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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Earthquake-induced impact of base-isolated buildings: theory, numerical modeling, and design solutions

Earthquake shaking more intense than that used to size the horizontal clearance between a base–isolated building and near–rigid perimeter moat wall will result in hard impact, producing high–frequency, high–amplitude acceleration response in the structure and supported equipment. Herein this paper provides a design solution for the damaging effects of hard impact by installing a compliant engineered element in the load path between the base–isolated building and the moat wall, resulting in soft impact and a much smaller acceleration response. The engineered element assumed herein is a commercial–off–the–shelf marine fender with mechanical properties determined by physical testing. The attachment of a flexible engineered element, with well–defined stiffness and damping, to a near–rigid moat wall, simplifies the numerical modeling of the building–moat wall system and eliminates the need to bound the lateral stiffness of the wall for impact calculations. The simple model of the engineered element can be implemented in commercial finite element codes. Theory is developed for two–sided impact of a single–degree–of–freedom oscillator. Analytical solutions are derived for the shifted first–mode frequency of the impacted oscillator and for its free–vibration response. The shifted first–mode frequency is a function of the composite lateral stiffness of the isolator–engineered element assembly and its earthquake–induced displacement. Local peaks in the spectral response of the impacted oscillator form at odd integer multiples of the shifted first–mode frequency. The analytical solutions can be used to verify, in part, the numerical model used for impact analysis.

42 ENGINEERING↗
DOE OSTI2021

Exactness of OPF Relaxation on Three-phase Radial Networks with Delta Connections

Simulations have shown that while semi-definite relaxations of AC optimal power flow (AC-OPF) on three-phase radial networks with only wye connections tend to be exact, the presence of delta connections seem to render them inexact. This paper shows that such inexactness originates from the non-uniqueness of relaxation solutions and numerical errors amplified by the non-uniqueness. This finding motivates two algorithms to recover the exact solution of AC-OPF in unbalanced distribution networks featuring both wye and delta connections. In simulations using IEEE 13, 37 and 123-bus systems, the proposed algorithms provide exact optimal solutions up to numerical precision.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Semi-Implicit Computation of Fast Modes in a Scheme Integrating Slow Modes by a Leapfrog Method Based on a Selective Implicit Time Filter

Abstract A scheme for integration of atmospheric equations containing terms with differing time scales is developed. The method employs a filtered leapfrog scheme utilizing a fourth-order implicit time filter with one function evaluation per time step to compute slow-propagating phenomena such as advection and rotation. The terms involving fast-propagating modes are handled implicitly with an unconditionally stable method that permits application of larger time steps and faster computations compared to fully explicit treatment. Implementation using explicit and recurrent formulation is provided. Stability analysis demonstrates that the method is conditionally stable for any combination of frequencies involved in the slow and fast terms as they approach the origin. The implicit filter used in the method damps the computational modes without noticeably sacrificing the accuracy of the physical mode. TheO[(Δt 4 )] accuracy for amplitude errors achieved by the implicitly filtered leapfrog is preserved in applications where terms responsible for fast propagation are integrated with a semi-implicit method. Detailed formulation of the method for soundproof nonhydrostatic anelastic equations is provided. Procedures for implementation in global spectral shallow-water models are also given. Examples comparing numerical and analytical solutions for linear gravity waves demonstrate the accuracy of the scheme. The performance is also shown in more practical nonlinear applications, where numerical solutions accomplished by the method are evaluated against those computed from a scheme where the slow terms are handled by the third-order Runge–Kutta scheme. It demonstrates that the method is able to accurately resolve fine-scale dynamics of Kelvin–Helmholtz shear instabilities, the evolution of density current, and nonlinear drifts of twin tropical cyclones.

