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At least 1,657 records · Page 92
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DOE OSTI2020

Energy conservative SBP discretizations of the acoustic wave equation in covariant form on staggered curvilinear grids

In this work, we develop a numerical method for solving the acoustic wave equation in covariant form on staggered curvilinear grids in an energy conserving manner. The use of a covariant basis decomposition leads to a rotationally invariant scheme that outperforms a Cartesian basis decomposition on rotated grids. The discretization is based on high order Summation-By-Parts (SBP) operators and preserves both symmetry and positive definiteness of the contravariant metric tensor. To improve accuracy and decrease computational cost, we also derive a modified discretization of the metric tensor that leads to a conditionally stable discretization. Bounds are derived that yield a point-wise condition that can be evaluated to check for stability of the modified discretization. This condition shows that the interpolation operators should be constructed such that their norm is close to one.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Deep learning of free boundary and Stefan problems

Free boundary problems appear naturally in numerous areas of mathematics, science and engineering. These problems present a great computational challenge because they necessitate numerical methods that can yield an accurate approximation of free boundaries and complex dynamic interfaces. In this work, we propose a multi-network model based on physics-informed neural networks to tackle a general class of forward and inverse free boundary problems called Stefan problems. Specifically, we approximate the unknown solution as well as any moving boundaries by two deep neural networks. Besides, we formulate a new type of inverse Stefan problems that aim to reconstruct the solution and free boundaries directly from sparse and noisy measurements. We demonstrate the effectiveness of our approach in a series of benchmarks spanning different types of Stefan problems, and illustrate how the proposed framework can accurately recover solutions of partial differential equations with moving boundaries and dynamic interfaces. All code and data accompanying this manuscript are publicly available at https://github.com/PredictiveIntelligenceLab/DeepStefan.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks

Electroconvection is a multiphysics problem involving coupling of the flow field with the electric field as well as the cation and anion concentration fields. Here, we use electroconvection as a benchmark problem to put forward a new data assimilation framework, the DeepM&Mnet, for simulating multiphysics and multiscale problems at speeds much faster than standard numerical methods using pre-trained neural networks. We first pre-train DeepONets that can predict independently each field, given general inputs from the rest of the fields of the coupled system. DeepONets can approximate nonlinear operators and are composed of two sub-networks, a branch net for the input fields and a trunk net for the locations of the output field. DeepONets, which are extremely fast, are used as building blocks in the DeepM&Mnet and form constraints for the multiphysics solution along with some sparse available measurements of any of the fields. We demonstrate the new methodology and document the accuracy of each individual DeepONet, and subsequently we present two different DeepM&Mnet architectures that infer accurately and efficiently 2D electroconvection fields for unseen electric potentials. Furthermore, the DeepM&Mnet framework is general and can be applied for building any complex multiphysics and multiscale models based on very few measurements using pre-trained DeepONets in a “plug-and-play” mode.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

First-passage time statistics on surfaces of general shape: Surface PDE solvers using Generalized Moving Least Squares (GMLS)

Here, we develop numerical methods for computing statistics of stochastic processes on surfaces of general shape with drift-diffusion dynamics d X t = a (X t ) dt + b(X t ) d W t . We formulate descriptions of Brownian motion and general drift-diffusion processes on surfaces. We consider statistics of the form u (x) = E x [$∫^{τ}_{0}$ g (X t ) dt ] + E x [ f (X τ )] for a domain Ω and the exit stopping time τ = inf t { t >0 | X i Ω}, where f , g are general smooth functions. For computing these statistics, we develop high-order Generalized Moving Least Squares (GMLS) solvers for associated surface PDE boundary-value problems based on Backward- Kolmogorov equations. We focus particularly on the mean First Passage Times (FPTs) given by the case f = 0, g = 1 where u (x) = E x [τ]. We perform studies for a variety of shapes showing our methods converge with high-order accuracy both in capturing the geometry and the surface PDE solutions. We then perform studies showing how statistics are influenced by the surface geometry, drift dynamics, and spatially dependent diffusivities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Scalable preconditioning for the stabilized contact mechanics problem

We present a family of preconditioning strategies for the contact problem in fractured and faulted porous media. We combine low-order continuous finite elements to simulate the bulk deformation with piecewise constant Lagrange multipliers to impose the frictional contact constraints. This formulation is not uniformly inf-sup stable and requires stabilization. We improve previous work by Franceschini et al. (2020) by introducing a novel jump stabilization technique that requires only local geometrical and mechanical properties. We then design scalable preconditioning strategies that take advantage of the block structure of the Jacobian matrix using a physics-based partitioning of the unknowns by field type, namely displacement and Lagrange multipliers. The key to the success of the proposed preconditioners is a pseudo-Schur complement obtained by eliminating the Lagrange multiplier degrees of freedom, which can then be efficiently solved using an optimal multigrid method. Numerical results, including complex real-world problems, are presented to illustrate theoretical properties, scalability and robustness of the preconditioner. A comparison with other approaches available in the literature is also provided.

