Results for “Numerical approximations” — Page 43

DOE OSTI2020

kasacr2cfrspccwrhicopol (a1)

The Ka-Band Scanning ARM Cloud Radar (KASACR) records cloud properties. ARM's scanning cloud radars are dual-frequency, dual-polarization Doppler radars mounted on a common scanning pedestal. Each pedestal includes a Ka-band radar (2kW peak power) and the deployment location determines whether the second radar is a W-band (1.7 kW peak power) or an X-band (20 kW peak power). Beamwidths for Ka-bands paired with W-bands are roughly matched at 0.3 degrees. The X-band beamwidth is approximately 1 degree. Due to the narrow antenna beamwidth, ARM’s scanning cloud radars use scanning strategies unlike typical weather radars. Rather than focusing on plan position indicator, or PPI, scans, the KASACR uses range height indicator, or RHI, scans at numerous azimuths to obtain cloud volume data. Measurements collected with the KASACR are copolar and cross-polar radar reflectivity, Doppler velocity, spectra width and spectra when not scanning, and linear depolarization ratio. KASACR data from the 2018–2019 Cloud, Aerosol, and Complex Terrain Interactions (CACTI) field campaign in Argentina are now available as b1-level products. Building on the original CACTI operational data, the b1-level products feature improved data quality resulting from extensive analyses and corrections. The data are cross-calibrated to a common point, datastreams are corrected for operational issues that occurred during the campaign, and several data quality masks and basic derived products are incorporated. For more information, read the CACTI radar b1-level processing report.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Ka-Band Scanning ARM Cloud Radar (KASACR), 2nd Generation CF-Radial Spectral Data, Vertically-Pointing Scan, Cross Mode (a1-level)

The Ka-Band Scanning ARM Cloud Radar (KASACR) records cloud properties. ARM's scanning cloud radars are dual-frequency, dual-polarization Doppler radars mounted on a common scanning pedestal. Each pedestal includes a Ka-band radar (2kW peak power) and the deployment location determines whether the second radar is a W-band (1.7 kW peak power) or an X-band (20 kW peak power). Beamwidths for Ka-bands paired with W-bands are roughly matched at 0.3 degrees. The X-band beamwidth is approximately 1 degree. Due to the narrow antenna beamwidth, ARM’s scanning cloud radars use scanning strategies unlike typical weather radars. Rather than focusing on plan position indicator, or PPI, scans, the KASACR uses range height indicator, or RHI, scans at numerous azimuths to obtain cloud volume data. Measurements collected with the KASACR are copolar and cross-polar radar reflectivity, Doppler velocity, spectra width and spectra when not scanning, and linear depolarization ratio. KASACR data from the 2018–2019 Cloud, Aerosol, and Complex Terrain Interactions (CACTI) field campaign in Argentina are now available as b1-level products. Building on the original CACTI operational data, the b1-level products feature improved data quality resulting from extensive analyses and corrections. The data are cross-calibrated to a common point, datastreams are corrected for operational issues that occurred during the campaign, and several data quality masks and basic derived products are incorporated. For more information, read the CACTI radar b1-level processing report.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

kasacr2cfrspccwrhixpol (a1)

The Ka-Band Scanning ARM Cloud Radar (KASACR) records cloud properties. ARM's scanning cloud radars are dual-frequency, dual-polarization Doppler radars mounted on a common scanning pedestal. Each pedestal includes a Ka-band radar (2kW peak power) and the deployment location determines whether the second radar is a W-band (1.7 kW peak power) or an X-band (20 kW peak power). Beamwidths for Ka-bands paired with W-bands are roughly matched at 0.3 degrees. The X-band beamwidth is approximately 1 degree. Due to the narrow antenna beamwidth, ARM’s scanning cloud radars use scanning strategies unlike typical weather radars. Rather than focusing on plan position indicator, or PPI, scans, the KASACR uses range height indicator, or RHI, scans at numerous azimuths to obtain cloud volume data. Measurements collected with the KASACR are copolar and cross-polar radar reflectivity, Doppler velocity, spectra width and spectra when not scanning, and linear depolarization ratio. KASACR data from the 2018–2019 Cloud, Aerosol, and Complex Terrain Interactions (CACTI) field campaign in Argentina are now available as b1-level products. Building on the original CACTI operational data, the b1-level products feature improved data quality resulting from extensive analyses and corrections. The data are cross-calibrated to a common point, datastreams are corrected for operational issues that occurred during the campaign, and several data quality masks and basic derived products are incorporated. For more information, read the CACTI radar b1-level processing report.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Ka-Band Scanning ARM Cloud Radar (KASACR), 2nd Generation CF-Radial Spectral Data, Vertically-Pointing Scan, Cross-Polarization Mode (a1-level)

