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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Improving the Numerical Stability of Fast Matrix Multiplication

Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few fast algorithms have been efficiently implemented or used in practical applications. However, there exist many practical alternatives to Strassen's algorithm with varying performance and numerical properties. Fast algorithms are known to be numerically stable, but because their error bounds are slightly weaker than the classical algorithm, they are not used even in cases where they provide a performance benefit. We argue in this study that the numerical sacrifice of fast algorithms, particularly for the typical use cases of practical algorithms, is not prohibitive, and we explore ways to improve the accuracy both theoretically and empirically. The numerical accuracy of fast matrix multiplication depends on properties of the algorithm and of the input matrices, and we consider both contributions independently. We generalize and tighten previous error analyses of fast algorithms and compare their properties. We discuss algorithmic techniques for improving the error guarantees from two perspectives: manipulating the algorithms, and reducing input anomalies by various forms of diagonal scaling. In conclusion, we benchmark performance and demonstrate our improved numerical accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

High Order Numerical Methods for the Dynamic SGS Model of Turbulent Flows with Shocks

Simulation of turbulent flows with shocks employing subgrid-scale (SGS) filtering may encounter a loss of accuracy in the vicinity of a shock. This paper addresses the accuracy improvement of LES of turbulent flows in two ways: (a) from the SGS model standpoint and (b) from the numerical method improvement standpoint. In an internal report, Kotov et al. ( “High Order Numerical Methods for large eddy simulation (LES) of Turbulent Flows with Shocks”, CTR Tech Brief, Oct. 2014, Stanford University), we performed a preliminary comparative study of different approaches to reduce the loss of accuracy within the framework of the dynamic Germano SGS model. The high order low dissipative method of Yee & Sjögreen (2009) using local flow sensors to control the amount of numerical dissipation where needed is used for the LES simulation. The considered improved dynamics model approaches include applying the one-sided SGS test filter of Sagaut & Germano (2005) and/or disabling the SGS terms at the shock location. For Mach 1.5 and 3 canonical shock-turbulence interaction problems, both of these approaches show a similar accuracy improvement to that of the full use of the SGS terms. The present study focuses on a five levels of grid refinement study to obtain the reference direct numerical simulation (DNS) solution for additional LES SGS comparison and approaches. As a result, one of the numerical accuracy improvements included here applies Harten's subcell resolution procedure to locate and sharpen the shock, and uses a one-sided test filter at the grid points adjacent to the exact shock location.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A subzone reconstruction algorithm for efficient staggered compatible remapping

Staggered-grid Lagrangian hydrodynamics algorithms frequently make use of subzonal discretization of state variables for the purposes of improved numerical accuracy, generality to unstructured meshes, and exact conservation of mass, momentum, and energy. For Arbitrary Lagrangian–Eulerian (ALE) methods using a geometric overlay, it is difficult to remap subzonal variables in an accurate and efficient manner due to the number of subzone–subzone intersections that must be computed. This becomes prohibitive in the case of 3D, unstructured, polyhedral meshes. A new procedure is outlined in this paper to avoid direct subzonal remapping. The new algorithm reconstructs the spatial profile of a subzonal variable using remapped zonal and nodal representations of the data. The reconstruction procedure is cast as an under-constrained optimization problem. Enforcing conservation at each zone and node on the remapped mesh provides the set of equality constraints; the objective function corresponds to a quadratic variation per subzone between the values to be reconstructed and a set of target reference values. Numerical results for various pure-remapping and hydrodynamics tests are provided. Ideas for extending the algorithm to staggered-grid radiation-hydrodynamics are discussed as well as ideas for generalizing the algorithm to include inequality constraints.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

ComPort: Rigorous Testing Methods to Safeguard Software Porting (Final Technical Report)

This is a technical report from the lead institution – University of Utah, Kahlert School of Computing – funded under the Department of Energy, Office of Science, Office of Advanced Scientific Computing Research under award number DE-SC0022252. We summarize our work done over the three years of funding received. The relevant papers and software have already been uploaded at the DOE site.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Implementation of the LAX-Wendroff Method in Cobra-TF for Solving Two-Phase Flow Transport Equations

COBRA-TF (Coolant Boiling in Rod Arrays Two Fluid), or CTF, is a subchannel code used to conduct the reactor core thermal hydraulic (T/H) solution in both standalone and coupled multi-physics applications. CTF applies the first-order upwind spatial discretization scheme for solving two-phase flow conservation equations. In this work, the second-order Lax-Wendroff (L-W) scheme has been implemented in CTF to solve the two-phase flow transport equations to improve numerical accuracy in both temporal and spatial discretization. To avoid the oscillation issue, a non-linear flux limiter VA (Van Albada) is employed for the convective terms in the transport equations. Assessments have been carried out to evaluate the performance and stability of the implemented second-order L-W scheme. It has been found that the L-W scheme performs better than the upwind scheme for the single-phase and two-phase flow problems in terms of numerical accuracy and computational efficiency.

