Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “convergence behaviors”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Multiscale thermal hydraulic coupling methods for boiling water reactor simulation

During the last two years, the Virtual Environment for Reactor Applications (VERA) has been extended to simulate boiling water reactors (BWRs). The thermal hydraulic effects present in BWRs are far more complex than those in pressurized water reactors (PWRs). Therefore, the runtime is significantly increase and convergence behavior worse compared to PWRs. Most of the additional runtime is spent during the first few coupled iterations, when the power shape is still rapidly evolving, dramatically affecting the thermal hydraulics (TH). To alleviate the increased computational expense, a multiscale TH coupling approach was developed in VERA in which a highly efficient, simplified TH model is solved for several coupled iterations until the power shape is partially converged. The simplified solution is used to inform the assembly-wise flow distribution in the high-fidelity TH solver CTF, reducing the amount of work required to properly balance the pressure drop in each channel and reducing runtime for the couple calculation. Because the final TH calculations are performed with CTF, there is ultimately no impact on the accuracy of the converged solution. This paper presents the details of this multiscale TH coupling approach, along with results for a 4x4 array of GE-14 fuel bundles and whole-core coupled simulations of the Hatch core. These two cases show that the multiscale approach dramatically reduces the runtime of coupled BWR simulations. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Lack of robustness and accuracy of many numerical schemes for phase-field simulations

In this paper, we study the stability, accuracy and convergence behavior of various numerical schemes for phase-field modeling through a simple ODE model. Both theoretical analysis and numerical experiments are carried out on this ODE model to demonstrate the limitation of most numerical schemes that have been used in practice. One main conclusion is that the first-order fully implicit scheme is the only robust algorithm for phase-field simulations while all other schemes (that have been analyzed) may have convergence issue if the time step size is not exceedingly small. More specifically, by rigorous analysis in most cases, we have the following conclusions: (i) The first-order fully implicit scheme converges to the correct steady state solution for all time step sizes. In the case of multiple solutions, one of the solution branches always converges to the correct steady state solution. (ii) The first-order convex splitting scheme, which is equivalent to the first-order fully implicit scheme with a different time scaling, always converges to the correct steady state solution but may seriously lack numerical accuracy for transient solutions. (iii) For the second-order fully implicit and convex splitting schemes, for any time step size $δt > 0$, there exists an initial condition $u_0$ , with $|u_0| > 1$, such that the numerical solution converges to the wrong steady state solution. (iv) For $|u_0|$ ≤ 1, all second-order schemes studied in this paper converge to the correct steady state solution although severe numerical oscillations occur for most of them if the time step size is not sufficiently small. (v) An unconditionally energy-stable scheme (such as the modified Crank–Nicolson scheme) is not necessarily better than a conditionally energy-stable scheme (such as the Crank–Nicolson scheme). Finally, most, if not all, of the above conclusions are expected to be true for more general Allen–Cahn and other phase-field models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Converged ab initio calculations of heavy nuclei

We propose a novel storage scheme for three-nucleon (3N) interaction matrix elements relevant for the normal-ordered two-body approximation used extensively in ab initio calculations of atomic nuclei. This scheme reduces the required memory by approximately two orders of magnitude, which allows the generation of 3N interaction matrix elements with the standard truncation of E 3max =28, well beyond the previous limit of 18. We demonstrate that this is sufficient to obtain the ground-state energy of 132 Sn converged to within a few MeV with respect to the E 3max truncation. In addition, we study the asymptotic convergence behavior and perform extrapolations to the un-truncated limit. Finally, we investigate the impact of truncations made when evolving free-space 3N interactions with the similarity renormalization group. We find that the contribution of blocks with angular momentum J rel > 9/2 to the ground-state energy is dominated by a basis-truncation artifact, which vanishes in the large-space limit, so these computationally expensive components can be neglected. For the two sets of nuclear interactions employed in this work, the resulting binding energy of 132 Sn agrees with the experimental value within theoretical uncertainties. This work enables converged ab initio calculations of heavy nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

