Search NASA⌕ Search

SEARCH · Search NASA

Results for “High Order”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Hybridized Discontinuous Galerkin Methods for Computational Fluid Dynamics

Hybridizable Discontinuous Galerkin (HDG) methods hold promise for any applications with significant advection character, including thermal hydraulics in light water reactors and advanced reactor concepts and fluid models of plasmas in magnetic confinement fusion. Its features include natural upwinding, local element conservation, and extensibility to arbitrarily high order accuracy. In the last fiscal year we have implemented HDG in the Multiphysics Object-Oriented Simulation Environment (MOOSE). We developed a first-of-its-kind automatic static condensation system in MOOSE’s underlying finite element library libMesh which can condense out arbitrarily many internal variables. Finally, we developed the first preconditioner for HDG discretizations of the Navier-Stokes equations which shows robust performance across a wide range of problem sizes and Reynolds numbers. This preconditioner yields solution times that are equivalent to the fastest developed for industry standard finite volume methods. Moreover, the arbitrarily high-order nature of HDG makes it a prime candidate for acceleration via graphical processing units (GPUs). We believe these developments will hold significant importance for future DOE Nuclear Energy (NE) and Fusion Energy Science (FES) programs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Directional Variations in Tidal Flow Multifractality and Intermittency

We explored distinct directional variations of multifractal and intermittent characteristics of ebb and flood flow velocities at nodule point, WA, tidal energy site, and complementary inspection on the East River, NY using scaling exponents of the structure function, distribution flatness, detrending moving average (DMA) analysis, multifractal detrended fluctuation analysis (MF-DFA), and high-order spectral moments. Our findings reveal that tidal flow presents higher long-range dependence (LRD) and intermittent levels for the ebb flow sections, whereas the flood flow sections exhibit a higher degree of multifractality and greater sensitivity to larger magnitude of turbulent fluctuations. We demonstrate that long-range dependence predominantly contributes to multifractal behavior in both ebb and flood flows, as evidenced by the significantly reduced multifractal spectrum width for temporally randomly permuted time series. Moreover, spectral kurtosis analysis uncovers a higher intermittent level across all frequency scales for ebb flow sections and reveals a distinct pattern of tidal flow intermittency differing from the monotonically increasing intermittent level observed in wall-bounded and grid turbulence. Finally, we demonstrate that DMA, MF-DFA, and high-order spectral moments provide more comprehensive insights than structure function scaling exponents and PDF flatness methods.

Cheng, Shyuan [Univ. of Illinois at Urbana-Champai↗
DOE OSTI2021

Improved optical standing-wave beam splitters for dilute Bose–Einstein condensates

Bose–Einstein condensate (BEC)-based atom interferometry exploits low temperatures and long coherence lengths to facilitate high-precision measurements. Progress in atom interferometry promises improvements in navigational devices like gyroscopes and accelerometers, as well as applications in fundamental physics such as accurate determination of physical constants. Previous work demonstrates that beam splitters and mirrors for coherent manipulation of dilute BEC momentum in atom interferometers can be implemented with sequences of non-resonant standing-wave light pulses. While previous work focuses on the optimization of the optical pulses’ amplitude and duration to produce high-order momentum states with high fidelity, we explore how varying the shape of the optical pulses affects optimal beam-splitter performance, as well as the effect of pulse shape on the sensitivity of optimized parameters in achieving high fidelity in high-momentum states. Here, in simulations of two-pulse beam splitters utilizing optimized square, triangle, and sinc-squared pulse shapes applied to dilute BECs, we, in some cases, reduce parameter sensitivity by an order of magnitude while maintaining fidelity.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

A Refinement-by-Superposition -Method for (curl)- and (div)-Conforming Discretizations

Here, we present refinement-by-superposition (RBS) hp-refinement infrastructure for computational electromagnetics (CEMs), which permits exponential rates of convergence. In contrast to dominant approaches to hp-refinement for continuous Galerkin methods, which rely on explicit constraint equations, the multilevel strategy presented drastically reduces the implementation complexity. Through the RBS methodology, enforcement of continuity occurs by construction, enabling arbitrary levels of refinement with ease, and without the practical (but not theoretical) limitations of constrained-node refinement. We outline the construction of the RBS hp-method for refinement with H (curl)- and H (div)-conforming finite cells. Numerical simulations for the 2-D finite element method (FEM) solution of the Maxwell eigenvalue problem demonstrate the effectiveness of RBS hp-refinement. As an additional goal of this work, we aim to promote the use of mixed-order (low- and high-order) elements in practical CEM applications.

