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At least 271 records · Page 15

Central Compact Finite‐Difference Scheme With High Spectral Resolution for KdV Equation

This work presents a combination of cell‐node and cell‐centered compact finite difference scheme for the approximation of third derivatives involved in Korteweg–de Vries (KdV) equations. This approach employs a half‐shifted derivative construction at cell centers, avoiding the need for compact interpolation, thereby removing transfer errors; hence, it improves spectral resolution and maintains high‐order accuracy. Fourier analysis is performed to show the spectral properties of the proposed formulation, which provides higher spectral resolutions as compared to node‐based compact schemes. A filtering strategy is incorporated to suppress high‐frequency oscillations without compromising the accuracy of the numerical scheme, and the total variation diminishing Runge Kutta (TVDRK3) method is applied for time integration. Numerical experiments on linear, nonlinear, and coupled KdV systems are conducted, and a comparative analysis with cell‐node compact schemes confirms that the proposed scheme consistently reduces errors by up to an order of magnitude and achieves high spectral resolution properties.

97 MATHEMATICS AND COMPUTING↗

Prospects for ${B}_{(s)}^0 $ → π$^0$π$^0$ and ${B}_{(s)}^0 $ → ηη modes and corresponding CP asymmetries at Tera-Z

The physics potential of measuring $B^0_{(s)}$ → $π^0π^0$ and $B^0_{(s)}$ → $ηη$ decays via four-photon final states at Tera-Z phase of CEPC or FCC-ee is investigated in this paper. We propose an electromagnetic calorimeter (ECAL) with both high energy resolution and excellent separation power to efficiently reconstruct $π^0$ and $η$ from hadronic final states with high photon multiplicity. The resulting B-meson mass resolution is approximately 30 MeV, allowing 3 $σ$ separation between B 0 and $B^0_{(s)}$. With the assistance of the b-jet tagging, the relative sensitivities to B 0 → $π^0π^0$, $B^0_{(s)}$ → $π^0π^0$, B 0 → $ηη$, and $B^0_{(s)}$ → $ηη$ signal strengths at Tera-Z are projected as 0.45%, 4.5%, 18%, and 0.95%, respectively. Their dependence on various detector performances is also discussed. In addition, B 0 → $π^0π^0$ and its two isospin-related modes are paid special attention due to their roles in the determination of the CKM angle α (Φ 2 ). The anticipated precisions of their branching-ratio and CP-asymmetry measurements at Tera-Z are evaluated. We show that the measurement of the time-integrated B 0 → $π^0π^0$ CP asymmetry at Tera-Z is complementary to B-factory ones. The precision on α combining Z- and B-factory results reaches 0.4°, lower than the systematic uncertainties attached to isospin breaking.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Dynamic modelling of slip in a wind turbine spherical roller main bearing

This paper considers the problem of the dynamic modelling of macro slip in spherical roller bearings. By revisiting the fundamental physics which drive these systems, potential issues in existing models have been identified. Furthermore, in pure rolling conditions it was found that governing differential equations become "stiff", requiring the use of implicit methods of time integration. The problem of individual roller macro slip in a wind turbine main bearing is then investigated using a simplified representation of system dynamics. Model results indicate clear links between slip/friction and the operational strategy of the wind turbine, as well as significantly higher frictional effects in the downwind main bearing row. Due to modelling simplifications, these results should not yet be considered conclusive, with further work required.

17 WIND ENERGY↗

Multirate linearly-implicit GARK schemes

Many complex applications require the solution of initial-value problems where some components change fast, while others vary slowly. Multirate schemes apply different step sizes to resolve different components of the system, according to their dynamics, in order to achieve increased computational efficiency. The stiff components of the system, fast or slow, are best discretized with implicit base methods in order to ensure numerical stability. To this end, linearly implicit methods are particularly attractive as they solve only linear systems of equations at each step. This paper develops the Multirate GARK-ROS/ROW (MR-GARK-ROS/ROW) framework for linearly-implicit multirate time integration. The order conditions theory considers both exact and approximative Jacobians. The effectiveness of implicit multirate methods depends on the coupling between the slow and fast computations; an array of efficient coupling strategies and the resulting numerical schemes are analyzed. Multirate infinitesimal step linearly-implicit methods, that allow arbitrarily small micro-steps and offer extreme computational flexibility, are constructed. The new unifying framework includes existing multirate Rosenbrock(-W) methods as particular cases, and opens the possibility to develop new classes of highly effective linearly implicit multirate integrators.