A fractional model for anomalous diffusion with increased variability: Analysis, algorithms and applications to interface problems

Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. Here, we introduce a new fractional operator characterized by a doubly-variable fractional order and possibly truncated interactions. Under certain conditions on the model parameters and on the regularity of the fractional order we show that the corresponding Poisson problem is well-posed. Additionally, we introduce a finite element discretization and describe an efficient implementation of the finite-element matrix assembly in the case of piecewise constant fractional order. Through several numerical tests, we illustrate the improved descriptive power of this new operator across media interfaces. Furthermore, we present one-dimensional and two-dimensional h-convergence results that show that the variable-order model has the same convergence behavior as the constant-order model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Theory and numerics of subspace approximation of eigenvalue problems

Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to mitigate the computational burden associated with high-fidelity systems. Furthermore, we provide general error estimates under non-simple eigenvalue conditions, establishing some theoretical foundations for understanding the convergence behavior of subspace approximations. Numerical examples, including problems with one-dimensional to three-dimensional spatial domain and one-dimensional to two-dimensional parameter domain, are presented to demonstrate the efficacy of reduced basis method in handling parametric variations in boundary conditions and coefficient fields to achieve significant computational savings while maintaining high accuracy, making them promising tools for practical applications in large-scale eigenvalue computations.

Eigenvalue problems↗
DOE OSTI2021

An experimental comparison of a space-time multigrid method with PFASST for a reaction-diffusion problem

We consider two parallel-in-time approaches applied to a (reaction) diffusion problem, possibly non-linear. In particular, we consider PFASST (Parallel Full Approximation Scheme in Space and Time) and space-time multigrid strategies. For both approaches, we start from an integral formulation of the continuous time dependent problem. Then, a collocation form for PFASST and a discontinuous Galerkin discretization in time for the space-time multi-grid are employed, resulting in the same discrete solution at the time nodes. Strong and weak scaling of both multilevel strategies are compared for varying orders of the temporal discretization. Moreover, we investigate the respective convergence behavior for non-linear problems and highlight quantitative differences in execution times

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

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↗
DOE OSTI2020

Matrix-free subcell residual distribution for Bernstein finite elements: Monolithic limiting

This paper is focused on the aspects of limiting in residual distribution (RD) schemes for high-order finite element approximations to advection problems. Both continuous and discontinuous Galerkin methods are considered in this work. Discrete maximum principles are enforced using algebraic manipulations of element contributions to the global nonlinear system. The required modifications can be carried out without calculating the element matrices and assembling their global counterparts. The components of element vectors associated with the standard Galerkin discretization are manipulated directly using localized subcell weights to achieve optimal accuracy. Low-order nonlinear RD schemes of this kind were originally developed to calculate local extremum diminishing predictors for flux-corrected transport (FCT) algorithms. In the present paper, we incorporate limiters directly into the residual distribution procedure, which makes it applicable to stationary problems and leads to well-posed nonlinear discrete problems. To circumvent the second-order accuracy barrier, the correction factors of monolithic limiting approaches and FCT schemes are adjusted using smoothness sensors based on second derivatives. Finally, the convergence behavior of presented methods is illustrated by numerical studies for two-dimensional test problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Additional considerations in analytical solution for time-dependent heat conduction in a three-dimensional multilayer sphere

This work presents an analytical method to solve the heat conduction equation in three dimensions for problems consisting of multilayer concentric spheres. The method can be used to treat time-varying heat conduction problems where the heat source that drives the transient is time-invariant. Equally applicable to all Poisson-type problems with concentric spherical geometry, the method consists of representing the solution as a summation of weighted eigenfunctions. The weights for each eigenfunction are computed algebraically. Previous work has already established the core constituents of the methodology. The current work augments the existing methods by including consideration of nonzero interface resistance between layers and explicit discussion on the boundary condition homogenization required to treat inhomogeneous problems. Also, two demonstration problems are presented. One demonstration problem is based on the method of manufactured solutions and therefore allows for comparison with exact expressions for the solution temperature distribution. The second, more complex, demonstration problem relies on the finite element method for comparisons. The expected convergence behavior is observed for both demonstration problems.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Development and validation of a software for simulating γ-γ coincidence emission and detection probabilities