42 ENGINEERING↗
DOE OSTI2022

In-Situ Nanoscale Focusing of Extreme Ultraviolet Solid-State High Harmonics

Extreme ultraviolet light delivering radiation with a wavelength shorter than approximately 100 nm is now available from solid-state sources. However, despite exceptional progress, efficient focusing of extreme ultraviolet photons to their ultimate diffraction limit remains a formidable challenge because of the precision of the focusing by curved, optical surfaces. Here we integrate coherent short-wavelength high-order harmonics from a MgO crystal, with a high-numerical-aperture, nanostructured, focusing element etched onto the surface of the crystal itself. We focus extreme ultraviolet light, seventh harmonic of an 800-nm laser, with a zone plate of numerical aperture 0.35, down to a waist radius of 150 nm, with 18% focusing efficiency. The estimated intensity approaches 10 7 W/cm 2 . Future developments may demonstrate nanoscale laser ablation and miniaturization of extreme ultraviolet coherent sources on a chip.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Highly cascaded first-order fiber Bragg gratings in highly multimode optical fibers for distributed temperature sensing under harsh environment conditions

This study presents a pioneering technique for fabricating highly cascaded first-order fiber Bragg gratings (FBGs) using a femtosecond laser-assisted point-by-point inscription method in highly multimode optical fibers, specifically Sapphire crystalline fiber, and pure silica coreless fiber. Notably, it marks the first successful demonstration of a distributed array comprising 10 FBGs within highly multimode fibers. This achievement is facilitated by a high-power laser technique that yields larger reflectors characterized by a Gaussian intensity profile. These first-order FBGs offer various advantages, including enhanced reflectivity, reduced fabrication time, and simplified spectral characteristics, enhancing their accessibility for interpretation when contrasted with higher-order FBGs. In addition to that it encompasses a comprehensive analysis of the robustness and efficacy of these FBGs, with particular emphasis on their ability to endure extreme temperatures. These FBGs demonstrate an advantageous capability for localized multi-point temperature monitoring, reaching temperatures up to 1500°C with sapphire crystalline fiber and 1100°C with pure silica coreless fiber. This resilience makes them suitable for deployment in harsh environmental conditions. This innovative approach substantially broadens the potential applications of highly multimode optical fibers, particularly in the arena of sensing and communication, where challenges related to thermal gradients and harsh environments prevail. Furthermore, these groundbreaking first-order FBGs signify a substantial advancement in the realm of distributed temperature sensing, offering supreme capabilities for temperature monitoring and signal stability. As such, our work holds the promise of a substantial impact on industries and applications that demand unwavering reliability under extreme conditions.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

A Condensed Constrained Nonconforming Mortar-Based Approach for Preconditioning Finite Element Discretization Problems

This paper presents and studies an approach for constructing auxiliary space preconditioners for finite element problems using a constrained nonconforming reformulation that is based on a proposed modified version of the mortar method. The well-known mortar finite element discretization method is modified to admit a local structure, providing an element-by-element or subdomain-by-subdomain assembly property. This is achieved via the introduction of additional trace finite element spaces and degrees of freedom (unknowns) associated with the interfaces between adjacent elements or subdomains. The resulting nonconforming formulation and a reduced-via-static-condensation Schur complement form on the interfaces are used in the construction of auxiliary space preconditioners for a given conforming finite element discretization problem. Overall, the properties of these preconditioners are studied and their performance is illustrated on model second order scalar elliptic problems utilizing high order elements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A note on higher-order and nonlinear limiting approaches for continuously bounds-preserving discontinuous Galerkin methods

In Dzanic (2024), a limiting approach for high-order discontinuous Galerkin schemes was introduced which allowed for imposing constraints on the solution continuously (i.e., everywhere within the element). While exact for linear constraint functionals, this approach only imposed a sufficient (but not the minimum necessary) amount of limiting for nonlinear constraint functionals. This short note shows how this limiting approach can be extended to allow exactness for general nonlinear quasiconcave constraint functionals through a nonlinear limiting procedure, reducing unnecessary numerical dissipation. Finally, some examples are shown for nonlinear pressure and entropy constraints in the compressible gas dynamics equations, where both analytic and iterative approaches are used.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