58 GEOSCIENCES↗
DOE OSTI2023

Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state

Here, this paper is concerned with the approximation of the compressible Euler equations supplemented with an arbitrary or tabulated equation of state. The proposed approximation technique is robust, formally second-order accurate in space, invariant-domain preserving, and works for every equation of state, tabulated or analytic, provided the pressure is nonnegative. An entropy surrogate functional that grows across shocks is proposed. The numerical method is verified with novel analytical solutions and then validated with several computational benchmarks seen in the literature including problems with composite waves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Dyn$\mathrm{AMO}$: Multi-agent reinforcement learning for dynamic anticipatory mesh optimization with applications to hyperbolic conservation laws

Here we introduce DynAMO, a reinforcement learning paradigm for Dynamic Anticipatory Mesh Optimization. Adaptive mesh refinement is an effective tool for optimizing computational cost and solution accuracy in numerical methods for partial differential equations. However, traditional adaptive mesh refinement approaches for time-dependent problems typically rely only on instantaneous error indicators to guide adaptivity. As a result, standard strategies often require frequent remeshing to maintain accuracy. In the DynAMO approach, multi-agent reinforcement learning is used to discover new local refinement policies that can anticipate and respond to future solution states by producing meshes that deliver more accurate solutions for longer time intervals. By applying DynAMO to discontinuous Galerkin methods for the linear advection and compressible Euler equations in two dimensions, we demonstrate that this new mesh refinement paradigm can outperform conventional threshold-based strategies while also generalizing to different mesh sizes, remeshing and simulation times, and initial conditions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A robust framework for frictional fault contact in geological formations using a stabilized augmented Lagrangian approach

Numerical simulations are essential to evaluate the performance and safety of engineered subsurface systems such as geological carbon storage sites, enhanced geothermal fields, and oil and gas reservoirs. A key challenge lies in accurately modeling the frictional contact behavior along fault surfaces. This problem involves inequality constraints that arise from the physics of frictional slip, requiring specialized numerical methods to handle the resulting highly nonlinear and path-dependent behavior. Here, in this work, we address this challenge using an Augmented Lagrangian Method (ALM) implemented via the Uzawa algorithm. The formulation employs mixed finite element spaces, combining low-order piecewise linear displacements within the 3D domain cells with piecewise constant tractions defined on the fault surfaces. Furthermore, to ensure stability and satisfy the inf-sup condition, the discrete displacement space is enriched with face bubble functions on both sides of the contact interfaces. This approach offers several advantages over other stabilization techniques that rely on additional terms, and it integrates naturally in the Uzawa framework.

58 GEOSCIENCES↗
DOE OSTI2023

Even spheres as joint spectra of matrix models

The Clifford spectrum is a form of joint spectrum for noncommuting matrices. This theory has been applied in photonics, condensed matter and string theory. In applications, the Clifford spectrum can be efficiently approximated using numerical methods, but this only is possible in low dimensional example. In this paper we examine the higher-dimensional spheres that can arise from theoretical examples. We also describe a constructive method to generate five real symmetric almost commuting matrices that have a K-theoretical obstruction to being close to commuting matrices. For this, we look to matrix models of topological electric circuits.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

MATAR: A performance portability and productivity implementation of data-oriented design with Kokkos

There is a need for simple, fast, and memory-efficient multidimensional data structures for dense and sparse storage that arise with numerical methods and in software applications. The data structures must perform equally well across multiple computer architectures, including CPUs and GPUs. For this purpose, we developed MATAR, a C++ software library that allows for simple creation and use of intricate data structures that is also portable across disparate architectures using Kokkos. Here, the performance aspect is achieved by forcing contiguous memory layout (or as close to contiguous as possible) for multidimensional and multi-size dense or sparse MATrix and ARray (hence, MATAR) types. Our results show that MATAR has the capability to improve memory utilization, performance, and programmer productivity in scientific computing. This is achieved by fitting more work into the available memory, minimizing memory loads required, and by loading memory in the most efficient order. This document describes the purpose of the work, the implementation of each of the data types, and the resulting performance both in some simple baseline test cases and in an application code.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Analysis of gas jetting and fumarole acoustics at Aso Volcano, Japan