Gamma-gamma coincidence spectrometers have the potential to significantly enhance detection sensitivity for ultra-trace radionuclide measurements. The implementation of these spectrometers, however, is limited by the complexity of acquisition hardware, data processing and quantification. This work reports development of a novel radionuclide quantification software for γ-γ coincidence measurements. For any radionuclide, the software parses the Evaluated Nuclear Structure Data File (ENSDF) database, recursively simulating all possible γ-γ coincidence signatures and their respective emission and detection probabilities. Implemented using Python programming language, the software employs several strategies to boost overall computational performance. Since coincidence-based spectrometers are of notable interest in monitoring compliance for the Comprehensive Nuclear-Test-Ban Treaty (CTBT), the software’s execution was tested for 84 CTBT-relevant radionuclides. To date, the software has been experimentally validated for 15 radionuclides using the Advanced Radionuclide Gamma spectrOmeter (ARGO) at Pacific Northwest National Laboratory, USA (PNNL). Notably, the software can be operated in convergence mode, whereby coincidence detection efficiency’s convergence behavior can help avoid unreliable radionuclide activity estimates. With growing number of coincidence spectrometers worldwide, this paper aims to assist the radiation metrology community in developing similar software for their system.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Excited State Intramolecular Proton Transfer with Nuclear-Electronic Orbital Ehrenfest Dynamics

The recent development of the Ehrenfest dynamics approach in the nuclear-electronic orbital (NEO) framework provides a promising way to simulate coupled nuclear-electronic dynamics. Our previous study showed that the NEO-Ehrenfest approach with a semi- classical traveling proton basis method yields accurate predictions of molecular vibrational frequencies. In this work, we provide a more thorough analysis of the semiclassical traveling proton basis method to elucidate its validity and convergence behavior. We also conduct NEO-Ehrenfest dynamics simulations to study an excited state intramolecular proton transfer process. These simulations reveal that nuclear quantum effects influence the predictions of proton transfer reaction rates and kinetic isotope effects due to the intrinsic delocalized nature of the quantum nuclear wave function. This work illustrates the importance of nuclear quantum effects in coupled nuclear-electronic dynamical processes and shows that the NEO-Ehrenfest approach can be a powerful tool to provide insights and predictions for these processes.

Zhao, Luning↗
DOE OSTI2023

Large-scale molecular dynamics simulations of bubble collapse in water: Effects of system size, water model, and nitrogen

Molecular dynamics simulations in the microcanonical ensemble are performed to study the collapse of a bubble in liquid water using the single-site mW and the four-site TIP4P/2005 water models. To study system size effects, simulations for pure water systems are performed using periodically replicated simulation boxes with linear dimensions, L, ranging from 32 to 512 nm with the largest systems containing 8.7 × 10 6 and 4.5 × 10 9 molecules for the TIP4P/2005 and mW water models, respectively. The computationally more efficient mW water model allows us to reach converging behavior when the bubble dynamics results are plotted in reduced units, and the limiting behavior can be obtained through linear extrapolation in L –1 . Qualitative differences are observed between simulations with the mW and TIP4P/2005 water models, but they can be explained by the models’ differences in predicted viscosity and surface tension. Although bubble collapse occurs on time scales of only hundreds of picoseconds, the system sizes used here are sufficiently large to obtain bubble dynamics consistent with the Rayleigh–Plesset equation when using the models’ thermophysical properties as input. For the conditions explored here, extreme heating of the interfacial water molecules near the time of collapse is observed for the larger mW water systems (but the model underpredicts the viscosity), whereas heating is less pronounced for the TIP4P/2005 water systems because its larger viscosity contribution slows the collapse dynamics. The presence of nitrogen within the bubble only starts to affect bubble dynamics near the very end of the initial collapse, leading to an incomplete collapse and strong rebound for the mW water model. Although nitrogen is non-condensable at 300 K, it becomes highly compressed and reaches a liquid-like density near the collapse point. We find that the dissolution of nitrogen is much slower than the movement of the collapsing water front, and the re-expansion of the dense nitrogen droplet gives rise to bubble rebound. The incompatibility of the collapse and dissolution time scales should be considered for continuum-scale modeling of bubble dynamics. Finally, we also confirm that the diffusion coefficient for dissolved nitrogen is insensitive to pressure as the liquid transitions from a compressed to a stretched state.