High harmonic generation in Haldane model quantum dots

We study theoretically the nonlinear electron dynamics of Haldane model quantum dots placed in the field of an ultrashort optical pulse. One of the tuning parameters of the Haldane model is the phase accumulated by an electron during its transfer between the next nearest neighbor sites. We study how this parameter affect the nonlinear electron dynamics and the generation of high optical harmonics. With increasing the phase from its zero value to 90°, the low-energy electron states in the conduction and valence bands become more localized near the edges of the quantum dot resulting in suppression of the band gap, enhancement of the dipole inter-band coupling, and strong suppression of the average low-energy electron density of the states. As a result, the nonlinear response of the electron system of a Haldane model quantum dot is the strongest at intermediate values of the phase, ≈ 30− 40°. At these values of the phase, the electron dynamics is irreversible and a few first high-order harmonics have the largest intensities. Here, when the phase approaches 90° value the generation of high harmonics is strongly suppressed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Tackling P3HT:Y‐Series Miscibility Through Advanced Processing for Tunable Aggregation

Abstract Polymer and small molecule blend thin films are of strong interest for organic electronics and particularly organic solar cells. The high miscibility in blends of ordinary P3HT and state‐of‐the‐art Y‐series non‐fullerene acceptors (NFAs) suppresses phase separation and aggregation challenging successful charge separation and transport. In a recent work, current‐induced doping (CID) is introduced, a method to precisely control the aggregation of Poly(3‐hexylthiophene) (P3HT) in solution. The highly ordered pre‐aggregation in solution is used here to control the P3HT aggregation in neat films and blends with Y12 (BTP‐4F‐12). This results in a 25‐fold increase in hole mobility in P3HT organic field‐effect transistor (OFET) devices and tunability of the P3HT aggregate quality in the presence of Y12 over large ranges. At the same time, particularly the Y12 long‐range ordering is heavily suppressed by increasing P3HT aggregation. However, solvent vapor annealing (SVA) leads to an extraordinarily high Y12 ordering, changes in the crystal orientation of Y12, and a further improvement of P3HT aggregation. A broad range of different degrees of aggregation of both materials can therefore be obtained in the final thin films solely by changing processing parameters without changing the composition of the material system.

Chemistry↗
DOE OSTI2025

Toward Higher-order Accuracy in Self-gravitating Hydrodynamics

High-order algorithms have emerged in numerical astrophysics as a promising avenue to reduce truncation error (proportional to a power of the linear resolution Δ x ) with only a moderate increase to computational expense. Significant effort has been placed in the development of finite-volume algorithms for (magneto)hydrodynamics; however, state-of-the-art astrophysical simulations tightly couple a plenitude of physics, additionally including gravity, photon transport, cosmic-ray transport, chemistry, and/or diffusion, to name a few. Algorithms frequently operator-split this additional physics (often a first-order error in time) and/or adopt a model wherein their evaluation is limited to second-order accuracy in space. In this work, we present a fourth-order-accurate finite-volume scheme for self-gravitating hydrodynamics on a uniform Cartesian grid. The method supplies source terms for the gravitational acceleration ( ρ g ) and gravitational energy release ( ρ v · g ) associated with fourth-order-accurate solutions to the Poisson equation. Our scheme (1) guarantees the conservation of total linear momentum while (2) decreasing (in proportion to Δ x 4 ) the effects of spurious heating and/or cooling associated with truncation error in the gravity. We demonstrate expected convergence rates for the algorithm by measuring errors in test problems evolving self-gravity modified linear waves and 3D polytropic equilibria. We test robustness of the algorithm by integrating an induced “inside-out” adiabatic collapse. We also discuss a method to smoothly downgrade the solution to second-order spatial accuracy to avoid spurious overshoots near steep density and/or pressure gradients.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

A parallel p ‐adaptive discontinuous Galerkin method for the Euler equations with dynamic load‐balancing on tetrahedral grids