CTF↗
DOE OSTI2020

The Adjoint Petrov–Galerkin method for non-linear model reduction

Here, we formulate a new projection-based reduced-order modeling technique for non-linear dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov–Galerkin (APG) method, is derived by decomposing the generalized coordinates of a dynamical system into a resolved coarse-scale set and an unresolved fine-scale set. A Markovian finite memory assumption within the Mori–Zwanzig formalism is then used to develop a reduced-order representation of the coarse scales. This procedure leads to a closed reduced-order model that displays commonalities with the adjoint stabilization method used in finite elements. The formulation is shown to be equivalent to a Petrov–Galerkin method with a non-linear, time-varying test basis, thus sharing some similarities with the Least-Squares Petrov–Galerkin method. Theoretical analysis examining a priori error bounds and computational cost is presented. Numerical experiments on the compressible Navier–Stokes equations demonstrate that the proposed method can lead to improvements in numerical accuracy, robustness, and computational efficiency over the Galerkin method on problems of practical interest. Improvements in numerical accuracy and computational efficiency over the Least-Squares Petrov–Galerkin method are observed in most cases.

42 ENGINEERING↗
DOE OSTI2017

Subleading power corrections for N -jettiness subtractions

Here, the N -jettiness observable T N provides a way of describing the leading singular behavior of the N -jet cross section in the τ = T N = Q → 0 limit, where Q is a hard interaction scale. We consider subleading power corrections in the τ << 1 expansion, and employ soft-collinear effective theory to obtain analytic results for the dominant α s τlnτ and α 2 s τln 3 τ subleading terms for thrust in e + e – collisions and 0-jettiness for q¯q-initiated Drell-Yan–like processes at hadron colliders. These results can be used to significantly improve the numerical accuracy and stability of the N -jettiness subtraction technique for performing fixed order calculations at next-to-leading order and next-to-next-to-leading order. They reduce the size of missing power corrections in the subtractions by an order of magnitude. We also point out that the precise definition of N -jettiness has an important impact on the size of the power corrections and thus the numerical accuracy of the subtractions. The sometimes employed definition of N -jettiness in the hadronic center-ofmass frame suffers from power corrections that grow exponentially with rapidity, causing the power expansion to deteriorate away from central rapidity. This degradation does not occur for the original N -jettiness definition, which explicitly accounts for the boost of the Born process relative to the frame of the hadronic collision, and has a well-behaved power expansion throughout the entire phase space. Integrated over rapidity, using this N -jettiness definition in the subtractions yields another order of magnitude improvement compared to employing the hadronic-frame definition.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Efficient Fourier transforms for transverse momentum dependent distributions

Hadron production at low transverse momenta in semi-inclusive deep inelastic scattering can be described by transverse momentum dependent (TMD) factorization. This formalism has also been widely used to study the Drell-Yan process and back-to-back hadron pair production in $e^+e^-$ collisions. These processes are the main ones for extractions of TMD parton distribution functions and TMD fragmentation functions, which encode important information about nucleon structure and hadronization. One of the most widely used TMD factorization formalism in phenomenology formulates TMD observables in coordinate $b_\perp$-space, the conjugate space of the transverse momentum. The Fourier transform from $b_\perp$-space back into transverse momentum space is sufficiently complicated due to oscillatory integrands that it requires a careful and computationally intensive numerical treatment in order to avoid potentially large numerical errors. Within the TMD formalism, the azimuthal angular dependence is analytically integrated and the two-dimensional $b_\perp$ integration reduces to a one-dimensional integration over the magnitude $b_\perp$. In this paper we develop a fast numerical Hankel transform algorithm for such a $b_\perp$-integration that improves the numerical accuracy of TMD calculations in all standard processes. Libraries for this algorithm are implemented in Python 2.7 and 3, C++, as well as FORTRAN77. All packages are made available open source.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Scalability of OpenFOAM Density-Based Solver with Runge–Kutta Temporal Discretization Scheme