97 MATHEMATICS AND COMPUTING↗

Preserving nonlinear constraints in variational flow filtering data assimilation

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems of interest obey nonlinear physical constraints, and the corresponding dynamics is confined to a certain sub-manifold of the state space. Standard data assimilation techniques applied to such systems yield posterior states lying outside the manifold, violating the physical constraints. This work focuses on particle flow filters which use stochastic differential equations to evolve state samples from a prior distribution to samples from an observation-informed posterior distribution. The variational Fokker-Planck (VFP)—a generic particle flow filtering framework—is extended to incorporate non-linear, equality state constraints in the analysis. To this end, two algorithmic approaches that modify the VFP stochastic differential equation are discussed: (i) VFPSTAB, to inexactly preserve constraints with the addition of a stabilizing drift term, and (ii) VFPDAE, to exactly preserve constraints by treating the VFP dynamics as a stochastic differential-algebraic equation (SDAE). Additionally, an implicit-explicit time integrator is developed to evolve the VFPDAE dynamics. The strength of the proposed approach for constraint preservation in data assimilation is demonstrated on three test problems: the double pendulum, Korteweg-de-Vries, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗

A smeared crack modeling framework accommodating multi-directional fracture at finite strains

A generic smeared crack modeling framework predicated on the deformation gradient decomposition (DGD) approach is proposed for use in dynamic fracture problems at finite strains, accommodating failure along multiple mutually orthogonal fracture planes embedded within an independently defined bulk material model. Within this constitutive framework, the traction equilibrium conditions imposed at each failure surface are used to determine the associated crack displacements stored as internal state variables. In general, the enforcement of interfacial equilibrium entails the implicit solution of a non-linear system of equations within the constitutive update procedure. However, if inertial effects arising due to the relative motion of the fractured material are incorporated within the model, the traction equilibrium conditions are shown to give rise to corresponding dynamic equations of motion governing the time-evolution of the crack opening displacements. For dynamic problems, an explicit time-integration procedure is devised to efficiently update the material state, subject to a set of internal frictionless contact constraints to prevent material inversion. Finally, the efficacy of the proposed modeling framework is investigated through several benchmark dynamic fracture problems run within the explicit finite element code DYNA3D.

42 ENGINEERING↗

Insights on the continuous representations of piecewise-smooth nonlinear systems: limits of applicability and effectiveness

Dynamical systems subject to intermittent contact are often modeled with piecewise-smooth contact forces. However, the discontinuous nature of the contact can cause inaccuracies in numerical results or failure in numerical solvers. Representing the piecewise contact force with a continuous and smooth function can mitigate these problems, but not all continuous representations may be appropriate for this use. Here, five representations used by previous researchers (polynomial, rational polynomial, hyperbolic tangent, arctangent, and logarithm-arctangent functions) are studied to determine which ones most accurately capture nonlinear behaviors including super- and subharmonic resonances, multiple solutions, and chaos. The test case is a single-DOF forced Duffing oscillator with freeplay nonlinearity, solved using direct time integration. This work intends to expand on past studies by determining the limits of applicability for each representation and what numerical problems may occur.

42 ENGINEERING↗

Laser-Induced Plasma as a Method for the Metallic Materials Hardness Estimation: An Alternative Approach

The application of an alternative laser-induced breakdown spectroscopy (LIBS) method based on transversely excited atmospheric (TEA) CO2 laser was investigated for the first time for estimating the hardness of metallic materials. The human eye-safe (TEA) CO2 laser, operating at 10.6 µm, was used for plasma generation. The LIBS spectra were recorded by employing a cost-effective CCD camera for the time-integrated and spatial resolved measurements. The cast iron and aluminum alloys samples with different hardness have been tested. The ratio between the magnesium ionic and neutral lines in LIBS spectra was applied for estimating the material hardness. In addition, the hardness of all samples included in this study was determined using the conventional method for material hardness determination, i.e. Vickers hardness test. The linear dependence of magnesium lines intensity ratio on the sample’s hardness was obtained for both kinds of materials. Profilometric measurements were used to verify that the newly-introduced method is almost nondestructive for the investigated metals. The results obtained in the present work confirmed the potential of using this original LIBS system not only for the fast elemental analysis but also for the direct estimation of the hardness of metals and alloys. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

36 MATERIALS SCIENCE↗

The Peridigm Meshfree Peridynamics Code

Abstract Peridigm is a meshfree peridynamics code written in C++ for use on large-scale parallel computers. It was originally developed at Sandia National Laboratories and is currently managed as an open-source, community driven software project. Its primary features include bond-based, state-based, and non-ordinary state-based constitutive models, bond failure laws, contact, and support for explicit and implicit time integration. To date, Peridigm has been used primarily by methods developers focused on solid mechanics and material failure. Peridigm utilizes foundational software components from Sandia’s Trilinos project and was designed for extensibility. This paper provides an overview of the solution methods implemented in Peridigm , a discussion of its software infrastructure, and demonstrates the use of Peridigm for the solution of several example problems.