Abstract A novel p ‐adaptive discontinuous Galerkin (DG) method has been developed to solve the Euler equations on three‐dimensional tetrahedral grids. Hierarchical orthogonal basis functions are adopted for the DG spatial discretization while a third order TVD Runge‐Kutta method is used for the time integration. A vertex‐based limiter is applied to the numerical solution in order to eliminate oscillations in the high order method. An error indicator constructed from the solution of order and is used to adapt degrees of freedom in each computational element, which remarkably reduces the computational cost while still maintaining an accurate solution. The developed method is implemented with under the Charm++ parallel computing framework. Charm++ is a parallel computing framework that includes various load‐balancing strategies. Implementing the numerical solver under Charm++ system provides us with access to a suite of dynamic load balancing strategies. This can be efficiently used to alleviate the load imbalances created by p ‐adaptation. A number of numerical experiments are performed to demonstrate both the numerical accuracy and parallel performance of the developed p ‐adaptive DG method. It is observed that the unbalanced load distribution caused by the parallel p ‐adaptive DG method can be alleviated by the dynamic load balancing from Charm++ system. Due to this, high performance gain can be achieved. For the testcases studied in the current work, the parallel performance gain ranged from 1.5× to 3.7×. Therefore, the developed p ‐adaptive DG method can significantly reduce the total simulation time in comparison to the standard DG method without p ‐adaptation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Effect of Molecular Structure of Quinones and Carbon Electrode Surfaces on the Interfacial Electron Transfer Process

Quinones can undergo thermodynamically reversible proton-coupled electron transfer reactions and are being applied as electroactive compounds in aqueous organic batteries. However, the electrochemical reversibility of these compounds is affected not only by their molecular structure but also by the properties of a carbon-based electrode surface. This study combines experimental and theoretical approaches to understand this dependence. Specifically, we study the electron transfer kinetics of two synthesized quinone derivatives and two commercially available ones with a glassy carbon, a highly ordered pyrolytic graphite, and a high-edge-density graphite electrode (HEDGE). The electrochemical reversibility is notably improved on the HEDGE, which shows a higher density of defects and presents oxygenated functional groups at its surface. The electron transfer kinetics are controlled by adsorbed species onto the HEDGE. Molecular dynamics simulation and quantum mechanics calculations suggest defects with oxygen-containing functional groups, such as C-O and C$=$O, on HEDGE surfaces drive the interaction with the functional groups of the molecules, during physisorption from van der Waals forces. The presence of sulfonic acid side groups and a greater number of aromatic rings in the molecular structure may contribute to a higher stabilization of quinone derivatives on HEDGEs. We propose that high-performance carbon-based electrodes can be obtained without catalysts for organic batteries, by the engineering of carbon-based surfaces with edge-like defects and oxygenated functional groups.

25 ENERGY STORAGE↗
DOE OSTI2020

Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation

We modify the well-known interior penalty finite element discretization method so that it allows for element-by-element assembly. This is possible due to the introduction of additional unknowns associated with the interfaces between neighboring elements. The resulting bilinear form, and a Schur complement (reduced) version of it, are utilized in a number of auxiliary space preconditioners for the original conforming finite element discretization problem. Furthermore, these preconditioners are analyzed on the fine scale, and their performance is illustrated on model second order scalar elliptic problems discretized with high order elements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Continuously bounds-preserving discontinuous Galerkin methods for hyperbolic conservation laws

For finite element approximations of transport phenomena, it is often necessary to apply a form of limiting to ensure that the discrete solution remains well-behaved and satisfies physical constraints. However, these limiting procedures are typically performed at discrete nodal locations, which is not sufficient to ensure the robustness of the scheme when the solution must be evaluated at arbitrary locations (e.g., for adaptive mesh refinement, remapping in arbitrary Lagrangian–Eulerian solvers, overset meshes, etc.). In this work, a novel limiting approach for discontinuous Galerkin methods is presented which ensures that the solution is continuously bounds-preserving (i.e., across the entire solution polynomial) for any arbitrary choice of basis, approximation order, and mesh element type. Through a modified formulation for the constraint functionals, the proposed approach requires only the solution of a single spatial scalar minimization problem per element for which a highly efficient numerical optimization procedure is presented. Here, the efficacy of this approach is shown in numerical experiments by enforcing continuous constraints in high-order unstructured discontinuous Galerkin discretizations of hyperbolic conservation laws, ranging from scalar transport with maximum principle preserving constraints to compressible gas dynamics with positivity-preserving constraints.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A short note on the accuracy of the discontinuous Galerkin method with reentrant faces