Compressible density-based solvers are widely used in OpenFOAM, and the parallel scalability of these solvers is crucial for large-scale simulations. In this paper, we report our experiences with the scalability of OpenFOAM’s native rhoCentralFoam solver, and by making a small number of modifications to it, we show the degree to which the scalability of the solver can be improved. The main modification made is to replace the first-order accurate Euler scheme in rhoCentralFoam with a third-order accurate, four-stage Runge-Kutta or RK4 scheme for the time integration. The scaling test we used is the transonic flow over the ONERA M6 wing. This is a common validation test for compressible flows solvers in aerospace and other engineering applications. Numerical experiments show that our modified solver, referred to as rhoCentralRK4Foam, for the same spatial discretization, achieves as much as a 123.2% improvement in scalability over the rhoCentralFoam solver. As expected, the better time resolution of the Runge–Kutta scheme makes it more suitable for unsteady problems such as the Taylor–Green vortex decay where the new solver showed a 50% decrease in the overall time-to-solution compared to rhoCentralFoam to get to the final solution with the same numerical accuracy. Finally, the improved scalability can be traced to the improvement of the computation to communication ratio obtained by substituting the RK4 scheme in place of the Euler scheme. All numerical tests were conducted on a Cray XC40 parallel system, Theta, at Argonne National Laboratory.

Li, Sibo↗
DOE OSTI2018

High-accuracy Geant4 simulation and semi-analytical modeling of nuclear resonance fluorescence

Nuclear resonance fluorescence (NRF) is a photonuclear interaction that enables highly isotope-specific measurements in both pure and applied physics scenarios. High-accuracy design and analysis of NRF measurements in complex geometries is aided by Monte Carlo simulations of photon physics and transport, motivating Jordan and Warren (2007) to develop the G4NRF codebase for NRF simulation in Geant4. In this work, we enhance the physics accuracy of the G4NRF code and perform improved benchmarking simulations. The NRF cross section calculation in G4NRF, previously a Gaussian approximation, has been replaced with a full numerical integration for improved accuracy in thick-target scenarios. A high-accuracy semi-analytical model of expected NRF count rates in a typical NRF measurement is then constructed and compared against G4NRF simulations for both simple homogeneous and more complex heterogeneous geometries. Furthermore, agreement between rates predicted by the semi-analytical model and G4NRF simulation is found at a level of ~1% in simple test cases and ~3% in more realistic scenarios, improving upon the ~20% level of the initial benchmarking study and establishing a highly-accurate NRF framework for Geant4.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Ground observations of a space laser for the assessment of its in-orbit performance

The wind mission Aeolus of the European Space Agency was a groundbreaking achievement for Earth observation. Between 2018 and 2023, the space-borne lidar instrument ALADIN onboard the Aeolus satellite measured atmospheric wind profiles with global coverage, which contributed to improving the accuracy of numerical weather prediction. The precision of the wind observations, however, declined over the course of the mission due to a progressive loss of the atmospheric backscatter signal. The analysis of the root cause was supported by the Pierre Auger Observatory in Argentina whose fluorescence detector registered the ultraviolet laser pulses emitted from the instrument in space, thereby offering an estimation of the laser energy at the exit of the instrument for several days in 2019, 2020, and 2021. The reconstruction of the laser beam not only allowed for an independent assessment of the Aeolus performance, but also helped to improve the accuracy in the determination of the laser beam’s ground track on single pulse level. The results presented in this paper set a precedent for the monitoring of space lasers by ground-based telescopes and open new possibilities for the calibration of cosmic-ray observatories.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2019

The Second Wind Forecast Improvement Project (WFIP2): Observational Field Campaign