97 MATHEMATICS AND COMPUTING↗

Spectral distortions to momentum and scalar exchanges by non-turbulent motion and patchy landscape variability

Modifications to the spectra of turbulent velocity and scalars and co-spectra of vertical fluxes of momentum and scalars due to patchy landscape heterogeneity and non-stationarity are explored for a Mediterranean ecosystem. About 9 months of high frequency measurements of the three velocity components, water vapor concentration, carbon dioxide concentration, and air temperature were analyzed for different seasons (spring/summer) and prevalent wind directions (southeast/northwest). The two wind directions sampled a contrast of clumped and patchy landscape comprised of olive trees (southeast) and wall bounded flow disturbed by the presence of few upwind trees (northwest). The measured spectra and co-spectra were also compared to theoretical scaling forms from stationary, planar homogeneous flow, in the absence of subsidence as derived from the Kansas experiment. To assess the role of low frequency non-turbulent motion on the spectral and co-spectral content, a 5-min Fourier cutoff was introduced and the analysis was limited to near-neutral conditions where the boundary layer depth is shallow compared to its unstable counterpart. It was shown that the velocity statistics were not appreciably impacted by the low-frequency motion causing non-stationarity. Moreover, the turbulent scalar fluxes were also shown not to be significantly impacted by such low frequency motion. The scalar variances were impacted, especially the water vapor variance and its concomitant spectral shape. When the non-turbulent motion was filtered, the scalar spectra at low wavenumbers followed expectations from the so-called attached eddy hypothesis (i.e. exhibited a $k^{-1}_x$ scaling with $k_x$ defining the longitudinal wavenumber) applicable for near-neutral conditions. For momentum co-spectra, the canonical shapes from the Kansas experiment appear to describe well the measurements here and in both dominant directions and seasons with some adjustment to the integral time scales based on wind direction. For the scalar co-spectra, deviations from the Kansas experiment were prevalent. The most noticeable and surprising deviations were their slow decay with increased sampling frequency at inertial subrange scales. This slow decay was shown not to contribute appreciably to the overall scalar fluxes. At those fine scales, predictions from local isotropy were expected to hold. The scalar co-spectral deviations from local isotropy were then discussed using a simplified co-spectral budget model where scalar–scalar co-spectra naturally emerged and the interplay between landscape heterogeneity and a scale-dependent pressure-scalar de-correlation time was postulated. It is also envisaged that the findings here offer a preliminary template for analyzing eddy-covariance data in situations that deviate from ideal conditions, especially regarding low-frequency modulations of scalar spectra and vertical scalar flux co-spectra.

Canopy turbulence↗

Development of a cosmic ray oriented trigger for the fluorescence telescope on EUSO-SPB2

The Extreme Universe Space Observatory on a Super Pressure Balloon 2 (EUSO-SPB2), in preparation, aims to make the first observations of Ultra-High Energy Cosmic Rays (UHECRs) from near space using optical techniques. EUSO-SPB2 will prototype instrumentation for future satellite-based missions, including the Probe of Extreme Multi-Messenger Astrophysics (POEMMA) and K-EUSO. The payload will consist of two telescopes. The first is a Cherenkov telescope (CT) being developed to quantify the background for future below-the-limb very high energy (E 10 PeV) astrophysical neutrino observations, and the second is a fluorescence telescope (FT) being developed for detection of UHECRs. The FT will consist of a Schmidt telescope, and a 6192 pixel ultraviolet camera with an integration time of 1.05 s. The first step in the data acquisition process for the FT is a hardware level trigger in order to decide which data to record. In order to maximize the number of UHECR induced extensive air showers (EASs) which can be detected, a novel trigger algorithm has been developed based on the intricacies and limitations of the detector. Finally, the expected performance of the trigger has been characterized by simulations and, pending hardware verification, shows that EUSO-SPB2 is well positioned to attempt the first near-space observation of UHECRs via optical techniques.