In this work, we study the convergence of the discontinuous Galerkin (DG) method applied to the advection–reaction equation on meshes with reentrant faces. On such meshes, the upwind numerical flux is not smooth, and so the numerical integration of the resulting face terms can only be expected to be first-order accurate. Despite this inexact integration, we prove that the DG method converges with order $\mathscr{O}$(h p+1/2 ), which is the same rate as in the case of exact integration. Consequently, specialized quadrature rules that accurately integrate the non-smooth numerical fluxes are not required for high-order accuracy. These results are numerically corroborated on examples of linear advection and discrete ordinates transport equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Real-fluid behavior in rapid compression machines: Does it matter?

Rapid compression machines (RCMs) have been extensively used to quantify fuel autoignition chemistry and validate chemical kinetic models at high-pressure conditions. Historically, the analyses of experimental and modeling RCM autoignition data have been conducted based on the adiabatic core hypothesis with ideal gas assumption, where real-fluid behavior has been completely overlooked, though this might be significant at common RCM test conditions. Here, this work presents a first-of-its-kind study that addresses two significant but overlooked questions for autoignition studies within RCMs in the fundamental combustion community: (i) experiment-wise, can unaccounted-for real-fluid behavior in RCMs affect the interpretation and analysis of RCM experimental data? and (ii) simulation-wise, can unaccounted-for real-fluid behavior in RCMs affect RCM autoignition modeling and the validation of chemical kinetic models? To this end, theories for real-fluid isentropic change are newly proposed and derived based on high-order Virial EoS, and are further incorporated into an effective-volume real-fluid autoignition modeling framework newly developed for RCMs. With detailed analyses, the strong real-fluid behavior in representative RCM tests is confirmed, which can greatly influence the interpretation of RCM autoignition experiments, particularly the determination of end-of-compression temperature and evolution of the adiabatic core in the reaction chamber. Furthermore, real-fluid RCM modeling results reveal that considerable error can be introduced into simulating RCM autoignition experiments when following the community-wide accepted effective-volume approach by assuming ideal-gas behavior, which can be as high as 64% in the simulated ignition delay time at compressed pressure of 125 bar and lead to contradictory validation results of chemical kinetic models. Therefore, we recommend the community to adopt frameworks with real-fluid behavior fully accounted for (e.g., the one developed in this study) to analyze and simulate past and future RCM experiments, so as to avoid misinterpretation of RCM autoignition experiments and eliminate the potential errors that can be introduced into the simulation results with the existing RCM modeling frameworks.

High-order Virial equation of state↗
DOE OSTI2023

Advanced Turbulence Models for Large-Scale Atmospheric Boundary Layer Flows

We present high-fidelity large-eddy-simulation (LES) modeling approaches for the turbulent atmospheric boundary layer (ABL) flows. Wind energy is a prime example of an application driven by ABL. Generation of electrical energy from farms of wind turbines at night in the stable ABL is a particularly interesting situation. In this report, we consider the well-known GEWEX (Global Energy and Water Cycle Experiment) Atmospheric Boundary Layer Study (GABLS) stably stratified benchmark LES case. We use a high-order spectral element code Nek5000/RS, which is supported under the DOE's Exascale Computing Project (ECP) Center for Efficient Exascale Discretizations (CEED) project, targeting application simulations on various acceleration-device based exascale computing platforms. In our earlier ANL report, we demonstrated our newly developed subgrid-scale (SGS) models based on high-pass filter (HPF), mean-field eddy viscosity (MFEV), and Smagorinsky (SMG) with no-slip and traction boundary conditions, provided with low-order statistics, convergence and turbulent structure analysis. In this report, we extend the range of our SGS modeling approaches in the context of the mean-field eddy viscosity (MFEV), to include the solution of an SGS turbulent kinetic energy equation (TKE). We demonstrate the model fidelity of Nek5000/RS in comparison to that of AMR-Wind, a block-structured second-order finite-volume code with adaptive-mesh-refinement capabilities, with which we studied scaling performance for both codes in comparison on DOE's leadership computing platforms.

17 WIND ENERGY↗