The gas-thrust region of a large volcanic eruption column is predominately a momentum-driven, fluid flow process that perturbs the atmosphere and produces sound akin to noise from jet and rocket engines, termed “jet noise”. In this paper, we aim to enhance understanding of large-scale volcanic jets by studying an accessible, less hazardous fumarolic jet. We characterize the acoustic signature of ~ 2.5-meter wide vigorously jetting fumarole at Aso Volcano, Japan using a 5-element infrasound array located on the nearby crater. The fumarole opened on 13 July 2015 on the southwest flank of the partially collapsed pyroclastic cone within Aso Volcano's Naka-dake crater and had persistent gas jetting, which produced significant audible jet noise. The array was ~ 220 m from the fumarole and 57.6° from the vertical jet axis, a recording angle not typically feasible in volcanic environments. Array processing is performed to distinguish fumarolic jet noise from wind. Highly correlated periods are characterized by sustained, low-amplitude signal with a 7–10 Hz spectral peak. Finite difference time domain method numerical modeling suggests the influence of topography near the vent and along the propagation path significantly affects the spectral content, complicating comparisons with laboratory jet noise. The fumarolic jet has a low estimated Mach number (0.3 to 0.4) and measured temperature of ~ 260 °C. The Strouhal number for infrasound from volcanic jet flows and geysers is not known; thus we assume a peak Strouhal number of 0.19 based on pure-air laboratory jet experiments. This assumption leads to an estimated exit velocity of the fumarole of ~ 79 to 132 m/s. Finally, using published gas composition data from 2003 to 2009, the fumarolic vent area estimated from thermal infrared images, and estimated jet velocity, we estimate total volatile flux at ~ 160–270 kg/s (14,000–23,000 t/d).

58 GEOSCIENCES↗
DOE OSTI2018

Simulation tools for atom probe tomography: A path for diagnosis and treatment of image degradation

The ideal picture of a near-perfect 3D microscope often presented regarding Atom Probe Tomography faces several issues. These issues degrade the metrological performance of the instrument and find their roots in the phenomena acting at the atomic to the mesoscopic level in the vicinity of the surface of a field emitter. From the field evaporation process at the atomic scale, to the macroscopic scale of the instrument, the path to model the imaging process and to develop more accurate and reliable reconstruction algorithms is not a single lane road. This paper focused on the numerical methods used to understand, treat, and potentially heal imaging issues commonly affecting the data in atom probe experiments. A lot of room for improvement exists in solving accuracy problems observed in complex materials by means of purely electrostatic models describing the image formation in a classical approach. Looking at the sample at the atomic scale, the phenomena perturbing the imaging process are subtle. An examination of atomic scale modifications of the sample surface in the presence of a high surface electric field is therefore mandatory. Atomic scale molecular dynamic models integrating the influence of the high surface electric are being developed with this aim. It is also demonstrated that the complex behavior of atoms and molecules in high fields, and consequences on collected data, can be understood through the use of accurate ab-initio models modified to include the impact of the extreme surface electric field.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

Harnessing structural stochasticity in the computational discovery and design of microstructures

This paper presents a deep generative model-based design methodology for tailoring the structural stochasticity of microstructures. Although numerous methods have been established for designing deterministic (periodic) or stochastic microstructures, a systematic design approach that allows the unified treatment of both deterministic and stochastic microstructure design domains has yet to be created. The proposed methodology resolves this issue by learning a unified feature space that embodies diverse structural patterns with continuously varying stochasticity levels. A highly diverse microstructure database is established to incorporate various types of deterministic and stochastic microstructure patterns. A property-aware deep generative model is proposed to learn a unified feature space of the structural characteristics, as well as the relationship between structure features and properties of interest. Autoencoder (AE), Variational Autoencoder (VAE), and Adversarial Autoencoder (AAE) are compared to understand their relative merits in the property-aware learning of the unified feature space. Microstructural designs with tailorable stochasticity and properties are obtained by searching the unified feature space. Multiple design cases are presented to demonstrate the capability of designing microstructures for structural stochasticity and properties. Furthermore, the proposed method is employed to create stochastically graded structures, which manipulate the mechanical behaviors by varying the local stochasticity of the structure.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Elevated temperature mechanical properties of Inconel 617 surface oxide using nanoindentation

Inconel 617 is a principal candidate material for helium gas cooled very-high-temperature reactors with outlet temperatures of 700–950 °C. Recent findings showed that this alloy develops unique surface oxide layers especially at high temperature (HT) helium environment with distinctive wear, friction and contact properties. This study investigates the elevated temperature mechanical properties of Inconel 617 top surface layers aged in HT helium environment. Nanoindentation technique is used to obtain load-displacement graphs of the alloy top surface oxide in temperatures ranging from 25 °C up to 600 °C. In addition, using finite element analysis along with an iterative regression technique, a semi-numerical method is developed to further measure and quantify the material parameters and, in particular, time-independent and creep characteristics of the oxide. Although Young's modulus of the oxide is found to be relatively close to the bulk for the tested temperatures, the yield strength and hardness, in comparison to the bulk material, increase significantly as the material is oxidized after aging. The oxide exhibits significant softening as the temperature increases to 600 °C. Unlike the bulk material, diffusion through the grains is found to be the dominant creep mechanism for the oxide. Considerable difference between the mechanical properties of the oxide and the bulk material shows the need for accurate measurements of near surface mechanical properties, if reliable predictive contact and tribological models are sought at elevated temperatures.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Precise Lifetime Measurements in Light Nuclei for Benchmarking Modern Ab-initio Nuclear Structure Models