79 ASTRONOMY AND ASTROPHYSICS↗

Air quality impacts from the development of unconventional oil and gas well pads: Air toxics and other volatile organic compounds

Unconventional oil and natural gas development (UOGD) has expanded rapidly across the United States in recent decades and raised concerns about associated air quality impacts. While significant effort has been made to quantify methane emissions, relatively few observations have been made of Volatile Organic Compounds (VOCs), especially during drilling and completion of new wells. Extensive air monitoring during development of several large, multi-well pads in Broomfield, Colorado, in the Denver-Julesburg Basin, provides a novel opportunity to examine changes in local air toxics and other VOC concentrations during well drilling and completions and production. These operations offer an especially useful case to study as several management practices were implemented to reduce emissions (e.g., electrified, grid-powered drill rigs and closed loop fluid handling systems to reduce truck traffic and limit fluid handling on the pad). With simultaneous measurements of methane and 50 VOCs from October 2018 to December 2022 at as many as 19 sites near well pads, in adjacent neighborhoods, and at a more distant reference location, we identify impacts from each phase of well development and production. Use of weekly, time-integrated canisters, a Proton Transfer Reaction Mass Spectrometer (PTR-MS), continuous photoionization detectors (PID) to trigger canister collection upon detection of VOC-rich plumes, and an instrumented vehicle, provided a powerful suite of measurements to characterize both transient plumes and longer-term changes in air quality. Prior to the start of well development, VOC gradients were small across Broomfield. Once drilling commenced, concentrations of oil and gas (O&G) related VOCs, including alkanes and aromatics, increased around active well pads. Concentration increases were clearly apparent during certain operations, including drilling, coil tubing/millout operations, and production tubing installation. Emissions of C 8 –C 10 n-alkanes during drilling operations highlighted the importance of VOC emissions from synthetic drilling mud chosen to reduce odor impacts. More than 90 samples were collected of transient plumes. Using composition measurements, meteorological data, and information about well pad activities, these plumes were connected with specific UOGD operations including drilling, flowback, and production equipment maintenance. The chemical signatures of these plumes differed by operation type (e.g., C 8 –C 10 n-alkanes constituted a larger fraction of measured VOCs in drilling-related plumes). Concentrations of individual, oil and gas-related VOCs in these plumes were often several orders of magnitude higher than in background air, with maximum ethane and benzene concentrations of 79,600 and 819 ppbv, respectively. Because these plumes typically impact a monitoring site for just several minutes, they are easily missed by slower-responding instruments. Study measurements highlight future emission mitigation opportunities during UOGD operations, including better control of emissions from shakers that separate drill cuttings from drilling mud, production separator maintenance operations, and periodic emptying of sand cans during flowback operations.

54 ENVIRONMENTAL SCIENCES↗

Mechanical ventilation and indoor air quality in recently constructed U.S. homes in marine and cold-dry climates

Data were collected to characterize whole-house mechanical ventilation (WHMV) and indoor air quality (IAQ) in 55 homes in the Marine climate of Oregon and the Cold-Dry climate of Colorado in the U.S. Sixteen homes were monitored for two weeks, with and without WHMV operating. Ventilation airflows; airtightness; time-resolved CO 2 , PM2.5 and radon; and time-integrated NO 2 , NO X and formaldehyde were measured. Participants provided information about IAQ-impacting activities, perceptions and ventilation use. All homes had operational cooktop ventilation and bathroom exhaust. Thirty homes had equipment that could meet the ASHRAE 62.2–2010 standard with continuous or controlled runtime and 34 had some WHMV operating as found. Thirty-five of 46 participants with WHMV reported they did not know how to operate it, and only half of the systems were properly labeled. Two-week homes had lower formaldehyde, radon, CO 2 and NO (NO X -NO 2 ) when operated with WHMV, and had faster PM 2.5 decays following indoor emission events. Overall IAQ satisfaction was similar in Oregon and Colorado, but more Colorado participants (19% vs 3%) felt their IAQ could be improved and more reported dryness as a problem (58% vs. 14%). The collected data indicate that there are benefits of operating WHMV, even when continuous use may not be needed because outdoor pollutant concentrations are low and indoor sources do not present substantial challenges.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Atomistically-informed modeling of point defect clustering and evolution in irradiated ThO 2

A cluster dynamics (CD) model has been developed to investigate the nucleation and growth of point defect clusters, i.e., interstitial prismatic loops and nanoscale and sub-nanoscale voids, in ThO 2 during irradiation by energetic particles. The model considers cluster off-stoichiometry due to the asymmetry of point defect generation on the O and Th sublattices under irradiation, as well as the point defect diffusivities and the defect binding energies to clusters. The energies were established using detailed molecular dynamics simulations considering the statistical variability of cluster configuration. A high-order adaptive time-integration has been used to solve the model. The predicted loop density and their average size is in good agreement with reported experimental observations for proton irradiated ThO 2 at 600°C. In conclusion, the model did not predict void evolution due to the sluggish kinetics of cation vacancies, explaining the absence of voids in proton irradiated ThO 2 (and other oxides) at relatively low temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On differentiable local bounds preserving stabilization for Euler equations