The science of wind energy forecasting has taken a leap forward with the unique meteorological observations gathered in complex terrain during the Second Wind Forecast Improvement Project (WFIP2). The Second Wind Forecast Improvement Project (WFIP2) is a U.S. Department of Energy (DOE) and National Oceanic and Atmospheric Administration (NOAA) funded program, with private-sector and university partners, which aims to improve the accuracy of numerical weather prediction (NWP) model forecasts of wind speed in complex terrain for wind energy applications. A core component of WFIP2 was an 18-month field campaign which took place in the U.S. Pacific Northwest between October 2015 and March 2017. A large suite of instrumentation was deployed in a series of telescoping arrays, ranging from 500 km across to a densely instrumented 2 x 2 km area similar in size to a high-resolution NWP model grid cell. Observations from these instruments are being used to improve our understanding of the meteorological phenomena that affect wind energy production in complex terrain, and to evaluate and improve model physical parameterization schemes. We present several brief case studies using these observations to describe phenomena that are routinely difficult to forecast, including wintertime cold pools, diurnally driven gap flows, and mountain waves/wakes. Observing system and data product improvements developed during WFIP2 are also described.

17 WIND ENERGY↗
DOE OSTI2024

A numerical Poisson solver with improved radial solutions for a self-consistent locally scaled self-interaction correction method

Abstract The universal applicability of density functional approximations is limited by self-interaction error made by these functionals. Recently, a novel one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange-correlation and Coulomb energy densities was proposed. The locally scaled SIC (LSIC) method is exact for the one-electron densities, and unlike the well-known Perdew–Zunger SIC (PZSIC) method recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to PZSIC method as a special case when isoorbital indicator is set to the unity. Here, we present a numerical scheme that we have adopted to evaluate the Coulomb potential of the electron density scaled by the iso-orbital indicator required for the self-consistent LSIC calculations. After analyzing the behavior of the finite difference method (FDM) and the green function solution to the radial part of the Poisson equation, we adopt a hybrid approach that uses the FDM for the Coulomb potential due to the monopole and the GF for all higher-order terms. The performance of the resultant hybrid method is assessed using a variety of systems. The results show improved accuracy than earlier numerical schemes. We also find that, even with a generic set of radial grid parameters, accurate energy differences can be obtained using a numerical Coulomb solver in standard density functional studies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

SU-C-207A-05: Feature Based Water Equivalent Path Length (WEPL) Determination for Proton Radiography by the Technique of Time Resolved Dose Measurement

Purpose: Studies show that WEPL can be determined from modulated dose rate functions (DRF). However, the previous calibration method based on statistics of the DRF is sensitive to energy mixing of protons due to scattering through different materials (termed as range mixing here), causing inaccuracies in the determination of WEPL. This study intends to explore time-domain features of the DRF to reduce the effect of range mixing in proton radiography (pRG) by this technique. Methods: An amorphous silicon flat panel (PaxScan™ 4030CB, Varian Medical Systems, Inc., Palo Alto, CA) was placed behind phantoms to measure DRFs from a proton beam modulated by a specially designed modulator wheel. The performance of two methods, the previously used method based on the root mean square (RMS) and the new approach based on time-domain features of the DRF, are compared for retrieving WEPL and RSP from pRG of a Gammex phantom. Results: Calibration by T{sub 80} (the time point for 80% of the major peak) was more robust to range mixing and produced WEPL with improved accuracy. The error of RSP was reduced from 8.2% to 1.7% for lung equivalent material, with the mean error for all other materials reduced from 1.2% to 0.7%. The mean error of the full width at half maximum (FWHM) of retrieved inserts was decreased from 25.85% to 5.89% for the RMS and T{sub 80} method respectively. Monte Carlo simulations in simplified cases also demonstrated that the T{sub 80} method is less sensitive to range mixing than the RMS method. Conclusion: WEPL images have been retrieved based on single flat panel measured DRFs, with inaccuracies reduced by exploiting time-domain features as the calibration parameter. The T{sub 80} method is validated to be less sensitive to range mixing and can thus retrieve the WEPL values in proximity of interfaces with improved numerical and spatial accuracy for proton radiography.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

An adaptive and stability-promoting layerwise training approach for sparse deep neural network architecture

This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a new layer is added each time and trained independently by freezing parameters in the previous layers. We impose desirable structures on the DNN by employing manifold regularization, sparsity regularization, and physics-informed terms. We introduce a ε – δ – stability-promoting concept as a desirable property for a learning algorithm and show that employing manifold regularization yields a ε – δ stability-promoting algorithm. Further, we also derive the necessary conditions for the trainability of a newly added layer and investigate the training saturation problem. In the second stage of the algorithm (post-processing), a sequence of shallow networks is employed to extract information from the residual produced in the first stage, thereby improving the prediction accuracy. Numerical investigations on prototype regression and classification problems demonstrate that the proposed approach can outperform fully connected DNNs of the same size. Moreover, by equipping the physics-informed neural network (PINN) with the proposed adaptive architecture strategy to solve partial differential equations, we numerically show that adaptive PINNs not only are superior to standard PINNs but also produce interpretable hidden layers with provable stability. As a result, we also apply our architecture design strategy to solve inverse problems governed by elliptic partial differential equations.

