the solution verification and validation work examines the effects of the associated parameter changes on model performance. Finally, a study is presented that compares the computational costs and fidelities from each of the different models.

42 ENGINEERING↗
DOE OSTI2024

Should We Conserve Entropy or Energy when Computing CAPE with Mixed-Phase Precipitation Physics?

Abstract The rapidly increasing resolution of global atmospheric reanalysis and climate model datasets necessitates finding methods for computing convective available potential energy (CAPE) both efficiently and accurately. To this end, this article compares two common methods for computing CAPE which conserve either energy or entropy. Inaccuracies in these computations arise from both physical and numerical errors. For instance, computing CAPE with entropy conserved results in physical errors from nonequilibrium phase transitions but minimizes numerical errors because solutions are analytic at each height. In contrast, computing CAPE with energy conserved avoids these physical errors, but accumulates numerical errors that are grid-resolution-dependent because the numerical integration of a differential equation is required. Analysis of CAPE computed with large databases of soundings from the tropical Amazon and midlatitude storm environments shows that physical errors from the entropy method are typically 1%–3% as large as CAPE, which is comparable to the numerical errors from conserving energy with grid spacing of 25 and 250 m using explicit first-order and second-order integration schemes, respectively. Errors in entropy-based CAPE calculations are also insensitive to vertical grid spacing, in contrast to energy-based calculations whose error strongly scales with the grid spacing. It is shown that entropy-based methods are advantageous when intercomparing datasets with differing vertical resolution because they produce accurate and reasonably fast results that are insensitive to grid resolution, whereas a second-order energy-based method is advantageous when analyzing data with a consistent vertical resolution because of its superior computational efficiency. Significance Statement Convective available potential energy (CAPE) is a measure of instability in the atmosphere that helps forecasters and researchers understand when and where thunderstorms will form. The purpose of this article is to identify the most efficient and accurate methods for computing CAPE. Two methods are considered here, one that relates to the entropy (a measure of thermodynamic disorder) of an air parcel and one that relates to the energy of an air parcel. Results indicate that the entropy method is most accurate and insensitive to the resolution of the data used for the calculation (which can vary considerably), whereas the energy method uses the least computation time.

Peters, John M.↗
DOE OSTI2024

SUNDIALS time integrators for exascale applications with many independent systems of ordinary differential equations

Many complex systems can be accurately modeled as a set of coupled time-dependent partial differential equations (PDEs). However, solving such equations can be prohibitively expensive, easily taxing the world’s largest supercomputers. One pragmatic strategy for attacking such problems is to split the PDEs into components that can more easily be solved in isolation. This operator splitting approach is used ubiquitously across scientific domains, and in many cases leads to a set of ordinary differential equations (ODEs) that need to be solved as part of a larger “outer-loop” time-stepping approach. The SUNDIALS library provides a plethora of robust time integration algorithms for solving ODEs, and the U.S. Department of Energy Exascale Computing Project (ECP) has supported its extension to applications on exascale-capable computing hardware. In this paper, we highlight some SUNDIALS capabilities and its deployment in combustion and cosmology application codes (Pele and Nyx, respectively) where operator splitting gives rise to numerous, small ODE systems that must be solved concurrently.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A physical basis for cosmological correlators from cuts

Significant progress has been made in our understanding of the analytic structure of FRW wavefunction coefficients, facilitated by the development of efficient algorithms to derive the differential equations they satisfy. Moreover, recent findings indicate that the twisted cohomology of the associated hyperplane arrangement defining FRW integrals overestimates the number of integrals required to define differential equations for the wave-function coefficient. We demonstrate that the associated dual cohomology is automatically organized in a way that is ideal for understanding and exploiting the cut/residue structure of FRW integrals. Utilizing this understanding, we develop a systematic approach to organize compatible sequential residues, which dictates the physical subspace of FRW integrals for any n -site, ℓ-loop graph. In particular, the physical subspace of tree-level FRW wavefunction coefficients is populated by differential forms associated to cuts/residues that factorize the integrand of the wavefunction coefficient into only flat space amplitudes. After demonstrating the validity of our construction using intersection theory, we develop simple graphical rules for cut tubings that enumerate the space of physical cuts and, consequently, differential forms without any calculation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Machine Learned Empirical Numerical Integrator from Simulated Data