This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A differentiable local bounds preserving method has been developed, which combines a Rusanov artificial diffusion operator and a differentiable shock detector. Nonlinear stabilization schemes are usually stiff and highly nonlinear. This issue is mitigated by the differentiability properties of the proposed method. Moreover, in order to further improve the nonlinear convergence, we also propose a continuation method for a subset of the stabilization parameters. The resulting method has been successfully applied to steady and transient problems with complex shock patterns. Numerical experiments show that it is able to provide sharp and well resolved shocks. Furthermore, the importance of the differentiability is assessed by comparing the new scheme with its non-differentiable counterpart. Numerical experiments suggest that, for up to moderate nonlinear tolerances, the method exhibits improved robustness and nonlinear convergence behavior for steady problems. Additionally, in the case of transient problem, we also observe a reduction in the computational cost.

42 ENGINEERING↗

Simulation of dynamic crystal plasticity with a Lagrangian discontinuous Galerkin hydrodynamic method

Here we present a new Lagrangian modal discontinuous Galerkin (DG) hydrodynamic method that supports a dynamic dislocation based crystal plasticity model for simulating the mechanical behavior of crystallographic materials, both single crystal and polycrystalline, under dynamic conditions. A modal DG approach is used to evolve fields relevant to conservation laws. These fields are approximated by Taylor series polynomials of varying degree. These polynomials describe macro-scale hydrodynamic behavior while their evolution is determined by evaluating the dynamic crystal plasticity model at material points within the element. The dynamic crystal plasticity model is sensitive to the time increment size, with too large of time increments leading to instability in the model. To mitigate this, the temporal evolution of the dynamic crystal plasticity model is achieved with the combination of a sub-incrementing scheme with Heun’s third-order time integration scheme, which is also used to temporally evolve the governing equations. The implementation of the dynamic crystal plasticity model within the DG framework is tested using a 2D approximation of the Taylor impact test with a single crystal material, using quadratic elements that have faces that can bend. In addition to the standard continuous material modeling, we propose a new simulation method that would represent the heterogeneous behavior of polycrystalline microstructures within an element by varying the position and material properties of the material points within the element. This method is demonstrated using random orientation distributions on materials points that are arranged in both structured and random configurations.

42 ENGINEERING↗

Combustion of metal powder with dinitrogen tetroxide

In this work, we present analysis of a novel reactive material system that employs dinitrogen tetroxide (N 2 O 4 ) as a liquid oxidizer with metal powder fuels. The oxidizer was added to micron scale aluminum and zirconium powders by a remote injection system. When ignited with a high voltage spark, the mixtures were observed to possess reactivity comparable to nanocomposite reactive materials, with open-tube flame expansion velocities from 500 to 1400 m/s depending on fuel/oxidizer ratio and tube diameter. Temperatures were observed to range from 3000 to 3500 K as measured with gray body fits to 16-channel time-resolved pyrometer and time-integrated spectrometer data. These values were significantly below calculated adiabatic flame temperatures, which we attribute to local deviations from stoichiometry and kinetic/energetic limitations similar to those observed in studies of particles burning in high pressures gaseous oxidizers. Al/N 2 O 4 reactivity was found to be most likely limited by the vaporization of the metal from the particle surface and Zr/N 2 O 4 was limited by slower burning and complex interactions involving the solubility of nitrogen and oxygen in the molten Zr. We also discuss the potential for these materials to be used to create an “on/off” reactive material, since N2O4 can be added remotely and driven to evaporate via vacuum or purge of inert gases to return it to a safe condition.

36 MATERIALS SCIENCE↗

Symbolic construction of the chemical Jacobian of quasi-steady state (QSS) chemistries for Exascale computing platforms

The Quasi-Steady State Approximation (QSSA) can be an effective tool for reducing the size and stiffness of chemical mechanisms for implementation in computational reacting flow solvers. However, for many applications, the resulting model still requires implicit methods for efficient time integration. Here, in this paper, we outline an approach to formulating the QSSA reduction that is coupled with a strategy to generate C++ source code to evaluate the net species production rates, and the chemical Jacobian. The code-generation component employs a symbolic approach enabling a simple and effective strategy to analytically compute the chemical Jacobian. For computational tractability, the symbolic approach needs to be paired with common subexpression elimination which can negatively affect memory usage. Several solutions are outlined and successfully tested on a 3D multipulse ignition problem, thus allowing portable application across chemical model sizes and GPU capabilities. The implementation of the proposed method is available at https://github.com/AMReX-Combustion/PelePhysics under an open-source license.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