42 ENGINEERING↗
DOE OSTI2013

Higher-order compositional modeling of three-phase flow in 3D fractured porous media based on cross-flow equilibrium

Numerical simulation of multiphase compositional flow in fractured porous media, when all the species can transfer between the phases, is a real challenge. Despite the broad applications in hydrocarbon reservoir engineering and hydrology, a compositional numerical simulator for three-phase flow in fractured media has not appeared in the literature, to the best of our knowledge. In this work, we present a three-phase fully compositional simulator for fractured media, based on higher-order finite element methods. To achieve computational efficiency, we invoke the cross-flow equilibrium (CFE) concept between discrete fractures and a small neighborhood in the matrix blocks. We adopt the mixed hybrid finite element (MHFE) method to approximate convective Darcy fluxes and the pressure equation. This approach is the most natural choice for flow in fractured media. The mass balance equations are discretized by the discontinuous Galerkin (DG) method, which is perhaps the most efficient approach to capture physical discontinuities in phase properties at the matrix-fracture interfaces and at phase boundaries. In this work, we account for gravity and Fickian diffusion. The modeling of capillary effects is discussed in a separate paper. We present the mathematical framework, using the implicit-pressure-explicit-composition (IMPEC) scheme, which facilitates rigorous thermodynamic stability analyses and the computation of phase behavior effects to account for transfer of species between the phases. A deceptively simple CFL condition is implemented to improve numerical stability and accuracy. We provide six numerical examples at both small and larger scales and in two and three dimensions, to demonstrate powerful features of the formulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Special Observing Period (SOP) data for the Year of Polar Prediction site Model Intercomparison Project (YOPPsiteMIP)

The rapid changes occurring in the polar regions require an improved understanding of the processes that are driving these changes. At the same time, increased human activities such as marine navigation, resource exploitation, aviation, commercial fishing, and tourism require reliable and relevant weather information. One of the primary goals of the World Meteorological Organization's Year of Polar Prediction (YOPP) project is to improve the accuracy of numerical weather prediction (NWP) at high latitudes. During YOPP, two Canadian “supersites” were commissioned and equipped with new ground-based instruments for enhanced meteorological and system process observations. Additional pre-existing supersites in Canada, the United States, Norway, Finland, and Russia also provided data from ongoing long-term observing programs. These supersites collected a wealth of observations that are well suited to address YOPP objectives. In order to increase data useability and station interoperability, novel Merged Observatory Data Files (MODFs) were created for the seven supersites over two Special Observing Periods (February to March 2018 and July to September 2018). All observations collected at the supersites were compiled into this standardized NetCDF MODF format, simplifying the process of conducting pan-Arctic NWP verification and process evaluation studies. This paper describes the seven Arctic YOPP supersites, their instrumentation, data collection and processing methods, the novel MODF format, and examples of the observations contained therein. MODFs comprise the observational contribution to the model intercomparison effort, termed YOPP site Model Intercomparison Project (YOPPsiteMIP). All YOPPsiteMIP MODFs are publicly accessible via the YOPP Data Portal (Whitehorse: https://doi.org/10.21343/a33e-j150, Huang et al., 2023a; Iqaluit: https://doi.org/10.21343/yrnf-ck57, Huang et al., 2023b; Sodankylä: https://doi.org/10.21343/m16p-pq17, O'Connor, 2023; Utqiagvik: https://doi.org/10.21343/a2dx-nq55, Akish and Morris, 2023c; Tiksi: https://doi.org/10.21343/5bwn-w881, Akish and Morris, 2023b; Ny-Ålesund: https://doi.org/10.21343/y89m-6393, Holt, 2023; and Eureka: https://doi.org/10.21343/r85j-tc61, Akish and Morris, 2023a), which is hosted by MET Norway, with corresponding output from NWP models.

54 ENVIRONMENTAL SCIENCES↗