Meteorology & Atmospheric Sciences↗
DOE OSTI2020

Uncoupling Electrokinetic Flow Solutions

The continuum-scale electrokinetic porous-media flow and excess charge redistribution equations are uncoupled using eigenvalue decomposition. The uncoupling results in a pair of independent diffusion equations for “intermediate” potentials subject to modified material properties and boundary conditions. The fluid pressure and electrostatic potential are then found by recombining the solutions to the two intermediate uncoupled problems in a matrix-vector multiplication. Expressions for the material properties or source terms in the intermediate uncoupled problem may require extended precision or careful rewriting to avoid numerical cancellation, but the solutions themselves can typically be computed in double precision. The approach works with analytical or gridded numerical solutions and is illustrated through two examples. The solution for flow to a pumping well is manipulated to predict streaming potential and electroosmosis, and a periodic one-dimensional analytical solution is derived and used to predict electroosmosis and streaming potential in a laboratory flow cell subjected to low frequency alternating current and pressure excitation. The examples illustrate the utility of the eigenvalue decoupling approach, repurposing existing analytical solutions or numerical models and leveraging solutions that are simpler to derive for coupled physics.

58 GEOSCIENCES↗
DOE OSTI2023

Physics–Informed Neural Networks of the Saint–Venant Equations for Downscaling a Large–Scale River Model

Large-scale river models are being refined over coastal regions to improve the scientific understanding of coastal processes, hazards and responses to climate change. However, coarse mesh resolutions and approximations in physical representations of tidal rivers limit the performance of such models at resolving the complex flow dynamics near the river-ocean interface, resulting in inaccurate simulations of flood inundation. In this research, we propose a machine learning (ML) framework based on the state-of-the-art physics-informed neural network (PINN) to simulate the downscaled flow at the subgrid scale. First, we demonstrate that PINN is able to assimilate observations of various types and solve the one-dimensional (1-D) Saint-Venant equations (SVE) directly. We perform the flow simulations over a floodplain and along an open channel in several synthetic case studies. The PINN performance is evaluated against analytical solutions and numerical models. Our results indicate that the PINN solutions of water depth have satisfactory accuracy with limited observations assimilated. In the case of flood wave propagation induced by storm surge and tide, a new neural network architecture is proposed based on Fourier feature embeddings that seamlessly encodes the periodic tidal boundary condition in the PINN's formulation. Furthermore, we show that the PINN-based downscaling can produce more reasonable subgrid solutions of the along-channel water depth by assimilating observational data. The PINN solution outperforms the simple linear interpolation in resolving the topography and dynamic flow regimes at the subgrid scale. This study provides a promising path towards improving emulation capabilities in large-scale models to characterize fine-scale coastal processes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

High-accuracy method for modeling nucleation and growth of particles

State-of-the-art numerical models describing the kinetics of aerosol particle nucleation and growth from a cooling vapor primarily use a nodal method, in which particles that are smaller than the critical size are omitted from consideration because they are thermodynamically unfavorable. This omission is based on the assumption that most newly formed particles are above the critical size, so that subcritical-size particles are not important to take into account. Due to the nature of the nodal method, it suffers from numerical diffusion, which can cause an artificial broadening of the cluster size distribution leading to a significant overestimation of the number of large-size particles. To address these issues, we propose a more accurate numerical method that explicitly models particles of all sizes, and uses a special numerical scheme that substantially reduces the numerical diffusion and provides high solution accuracy and numerical stability. We extensively compare this novel method to the commonly used nodal solver of the general dynamic equation (GDE) for particle growth and demonstrate that it offers GDE solutions with higher accuracy with low numerical diffusion. Incorporating small subcritical clusters into the solution is crucial for: 1) more precise determination of the entire particle size distribution function and 2) wider applicability of the model to experimental studies with non-monotonic temperature variations leading to particle evaporation. The computational code implementing this numerical method in Python is available upon request.

