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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.

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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Solving a class of infinite-dimensional tensor eigenvalue problems by translational invariant tensor ring approximations

Here, we examine a method for solving an infinite-dimensional tensor eigenvalue problem Hx = λx, where the infinite-dimensional symmetric matrix H exhibits a translational invariant structure. We provide a formulation of this type of problem from a numerical linear algebra point of view and describe how a power method applied to e -Ht is used to obtain an approximation to the desired eigenvector. This infinite-dimensional eigenvector is represented in a compact way by a translational invariant infinite Tensor Ring (iTR). Low rank approximation is used to keep the cost of subsequent power iterations bounded while preserving the iTR structure of the approximate eigenvector. We show how the averaged Rayleigh quotient of an iTR eigenvector approximation can be efficiently computed and introduce a projected residual to monitor its convergence. In the numerical examples, we illustrate that the norm of this projected iTR residual can also be used to automatically modify the time step to ensure accurate and rapid convergence of the power method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Fundamentally New Coupled Approach to Contact Mechanics via the Dirichlet‐Neumann Schwarz Alternating Method

Contact phenomena are crucial for understanding the behavior of mechanical systems. However, existing computational approaches for simulating mechanical contact often face numerical challenges, such as inaccurate physical predictions, energy conservation errors, and unwanted oscillations. Here, we introduce an alternative technique for simulating dynamic contact based on the non‐overlapping Schwarz alternating method, originally developed for domain decomposition. In multibody contact scenarios, this method treats each body as a separate, non‐overlapping domain and prevents interpenetration using an alternating Dirichlet–Neumann iterative process. This approach has a strong theoretical foundation, eliminates the need for contact constraints, and offers flexibility, making it ideal for multiscale and multiphysics applications. We conducted a numerical comparison between the Schwarz method and traditional methods, such as the Lagrange multiplier and penalty methods, focusing on a benchmark impact problem. Our results indicate that the Schwarz alternating method outperforms traditional methods in several key areas: it provides more accurate predictions for various measurable quantities and demonstrates exceptional energy conservation capabilities. To address unwanted oscillations in contact velocities and forces, we explored various algorithms and stabilization techniques, ultimately opting for the naïve‐stabilized Newmark scheme for its simplicity and effectiveness. Additionally, we validated the efficiency of the Schwarz method in a three‐dimensional impact problem, highlighting its inherent capacity to accommodate different mesh topologies, time‐integration schemes, and time steps for each interacting body.

Schwarz alternating method↗
DOE OSTI2022

State elimination for mixed‐integer optimal control of partial differential equations by semigroup theory

Abstract Mixed‐integer optimal control problems governed by partial differential equations (MIPDECOs) are powerful modeling tools but also challenging in terms of theory and computation. We propose a highly efficient state elimination approach for MIPDECOs that are governed by partial differential equations that have the structure of an abstract ordinary differential equation in function space. This allows us to avoid repeated calculations of the states for all time steps, and our approach is applied only once before starting the optimization. The presentation of theoretical results is complemented by numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A high-order WENO-limited finite-volume algorithm for atmospheric flow using the ADER-differential transform time discretization

A high-order-accurate weighted essentially non-oscillatory (WENO) limited upwind finite-volume scheme is detailed for the compressible, nonhydrostatic, inviscid Euler equations using an arbitrary derivatives (ADER) time-stepping scheme based on differential transforms (DTs). A second-order-accurate alternating Strang dimensional splitting is compared against multidimensional simulation with 2D transport using solid body rotation of various data. The two were found to give nearly identical accuracy in orthogonal, Cartesian coordinates. Orders of convergence are demonstrated at up to ninth-order accuracy with 2D transport. 1D transport is used to confirm that error decreases monotonically with increasing order of accuracy with WENO limiting even for discontinuous data. Further, WENO limiting always decreased the error compared with simulation without limiting in the L 1 norm. A series of standard 2D compressible nonhydrostatic Euler equation test cases were validated against previous results from literature. Finally, it was demonstrated that increasing the order of accuracy led to better resolved features and increased power for kinetic energy at small wavelengths.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

A two-fluid single-column model of turbulent shallow convection. Part II: Single-column model formulation and numerics