A new generation of ab-initio calculations, based on realistic two- and three-body forces, is having a profound impact on our view of how nuclei work. To improve the numerical methods, and the parameterization of 3-body forces, new precise data are needed. Electromagnetic transitions are very sensitive to the dynamics which drive mixing between configurations. We have made a series of precise (< 3%) measurements of electromagnetic transitions in the A=10 nuclei {sup 10}C and {sup 10}Be by using the Doppler Shift Attenuation method carefully. Many interesting features can be reproduced including the strong α clustering. New measurements on {sup 8}Be and {sup 12}Be highlight the interplay between the alpha clusters and their valence neutrons.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Optimization of the magnetic horn for the nuSTORM non-conventional neutrino beam using the genetic algorithm

This paper describes the strategy for optimizing the magnetic horn for the neutrinos from STORed Muons (nuSTORM) facility. The nuSTORM magnetic horn is the primary collection device for the secondary particles generated by bombarding a solid target with 120 GeV protons. As a consequence of the non-conventional beamline designed for nuSTORM, the requirements on the horn are different from those for a conventional neutrino beamline. At nuSTORM, muons decay while circulating in the storage ring, and the detectors are placed downstream of the production straight so as to be exposed to the neutrinos from muon decay. nuSTORM aims at precisely measuring the neutrino cross sections, and providing a definitive statement about the existence of sterile neutrinos. The nuSTORM horn aims at focusing the pions into a certain phase space so that more muons from pion decay can be accepted by the decay ring. The paper demonstrates a numerical method that was developed to optimize the horn design to gain higher neutrino flux from the circulating muons. A Genetic Algorithm (GA) was applied to the simultaneous optimization of the two objectives in this study. In conclusion, the application of the technique discussed in this paper is not limited to either the nuSTORM facility or muon based facilities, but can be used for other neutrino facilities that use magnetic horns as collection devices.

43 PARTICLE ACCELERATORS↗
DOE OSTI2019

Numerical study and test of the APS linac transverse deflecting cavity

The transverse deflecting cavity can be used to transform particle distributions in the 6D phase space, which makes it a promising component in phase space beam diagnostics and beam manipulations. In the Advanced Photon Source (APS) Linac, a LOLA-type traveling wave deflecting cavity was installed for the diagnostics of beam characteristics, such as the bunch length, bunch temporal profile, time-dependent energy spread and slice (time-correlated) transverse emittance. In this paper, this deflecting cavity is modeled and analyzed with the numerical method. The effects of the center cell and coupler cell dimensions on the performance of the whole structure are studied, which shows the coupler cell radius has a dominant effect over the coupler cell length and slot width on the global reflection coefficient and field flatness. Important RF parameters, such as S-11, field flatness and phase advance etc., of the LOLA-II cavity in tuning are calculated and discussed. After optimization, the field flatness of the cavity is 2.1%, the phase advance is 119.66 degrees degrees with a standard deviation smaller than 0.5 degrees and the bandwidth is 15.738 MHz when VSWR < 1.1 (i.e. the S-11, < -26 dB). Bead-pull measurements and RF conditioning have been also performed and discussed. Finally, the initial cavity commissioning with electron beam of 375 MeV is reported, and compared with simulation.

coupler↗
DOE OSTI2017

Simulations of single- and two-phase shock tubes and gravity-driven wave problems with the RELAP-7 nuclear reactor system analysis code

Propagation of pressure waves in single and two-phase flows is of key interest for nuclear safety analyses, reactor design, construction and life extension of nuclear reactors. In this work, we assess the capabilities of RELAP-7, the next-generation nuclear reactor system code, to solve single- and two-phase flows developing pressure waves. RELAP-7 is based on a 7-equation, two-phase flow model, with distinct phasic pressures. It is well established that these hyperbolic conservation laws can develop shocks and discontinuities and thus, require a stabilization numerical method. The all-Mach flow Entropy Viscosity Method (EVM) is now employed in RELAP-7 as a viscous stabilization approach. In this paper, we briefly describe the implementation of the EVM and use open-literature test cases that exhibit pressure waves to show that the entropy viscosity method performs adequately for these single- and two-phase cases.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