The Ka-Band Scanning ARM Cloud Radar (KASACR) records cloud properties. ARM's scanning cloud radars are dual-frequency, dual-polarization Doppler radars mounted on a common scanning pedestal. Each pedestal includes a Ka-band radar (2kW peak power) and the deployment location determines whether the second radar is a W-band (1.7 kW peak power) or an X-band (20 kW peak power). Beamwidths for Ka-bands paired with W-bands are roughly matched at 0.3 degrees. The X-band beamwidth is approximately 1 degree. Due to the narrow antenna beamwidth, ARM’s scanning cloud radars use scanning strategies unlike typical weather radars. Rather than focusing on plan position indicator, or PPI, scans, the KASACR uses range height indicator, or RHI, scans at numerous azimuths to obtain cloud volume data. Measurements collected with the KASACR are copolar and cross-polar radar reflectivity, Doppler velocity, spectra width and spectra when not scanning, and linear depolarization ratio. KASACR data from the 2018–2019 Cloud, Aerosol, and Complex Terrain Interactions (CACTI) field campaign in Argentina are now available as b1-level products. Building on the original CACTI operational data, the b1-level products feature improved data quality resulting from extensive analyses and corrections. The data are cross-calibrated to a common point, datastreams are corrected for operational issues that occurred during the campaign, and several data quality masks and basic derived products are incorporated. For more information, read the CACTI radar b1-level processing report.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

kasacr2cfrspccwrhicross (a1)

The Ka-Band Scanning ARM Cloud Radar (KASACR) records cloud properties. ARM's scanning cloud radars are dual-frequency, dual-polarization Doppler radars mounted on a common scanning pedestal. Each pedestal includes a Ka-band radar (2kW peak power) and the deployment location determines whether the second radar is a W-band (1.7 kW peak power) or an X-band (20 kW peak power). Beamwidths for Ka-bands paired with W-bands are roughly matched at 0.3 degrees. The X-band beamwidth is approximately 1 degree. Due to the narrow antenna beamwidth, ARM’s scanning cloud radars use scanning strategies unlike typical weather radars. Rather than focusing on plan position indicator, or PPI, scans, the KASACR uses range height indicator, or RHI, scans at numerous azimuths to obtain cloud volume data. Measurements collected with the KASACR are copolar and cross-polar radar reflectivity, Doppler velocity, spectra width and spectra when not scanning, and linear depolarization ratio. KASACR data from the 2018–2019 Cloud, Aerosol, and Complex Terrain Interactions (CACTI) field campaign in Argentina are now available as b1-level products. Building on the original CACTI operational data, the b1-level products feature improved data quality resulting from extensive analyses and corrections. The data are cross-calibrated to a common point, datastreams are corrected for operational issues that occurred during the campaign, and several data quality masks and basic derived products are incorporated. For more information, read the CACTI radar b1-level processing report.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Determining Compression Characteristics of Honeycomb Material - 19674