Recently, a number of state-of-the-art surrogate machine learning (ML) models have been designed for global weather and climate prediction, which have been trained using reanalysis data products. Reanalysis data products are constructed using numerical model simulations that combine numerical integration of partial differential equations and parameterization schemes. These products are typically only archived and made available using coarsened spatial and temporal resolutions. This study explores the impact of the numerical generation methods used to produce the training datasets and the temporal resolution of those datasets on machine learning surrogate models. Using the nonlinear vector autoregression (NVAR) machine as an explainable ML technique, simple dynamical systems are emulated with ML models trained on data produced by three classical numerical integration schemes. NVAR is validated as a skillful ML method, capable of producing accurate predictions and, more importantly, reconstructing both the underlying dynamics and the numerical integration scheme used to generate the training data. However, the machine fails to generalize predictions on unseen test data generated by different numerical integration schemes, despite the underlying dynamical system being the same. This result provides a word of caution for the growing field of machine learning emulation of weather and climate dynamics. Furthermore, we illustrate using NVAR that training on temporally coarsened data may increase the required complexity of ML models and potentially introduce new numerical challenges. Finally, we discover that empirical integration schemes with arbitrary time-stepping sizes can be constructed directly from the data, which implies a potential for the development of empirical numerical integration schemes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Helicity evolution at small x: the single-logarithmic contribution

We calculate single-logarithmic corrections to the small-x flavor-singlet helicity evolution equations derived recently [1–3] in the double-logarithmic approximation. The new single-logarithmic part of the evolution kernel sums up powers of α s ln(1/x), which are an important correction to the dominant powers of α s ln 2 (1/x) summed up by the double-logarithmic kernel from [1–3] at small values of Bjorken x and with α s the strong coupling constant. The single-logarithmic terms arise separately from either the longitudinal or transverse momentum integrals. Consequently, the evolution equations we derive employing the light-cone perturbation theory simultaneously include the small-x evolution kernel and the leading-order polarized DGLAP splitting functions. We further enhance the equations by calculating the running coupling corrections to the kernel.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Semi-Empirical Shadow Molecular Dynamics: A PyTorch Implementation

Here, extended Lagrangian Born–Oppenheimer molecular dynamics (XL-BOMD) in its most recent shadow potential energy version has been implemented in the semiempirical PyTorch-based software PySeQM. The implementation includes finite electronic temperatures, canonical density matrix perturbation theory, and an adaptive Krylov subspace approximation for the integration of the electronic equations of motion within the XL-BOMB approach (KSA-XL-BOMD). The PyTorch implementation leverages the use of GPU and machine learning hardware accelerators for the simulations. The new XL-BOMD formulation allows studying more challenging chemical systems with charge instabilities and low electronic energy gaps. The current public release of PySeQM continues our development of modular architecture for large-scale simulations employing semi-empirical quantum-mechanical treatment. Applied to molecular dynamics, simulation of 840 carbon atoms, one integration time step executes in 4 s on a single Nvidia RTX A6000 GPU.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Internal energy balance and aerodynamic heating predictions for hypersonic turbulent boundary layers

The elemental equation governing heat transfer in aerodynamic flows is the internal energy equation. For a boundary layer flow, a double integration of the Reynolds-averaged form of this equation provides an expression of the wall heat flux in terms of the integrated effects, over the boundary layer, of various physical processes: turbulent dissipation, mean dissipation, turbulent heat flux, etc. Recently available direct numerical simulation data for a Mach 11 cold-wall turbulent boundary layer allows a comparison of the exact contributions of these terms in the energy equation to the wall heat flux with their counterparts modeled in the Reynolds-averaged Navier-Stokes (RANS) framework. Various approximations involved in RANS, both closure models as well as approximations involved in adapting incompressible RANS models to a compressible form, are assessed through examination of the internal energy balance. There are a number of potentially problematic assumptions and terms identified through this analysis. Here, the effect of compressibility corrections of the dilatational dissipation type is explored, as is the role of the modeled turbulent dissipation, in the context of wall heat flux predictions. The results indicate several potential avenues for RANS model improvement for hypersonic cold-wall boundary-layer flows.

42 ENGINEERING↗