42 ENGINEERING↗
DOE OSTI2022

A Higher Order, Stable Partitioned Scheme for Fluid-Structure Interaction Problems

Although still a very active area of research with many open questions, there exist highly-accurate and efficient algorithms for numerically estimating solutions to the equations of fluid motion. Similarly, great strides have been made in numerically modeling the motion of solids. However, there exist many practical applications where one must solve both fluid and structure in tandem. There is a gap in the literature for high order unconditionally stable partitioned algorithms for problems of this type. We investigate a new partitioned scheme which shows promise in filling this gap. We use a finite-element-based model with an added mass approach on problems coupling the Euler beam equation with the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Parallelized POD-based suboptimal economic model predictive control of a state-constrained Boussinesq approximation

Motivated by an energy efficient building application, we want to optimize a quadratic cost functional subject to the Boussinesq approximation of the Navier-Stokes equations and to bilateral state and control constraints. Since the computation of such an optimal solution is numerically costly, we design an efficient strategy to compute a sub-optimal (but applicationally acceptable) solution with significantly reduced computational effort. We employ an economic Model Predictive Control (MPC) strategy to obtain a feedback control. The MPC sub-problems are based on a linear-quadratic optimal control problem subjected to mixed control and state constraints and a convection-diffusion equation, reduced with proper orthogonal decomposition. Finally, to solve each sub-problem, we apply a primal-dual active set strategy. The method can be fully parallelized, which enables the solution of large problems with real-world parameters.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Sensitivity Analysis for Solutions to Heterogeneous Nonlocal Systems. Theoretical and Numerical Studies

The paper presents a collection of results on continuous dependence for solutions to nonlocal problems under perturbations of data and system parameters. The integral operators appearing in the systems capture interactions via heterogeneous kernels that exhibit different types of weak singularities, space dependence, even regions of zero-interaction. Here, the stability results showcase explicit bounds involving the measure of the domain and of the interaction collar size, nonlocal Poincaré constant, and other parameters. In the nonlinear setting, the bounds quantify in different L p norms the sensitivity of solutions under different nonlinearity profiles. The results are validated by numerical simulations showcasing discontinuous solutions, varying horizons of interactions, and symmetric and heterogeneous kernels.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Numerical Study of Mineral Nucleation and Growth on a Substrate

We report nucleation and growth processes of minerals and other crystals can significantly affect one another due to the transport limitations and local depletion of reactive ions in the solution. Most numerical models and experimental measurements have typically focused on either growth or nucleation, but not both. In this work, we incorporate a heterogeneous nucleation process based on classical nucleation theory into a microcontinuum model that implements the Darcy–Brinkman–Stokes approach to study the interplay between nucleation and crystal growth on a substrate in diffusive systems. We demonstrate how the Damköhler number (reaction rate) and nucleation rate prefactor change the effective nucleation rate on a substrate. Higher surface growth rates deplete the solute concentration around the nuclei that appear initially on the substrate, creating islands that screen against further nucleation. The model predicts that measured nucleation rates may be affected by the history of crystal nucleation on the substrate. In the extreme case of high growth rates relative to diffusion, it predicts that the rate of subsequent nucleation is limited by reactant depletion. We introduce a nondimensional number α to represent the relation between surface propagation rate during growth and the heterogeneous nucleation rate. We show that it is important to control Damköhler number and α to achieve similar precipitation regimes at different reaction and nucleation rates. We suggest that the observed universality can guide the interpretation of experimental results on nucleation rates, since matching experiment can be achieved by tuning transport, reaction, and nucleation parameters simultaneously. In addition, we show how the bulk solution concentration affects the structure and topology of precipitation on a substrate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Lattice Green’s Functions for High-Order Finite Difference Stencils