The objective is to determine compression test characteristics of stainless steel honeycomb material to be able to represent honeycomb structures accurately in analytical models used to simulate hypothetical accident scenarios of shipping packages. Honeycomb is a material used primary in the aerospace industry due to its high strength-to-weight ratio. Because it doesn't have a shelf life and can withstand high heats, it is an excellent candidate for a structural material in package designs. Honeycomb has orthotropic material properties. The honeycomb currently being evaluated is made of metal ribbons spot welded together to form hexagon pattern between metal plates. The hexagon ribbons are brazed to the metal plates. The complexity of the honeycomb significantly lengthens the simulation time, which is further complicated when the brazing, welding, and imperfections of the material is considered. This means to affectively represent the honeycomb in simulation programs, such as Abaqus, the material needs to be approximated as a uniform orthotropic material. This requires material properties in each of the three directions, T, W, and L. The T direction is defined as the 'strong' direction, perpendicular to the honeycomb sheet. The L direction is parallel the ribbon and the W direction is perpendicular to the ribbon. Honeycomb has 3 different compression stages. Stage 1 is the initial compression where the honeycomb maintains its structural integrity and does not permanently deform from loads from normal operations. Stage 2 is when the initial buckling causes irreversible damage to the honeycomb. Stage 2 is the one we are most interested in because it absorbs the most energy from a hypothetical accident scenario. During Stage 2, the honeycomb fails layer-by-layer, indicating that the more layers, the longer material crushing is sustained, and thus the more energy that is absorbed. Stage 3 is final compression, similar to compressing solid metal. During stage 3 the stress increases with a diminishing rate of elongation and the honeycomb is completely failed where the plates between the honeycomb core sandwich the crushed honeycomb ribbon. The stress-strain graph bellow shows compression test of 3 different samples in the T direction. The red lines divide the three stages. The far left is Stage 1, the middle stage 2, and the right stage 3. The data collected is displayed in the table below. The expressions in the table represent the regression formula that represents each stage of the compression on a stress-strain graph. Stage 1 is assumed to intersect with the origin; data for stage 3 for the crush in W and L directions where unable to be gathered due to the nature of failure for those directions. Stage 1 and 2 are linear regressions while stage 3 is a degree 2, to best match the curve. Linear regression is used on stage 2 because ultimately that represents the energy absorbed. With more data, a degree n x 2 regression would be a more appropriate regression for stage 2, where n is the number of layers. The table below is the approximation of each scenario and stage. Each stage starts and ends at the intersection of the next stage. There where two main objectives for these tests: firstly to understand how honeycomb performs under extreme compression, and secondly to be able to numerically represent the honeycomb structure. Both of these where completed to varying degrees. It is important understood how the honeycomb fails. If it is crushed in the T direction it retains its integrity even after being crushed, however when crushed in the L and W crush direction, if it fails, it disintegrates, and loses all integrity. Also, the more layers the more time the material spends in stage 2. Failure is started by buckling, thus if there is any imperfection, the stress will not spike but transition straight into stage 2. The data collected and aggregated can be used for initial simulation of honeycomb used in packages. The initial testing has set the ground work for more data to be collected in order to verify results and to allow more confidence in the simulation results. This is only the initial data collected. The next steps is to continue to collect more data to verify results and to test more variants of honeycomb, with different brazing, layers, and shape.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Thermal conductivity of two-dimensional disordered fibrous materials defined by interfiber thermal contact conductance and intrinsic conductivity of fibers

A general framework for the theoretical analysis and numerical calculations of the effective thermal conductivity of two-dimensional homogeneous and isotropic disordered fibrous materials is developed in this work based on the model of random contacts between soft-core spherocylinders. The analysis accounts for the interfiber contact conductance and intrinsic conductivity of fibers and is performed in a wide space of governing parameters that includes the fiber aspect ratio, Biot number calculated for a single thermal contact between fibers, and material density ranging from values corresponding to the percolation threshold up to those characteristic of dense fiber networks. For dense networks, exact theoretical equations for the thermal conductivity of materials composed of spherocylinders with an arbitrary aspect ratio and Biot number are derived. The effect of the intrinsic conductivity of fibers on the thermal transport in fibrous materials is found to depend on the density of contacts and can be significant in sufficiently dense fiber networks even if the Biot number for a single thermal contact is small. Semiempirical corrections to the theoretical equations are derived for small and moderate fiber densities. The power law exponent describing the approximate dependence of the conductivity on the density parameter is found to vary from values close to 1 up to values exceeding 2 when evaluated within different finite ranges of the density parameter. This finding explains the variability of scaling laws for thermal conductivity of fibrous materials suggested in the literature based on numerical simulations performed in different regions of the space of material parameters.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Simulating combustion of a seven-component surrogate for a gasoline/ethanol blend including soot formation and comparison with experiments

Combustion of a seven-component surrogate for a research grade 87 octane gasoline mixed with 10% ethanol is investigated experimentally and numerically from the perspective of an isolated droplet burning under conditions that promote one-dimensional gas transport. The numerical analysis included a kinetic mechanism comprised of 398 species and 24,814 reactions and a soot model that accounted for nucleation, surface growth, coalescence/aggregation of soot particles, and luminous flame radiation. Measurements of droplet and flame diameters were made for an initial droplet diameter (D o ) of approximately 0.63 mm. The simulations agreed well with the measurements including the location of the soot shell. Preferential vaporization was revealed by simulations of the liquid concentrations in the droplet. Predicted peak soot volume fractions coincided with temperatures between 1300 K and 1400 K as a soot inception temperature. Simulations were also carried out for D o between 0.25 mm and 5 mm to explore the effect of radiation and D o on burning. Below 0.25 mm radiation was negligible and burning rates and flame temperatures converged to a single value. Increasing D o up to 1.8 mm lowered the burning rate with luminous radiation having a strong effect. When radiation was entirely removed from the model the burning rate was nearly constant. Above D o = 2 mm droplets extinguished almost immediately after ignition. The flame temperature decreased with increasing D o while it increased when radiation was omitted. As a result, the simulations show that soot precursors including polyaromatic hydrocarbons were concentrated around the soot shell.