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

A fast, matrix-based method to perform omnidirectional pressure integration

Abstract Experimentally-measured pressure fields play an important role in understanding many fluid dynamics problems. Unfortunately, pressure fields are difficult to measure directly with non-invasive, spatially resolved diagnostics, and calculations of pressure from velocity have proven sensitive to error in the data. Omnidirectional line integration methods are usually more accurate and robust to these effects as compared to implicit Poisson equations, but have seen slower uptake due to the higher computational and memory costs, particularly in 3D domains. This paper demonstrates how omnidirectional line integration approaches can be converted to a matrix inversion problem. This novel formulation uses an iterative approach so that the boundary conditions are updated each step, preserving the convergence behavior of omnidirectional schemes while also keeping the computational efficiency of Poisson solvers. This method is implemented in Matlab and also as a GPU-accelerated code in CUDA-C++. The behavior of the new method is demonstrated on 2D and 3D synthetic and experimental data. Three-dimensional grid sizes of up to 125 million grid points are tractable with this method, opening exciting opportunities to perform volumetric pressure field estimation from 3D PIV measurements.

42 ENGINEERING↗
DOE OSTI2026

MATEY: multiscale adaptive transformer models for spatiotemporal physical systems

Accurate representation of the multiscale features in spatiotemporal physical systems using vision transformer architectures requires extremely long, computationally prohibitive token sequences. To address this issue, we propose two novel adaptive tokenization schemes that dynamically adjust patch sizes based on local features: one ensures convergent behavior to uniform patch refinement, while the other offers better computational efficiency. Moreover, we present a set of spatiotemporal attention schemes, where the temporal or axial spatial dimensions are decoupled, to evaluate their baseline computational and data efficiencies and to determine whether adaptive tokenization can improve this performance. We assess the performance of the proposed multiscale adaptive model, MATEY, in a sequence of experiments. Compared to a full spatiotemporal attention scheme or a scheme that decouples only the temporal dimension, we find that fully decoupled axial attention is less efficient and expressive, requiring more training time and model parameters to achieve the same accuracy. The experiments on the adaptive tokenization schemes show that, compared to a uniformly refined model, the proposed schemes achieve comparable or improved accuracy at a much lower cost in the tested two-dimensional settings. While the asymptotic analysis suggests the potential for favorable scaling, empirical validation at substantially longer sequence lengths remains to be performed in future work. Finally, we demonstrate in two fine-tuning tasks featuring different physics that models pretrained on PDEBench data outperform the ones trained from scratch, especially in the low data regime with frozen attention.

adaptive tokenization↗
DOE OSTI2026

Higher-order Zeno sequences

The quantum Zeno effect typically refers to freezing the dynamics of a quantum system through frequent observations. In general, quantum Zeno dynamics is obtained with an error of order 𝒪⁢(1/𝑁), where 𝑁 is the number of projective measurements performed within a fixed evolution time. In this work, we develop higher-order Zeno sequences that achieve faster convergence to Zeno dynamics, yielding an improved error scaling of 𝒪⁢(1/𝑁 2⁢𝑘 ), where 𝑘 describes the order of the Zeno sequence. This is achieved by relating higher-order Zeno sequences to higher-order Trotter formulas that achieve similar convergence behavior. We leverage this relation to develop higher-order Zeno sequences for different manifestations of the quantum Zeno effect, including frequent projective measurements and unitary kicks. We go on to discuss achieving quantum Zeno dynamics through periodic control fields of high frequency. We explicitly develop control fields that yield a second-order type improvement in the Zeno error scaling and present shorter Zeno sequences. Finally, we discuss the connection to randomized and Uhrig dynamical decoupling to develop more efficient implementations in the weak-coupling regime.