Lattice Green's Functions (LGFs) are fundamental solutions to discretized linear operators, and as such they are a useful tool for solving discretized elliptic PDEs on domains that are unbounded in one or more directions. The majority of existing numerical solvers that make use of LGFs rely on a second-order discretization and operate on domains with free-space boundary conditions in all directions. Under these conditions, fast expansion methods are available that enable precomputation of 2D or 3D LGFs in linear time, avoiding the need for brute-force multi-dimensional quadrature of numerically unstable integrals. Here we focus on higher-order discretizations of the Laplace operator on domains with more general boundary conditions, by (1) providing an algorithm for fast and accurate evaluation of the LGFs associated with high-order dimension-split centered finite differences on unbounded domains, and (2) deriving closed-form expressions for the LGFs associated with both dimension-split and Mehrstellen discretizations on domains with one unbounded dimension. Through numerical experiments we demonstrate that these techniques provide LGF evaluations with near machine-precision accuracy, and that the resulting LGFs allow for numerically consistent solutions to high-order discretizations of the Poisson's equation on fully or partially unbounded 3D domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Nonlinear dynamics of quadratic gravity in spherical symmetry

We present the first numerically stable nonlinear evolution for the leading-order gravitational effective field theory (quadratic gravity) in the spherically-symmetric sector. The formulation relies on (i) the harmonic gauge to cast the evolution system into quasilinear form (ii) the Cartoon method to reduce to spherical symmetry in keeping with the harmonic gauge, and (iii) order reduction to first order (in time) by means of introducing auxiliary variables. The well posedness of the respective initial-value problem is numerically confirmed by evolving randomly perturbed flat-space and black-hole initial data. In conclusion, our study serves as a proof-of-principle for the possibility of stable numerical evolution in the presence of higher derivatives.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

An asymptotic-preserving 2D-2P relativistic Drift-Kinetic-Equation solver for runaway electron simulations in axisymmetric tokamaks

We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of tokamak devices. The approach is derived from an exact Green's function solution with numerical approximations of quantifiable impact, and results in a simple, two-step operator-split algorithm, consisting of a collisional Eulerian step, and a Lagrangian orbit-integration step with analytically prescribed kernels. The AP character of the approach is demonstrated by analysis of the dominant numerical errors, as well as by numerical experiments. We demonstrate the ability of the algorithm to provide accurate answers regardless of plasma collisionality on a circular axisymmetric tokamak geometry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Time-periodic steady-state solution of fluid-structure interaction and cardiac flow problems through multigrid-reduction-in-time

In this study, a time-periodic MGRIT algorithm is proposed as a means to reduce the time-to-solution of numerical algorithms by exploiting the time periodicity inherent to many applications in science and engineering. The time-periodic MGRIT algorithm is applied to a variety of linear and nonlinear single- and multiphysics problems that are periodic-in-time. It is demonstrated that the proposed parallel-in-time algorithm can obtain the same time-periodic steady-state solution as sequential time-stepping. It is shown that the required number of MGRIT iterations can be estimated a priori and that the new MGRIT variant can significantly and consistently reduce the time-to-solution compared to sequential time-stepping, irrespective of the number of dimensions, linear or nonlinear PDE models, single-physics or coupled problems and the employed computing resources. The numerical experiments demonstrate that the time-periodic MGRIT algorithm enables a greater level of parallelism yielding faster turnaround, and thus, facilitating more complex and more realistic problems to be solved.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

$\mathrm{SageNet}$: Fast Neural Network Emulation of the Stiff-amplified Gravitational Waves from Inflation

Accurate modeling of the inflationary gravitational waves (GWs) requires time-consuming, iterative numerical integrations of differential equations to take into account their backreaction on the expansion history. To improve computational efficiency while preserving accuracy, we present the Stiff-amplified Gravitational-wave Emulator Network (SageNet), a deep learning framework designed to replace conventional numerical solvers (code available at https://github.com/YifangLuo/SageNet). SageNet employs a long short-term memory architecture to emulate the present-day energy density spectrum of the inflationary GWs with possible stiff amplification, Ω GW (f). Trained on a data set of 25,689 numerically generated solutions, SageNet allows accurate reconstructions of Ω GW (f) and generalizes well to a wide range of cosmological parameters; 90.9% of the test emulations with randomly distributed parameters exhibit errors of under 4%. In addition, SageNet demonstrates its ability to learn and reproduce the artificial, adaptive sampling patterns in numerical calculations, which implement denser sampling of frequencies around changes in spectral indices in Ω GW (f). The dual capability of learning both physical and artificial features of the numerical GW spectra establishes SageNet as a robust alternative to exact numerical methods. Finally, our benchmark tests show that SageNet reduces the computation time from tens of seconds to milliseconds, achieving a speedup of ∼10 4 times over standard CPU-based numerical solvers with the potential for further acceleration on GPU hardware. These capabilities make SageNet a powerful tool for accelerating Bayesian inference procedures for extended cosmological models. In a broad sense, the SageNet framework offers a fast, accurate, and generalizable solution to modeling cosmological observables whose theoretical predictions demand costly differential equation solvers.