42 ENGINEERING↗

DOE OSTI2021

Physics-Informed Neural Network Method for Forward and Backward Advection-Dispersion Equations

Advection-dispersion equations (ADEs) are commonly used to describe transport phenomena in porous media. Even though mature discretization-based numerical methods for ADEs exist, some challenges still remain, especially when it comes to solving advection-dominated forward ADEs and diffusion-dominated backward ADEs. The latter problem usually arises in the source identification context and leads to numerically unstable grid-based solutions that require a form of regularization or should be treated as an inverse problem that is computationally more expensive because it requires solving the forward problem multiple times. In this study, we propose a discretization-free approach based on the physics-informed neural network (PINN) method for solving coupled ADE and Darcy flow equations with space-dependent hydraulic conductivity. In this approach, the hydraulic conductivity, hydraulic head, and concentration fields are approximated with deep neural networks (DNNs). We assume that the conductivity field is given by its values on a grid, and we use these values to train the conductivity DNN. The head and concentration DNNs are trained by minimizing the residuals of the flow equation and ADE and using the initial and boundary conditions as additional constraints. The PINN method is applied to one- and two-dimensional forward ADE problems, where its performance for various P\'{e}clet numbers ($Pe$) is compared with the analytical and numerical solutions. We find that the PINN method is accurate with errors of less than 1\% and outperforms some conventional discretization-based methods for $Pe$ larger that 100. Next, we demonstrate that the PINN method remains accurate for the backward ADEs, with the relative errors in most cases staying under 5\% compared to the reference concentration field. Finally, we show that when available, the concentration measurements can be easily incorporated in the PINN method and significantly improve (by more than 50\% in the considered cases) the accuracy of the PINN solution of the backward ADE.

He, Qizhi↗

DOE OSTI2021

Calibration of elastoplastic constitutive model parameters from full-field data with automatic differentiation-based sensitivities

Here, we present a framework for calibration of parameters in elastoplastic constitutive models that is based on the use of automatic differentiation (AD). The model calibration problem is posed as a partial differential equation-constrained optimization problem where a finite element (FE) model of the coupled equilibrium equation and constitutive model evolution equations serves as the constraint. The objective function quantifies the mismatch between the displacement predicted by the FE model and full-field digital image correlation data, and the optimization problem is solved using gradient-based optimization algorithms. Forward and adjoint sensitivities are used to compute the gradient at considerably less cost than its calculation from finite difference approximations. Through the use of AD, we need only to write the constraints in terms of AD objects, where all of the derivatives required for the forward and inverse problems are obtained by appropriately seeding and evaluating these quantities. We present three numerical examples that verify the correctness of the gradient, demonstrate the AD approach's parallel computation capabilities via application to a large-scale FE model, and highlight the formulation's ease of extensibility to other classes of constitutive models.

42 ENGINEERING↗

DOE OSTI2020

Quantum Spectral Methods for Differential Equations

Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a d-dimensional system of linear equations or linear differential equations with complexity poly(logd). While several of these algorithms approximate the solution to within ϵ with complexity poly(log(1/ϵ)), no such algorithm was previously known for differential equations with time-dependent coefficients. In this work, we develop a quantum algorithm for linear ordinary differential equations based on so-called spectral methods, an alternative to finite difference methods that approximates the solution globally. Using this approach, we give a quantum algorithm for time-dependent initial and boundary value problems with complexity poly(logd, log(1/ϵ)).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A solution framework for linear PDE-constrained mixed-integer problems

Abstract We present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Compact representations of structured BFGS matrices

For general large-scale optimization problems compact representations exist in which recursive quasi-Newton update formulas are represented as compact matrix factorizations. For problems in which the objective function contains additional structure, recent structured quasi-Newton methods exploit available second-derivative information and approximate unavailable second derivatives. Here, this article develops the compact representations of two structured Broyden-Fletcher-Goldfarb-Shanno update formulas. The compact representations enable efficient limited memory and initialization strategies. Two limited memory line search algorithms are described for which extensive numerical results demonstrate the efficacy of the algorithms, including comparisons to IPOPT on large machine learning problems, and to L-BFGS on a real world large scale ptychographic imaging application.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

An extrapolation method to remove spurious stress concentration in micromechanical analyses of composites using pixel-based meshes