Quantum Zeno dynamics↗
DOE OSTI2025

Noncollinear ground states of solids with a source-free exchange correlation functional

In this paper, we expand upon the source-free (SF) exchange correlation (XC) functional developed by Sangeeta Sharma and coworkers to plane-wave density functional theory (DFT) based on the projector augmented wave (PAW) method. This constraint is implemented by the current authors within the VASP source code, using a fast Poisson solver that capitalizes on the parallel three-dimensional fast Fourier transforms (FFTs) implemented in VASP. Using this modified XC functional, we explore the improved convergence behavior that results from applying this constraint to the GGA-PBE+U+J functional. In the process, we compare the noncollinear magnetic ground state computed by each functional and their SF counterpart for a select number of magnetic materials in order to provide a metric for comparing with experimentally determined magnetic orderings. We observe significantly improved agreement with experimentally measured magnetic ground-state structures after applying the source-free constraint. Furthermore, we explore the importance of considering probability current densities in spin-polarized systems, even under no applied field. We analyze the XC torque as well, in order to provide theoretical and computational analyses of the net XC magnetic torque induced by the source-free constraint. Along these lines, we highlight the importance of properly considering the real-space integral of the source-free local magnetic XC field. Our analyses on probability currents, net torque, and constant terms draw additional links to the rich body of previous research on spin-current density functional theory (SCDFT), and pave the way for future extensions and corrections to the SF corrected XC functional.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

AMG Preconditioners based on parallel hybrid coarsening and multi-objective graph matching

We describe preliminary results from a multi-objective graph matching algorithm, in the coarsening step of an aggregation-based Algebraic MultiGrid (AMG) preconditioner, for solving large and sparse linear systems of equations on high-end parallel computers. We have two objectives. First, we wish to improve the convergence behavior of the AMG method when applied to highly anisotropic problems. Second, we wish to extend the parallel package \texttt{PSCToolkit} to exploit multi-threaded parallelism at the node level on multi-core processors. Our matching proposal balances the need to simultaneously compute high weights and large cardinalities by a new formulation of the weighted matching problem combining both these objectives using a parameter $\lambda$. We compute the matching by a parallel $2/3-\varepsilon$-approximation algorithm for maximum weight matchings. Results with the new matching algorithm show that for a suitable choice of the parameter $\lambda$ we compute effective preconditioners in the presence of anisotropy, i.e., smaller solve times, setup times, iterations counts, and operator complexity.

D'Ambra, Pasqua↗
DOE OSTI2025

Assessing VQLS for Fluid Dynamics on a Hybrid Quantum-HPC Stack

Recent advances in quantum linear solvers offer a promising direction for accelerating extreme scientific computations such as fluid dynamics. However, the deep and complex circuits required by many quantum algorithms limit their practical use on current quantum hardware. The Variational Quantum Linear Solver (VQLS) presents a viable alternative for near-term quantum devices (NISQ), and initial efforts have explored its application to select fluid dynamics problems. In this work, we evaluate the use of VQLS for canonical fluid dynamics problems, aiming to identify pathways for generalizing its implementation across a broader class of systems. We analyze the impact of various circuit ansatz and classical optimizers on solution quality and convergence behavior. Furthermore, we assess the algorithm's feasibility within a hybrid quantum–high-performance computing (HPC) framework by porting it to QFw, a state-of-the-art quantum-HPC software stack. 11This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the US DOE under Contract No. DE-AC05-00OR22725.

Gopalakrishnan Meena, Murali [ORNL] (ORCID:0000000↗