Astronomy data modeling↗
DOE OSTI2020

Solving Stochastic Inverse Problems for Property–Structure Linkages Using Data-Consistent Inversion and Machine Learning

Determining process–structure–property linkages is one of the key objectives in material science, and uncertainty quantification plays a critical role in understanding both process–structure and structure–property linkages. In this work, we seek to learn a distribution of microstructure parameters that are consistent in the sense that the forward propagation of this distribution through a crystal plasticity finite element model matches a target distribution on materials properties. This stochastic inversion formulation infers a distribution of acceptable/consistent microstructures, as opposed to a deterministic solution, which expands the range of feasible designs in a probabilistic manner. Furthermore, to solve this stochastic inverse problem, we employ a recently developed uncertainty quantification framework based on push-forward probability measures, which combines techniques from measure theory and Bayes’ rule to define a unique and numerically stable solution. This approach requires making an initial prediction using an initial guess for the distribution on model inputs and solving a stochastic forward problem. To reduce the computational burden in solving both stochastic forward and stochastic inverse problems, we combine this approach with a machine learning Bayesian regression model based on Gaussian processes and demonstrate the proposed methodology on two representative case studies in structure–property linkages.

36 MATERIALS SCIENCE↗
DOE OSTI2023

On the use of dielectric elements in axion searches with microwave resonant cavities

This study explores the primary effects of dielectric materials in a resonant cavity-based search for axion dark matter. While dielectrics prove beneficial in numerous cases, their incorporation may lead to less-than-optimal performance, especially for the lowest TM mode. Additionally, the stronger confinement of the electric field inside the dielectrics can exacerbate mode mixings, in particular for higher-order modes. Case studies have been carried out using a combination of analytical solutions and numerical simulations. The findings indicate dielectric cavities employing the TM 010 mode experience a significant reduction in sensitivity when compared to a similar search conducted in a cavity at equivalent frequency using no dielectrics.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Penetration of Fission Products Ions into Complex Solids and the Effect of Ionic Wash Methods

During washing of radiologically impacted building surfaces, penetration of radionuclide ions into complex solids associated with these surfaces may occur. This study investigates the penetration of Cs-137, Sr-85, and Eu-152 solutions into numerous common building materials and radionuclide behavior when these materials were exposed to a static bath or low-pressure flow of tap water, 0.1 M potassium chloride (KCl), and 0.5 M KCl. The decontamination efficacy and the depth profile for residual contamination were measured to determine the conditions under which applying a wash solution has benefit compared to physically removing the surface material. On asphalt, 70-80% of the radionuclides were found to be within 0.02 mm of the surface. Concrete is more porous than asphalt, and 80% of the radionuclides were within 0.2 mm of the surface for Cs-137 and Eu-152 and 50-80% for Sr-85. Water effectively removed all contaminants from hard nonporous surfaces. Finally, this paper illustrates that a wash penalty factor concept-defined as ratio of the depth at which 50% of the radioactivity is found in the washed sample divided by the depth at which 50% of radioactivity is found in the control-can serve as a way to quantify whether the wash method increases the depth at which contamination penetrates into the material and thus the material becomes more difficult to decontaminate.

building materials↗