It is easier to generate a finite element mesh of complicated geometries with voxel-based meshes compared to conformal meshes. However, the local stresses in voxel-based meshes are higher owing to artificial stress concentration caused due to jagged lines that approximate a curve. Here, we propose a method that accounts for this anomaly which would lead to accurate prediction of maximum von Mises stress in voxel-based meshes. The method is based on the variation of reciprocal of stresses and associated numerical gradient. The prediction of the proposed method is compared against the results of a conformal mesh by considering four two-dimensional example problems. The accuracy of the proposed method is verified using different mesh densities, material properties, and integration schemes. The proposed method was also implemented on a conformal mesh to verify that it filters out just the spurious stress concentration and not the realistic stress concentration.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Enhancing approximate modular Bayesian inference by emulating the conditional posterior

In modular Bayesian analyses, complex models are composed of distinct modules, each representing different aspects of the data or prior information. In this context, fully Bayesian approaches can sometimes lead to undesirable feedback between modules, compromising the integrity of the inference. The “cut-distribution” prevents unwanted influence between modules by “cutting” feedback. The direct sampling (DS) algorithm is standard practice for approximating the cut-distribution, but it can be computationally intensive, especially when the number of imputations required is large. An enhanced method is proposed, the Emulating the Conditional Posterior (ECP) algorithm, which leverages emulation to increase the number of imputations. Through numerical experiment it is demonstrated that the ECP algorithm outperforms the traditional DS approach in terms of accuracy and computational efficiency, particularly when resources are constrained. Here, it is also shown how the DS algorithm can be improved using ideas from design of experiments. Some practical recommendations are given for algorithm choice in modular Bayesian analyses.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Conjectures about the Chiral Phase Transition in QCD from Anomalous Multi-Instanton Interactions

To date numerical simulations of lattice QCD have not found a chiral phase transition of first order that is expected to occur for sufficiently light pions. We show how the restoration of an exact global chiral symmetry can strongly decrease the breaking of the approximate, anomalous U A ( 1 ) symmetry. This is testable on the lattice through simulations for one through four flavors. In QCD a small breaking of the U A ( 1 ) symmetry in the chirally symmetric phase generates novel experimental signals. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Real-Time Krylov Theory for Quantum Computing Algorithms

Quantum computers provide new avenues to access ground and excited state properties of systems otherwise difficult to simulate on classical hardware. New approaches using subspaces generated by real-time evolution have shown efficiency in extracting eigenstate information, but the full capabilities of such approaches are still not understood. In recent work, we developed the variational quantum phase estimation (VQPE) method, a compact and efficient real-time algorithm to extract eigenvalues on quantum hardware. Here we build on that work by theoretically and numerically exploring a generalized Krylov scheme where the Krylov subspace is constructed through a parametrized real-time evolution, which applies to the VQPE algorithm as well as others. We establish an error bound that justifies the fast convergence of our spectral approximation. We also derive how the overlap with high energy eigenstates becomes suppressed from real-time subspace diagonalization and we visualize the process that shows the signature phase cancellations at specific eigenenergies. We investigate various algorithm implementations and consider performance when stochasticity is added to the target Hamiltonian in the form of spectral statistics. To demonstrate the practicality of such real-time evolution, we discuss its application to fundamental problems in quantum computation such as electronic structure predictions for strongly correlated systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Asymptotic-preserving dynamical low-rank method for the stiff nonlinear Boltzmann equation

In kinetic theory, numerically solving the full Boltzmann equation is extremely expensive. This is because the Boltzmann collision operator involves a high-dimensional, nonlinear integral that must be evaluated at each spatial grid point and every time step. The challenge becomes even more pronounced in the fluid (strong collisionality) regime, where the collision operator exhibits strong stiffness, causing explicit time integrators to impose severe stability restrictions. In this paper, we propose addressing this problem through a dynamical low-rank (DLR) approximation. The resulting algorithm requires evaluating the Boltzmann collision operator only r 2 times, where r, the rank of the approximation, is much smaller than the number of spatial grid points. We propose a novel DLR integrator, called the XL integrator, which reduces the number of steps compared to the available alternatives (such as the projector splitting or basis update & Galerkin (BUG) integrator). For a class of problems including the Boltzmann collision operator which enjoys a separation property between physical and velocity space, we further propose a specialized version of the XL integrator, called the sXL integrator. This version requires solving only one differential equation to update the low-rank factors. Furthermore, the proposed low-rank schemes are asymptotic-preserving, meaning they can capture the asymptotic fluid limit in the case of strong collisionality. Our numerical experiments demonstrate the efficiency and accuracy of the proposed methods across a wide range of regimes, from non-stiff (kinetic) to stiff (fluid).

97 MATHEMATICS AND COMPUTING↗