The two-fluid single-column model of Thuburn et al. (Quart. J. R. Meteorol. Soc., 2019, 145, 1535–1550) is extended to include moisture and horizontal wind shear. Turbulent kinetic energy is introduced as a prognostic variable, dependence on a diagnosed boundary-layer height is removed, and subfilter fluxes are approximated using a two-fluid version of a Mellor–Yamada scheme. Three mechanisms for entrainment and detrainment processes are introduced, which represent entrainment of unstable air at the surface, forced detrainment of air at the top of the boundary/cloud layers, and turbulent mixing that relaxes the convective fluid to a reference profile. A semi-implicit Eulerian discretization replaces the semi-implicit semi-Lagrangian implementation of Thuburn et al. (Quart. J. R. Meteorol. Soc., 2019, 145, 1535–1550) to improve numerical stability and conservation. The equations for the implicit time step are solved using a quasi-Newton method, which is shown to perform well in numerical tests for conservation and convergence. The two-fluid single-column model presented in this article will be applied to simulations of shallow cumulus convection in Part III.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Algorithm advances and applications of time‐dependent first‐principles simulations for ultrafast dynamics

Abstract Far from equilibrium phenomenon is a central theme of contemporary material research. Such phenomenon can exhibit itself in atomic structure and dynamics, but very often it also happens as non‐equilibrium phenomenon in the electronic structure. In ab initio material simulation, density functional theory (DFT) has played an essential role in studying electronic ground state problems. For excited states, besides many‐body perturbation theory, another powerful tool is the time dependent DFT (TDDFT) method. In particular, the real‐time TDDFT (rt‐TDDFT) method can be used to simulate many non‐equilibrium phenomena directly. Here we introduce our works on some algorithm advances based on our recently rt‐TDDFT method. This method uses the plane‐wave basis set, and significantly accelerates its efficiency by increasing the time step from 0.1–1 as in traditional methods to 0.2–0.5 fs. The noncollinear magnetic moments and spin–orbit coupling have also been included in our rt‐TDDFT method. Furthermore, a Boltzmann‐TDDFT algorithm has been developed to solve the hot carrier overheating problem in Ehrenfest dynamics, and a natural orbital branching algorithm has been developed to overcome the mean‐field approximation in Ehrenfest dynamics nuclear trajectory, thus allows stochastic multiple paths in chemical reactions. Utilizing these methods, we have studied the photoinduced ultrafast demagnetization, ultrafast phase transition, energy transfer between plasmon and hot carriers, as well as the high‐energy ion implantation and low‐energy atomic diffusion in semiconductors. We believe the tools as the ones introduced here can enable us to study a wide range of phenomena which are of great interest in modern day material research. This article is categorized under: Structure and Mechanism > Computational Materials Science Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Density Functional Theory

Liu, Wen‐Hao↗
DOE OSTI2020

Multimodel validation of single wakes in neutral and stratified atmospheric conditions

Previous research has revealed the need for a validation study that considers several wake quantities and code types so that decisions on the trade-off between accuracy and computational cost can be well informed and appropriate to the intended application. In addition to guiding code choice and setup, rigorous model validation exercises are needed to identify weaknesses and strengths of specific models and guide future improvements. Here, we consider 13 approaches to simulating wakes observed with a nacelle-mounted lidar at the Scaled Wind Technology Facility (SWiFT) under varying atmospheric conditions. We find that some of the main challenges in wind turbine wake modeling are related to simulating the inflow. In the neutral benchmark, model performance tracked as expected with model fidelity, with large-eddy simulations performing the best. In the more challenging stable case, steady-state Reynolds-averaged Navier–Stokes simulations were found to outperform other model alternatives because they provide the ability to more easily prescribe noncanonical inflows and their low cost allows for simulations to be repeated as needed. Dynamic measurements were only available for the unstable benchmark at a single downstream distance. These dynamic analyses revealed that differences in the performance of time-stepping models come largely from differences in wake meandering. This highlights the need for more validation exercises that take into account wake dynamics and are able to identify where these differences come from: mesh setup, inflow, turbulence models, or wake-meandering parameterizations. In addition to model validation findings, we summarize lessons learned and provide recommendations for future benchmark exercises.

17 WIND ENERGY↗
DOE OSTI2026

Discrete Superconvergence Analysis for Quantum Magnus Algorithms of Unbounded Hamiltonian Simulation

Motivated by various applications, unbounded Hamiltonian simulation has recently garnered great attention. Quantum Magnus algorithms, designed to achieve commutator scaling for time-dependent Hamiltonian simulation, have been found to be particularly efficient for such applications. When applied to unbounded Hamiltonian simulation in the interaction picture, they exhibit an unexpected superconvergence phenomenon. However, existing proofs are limited to the spatially continuous setting and do not extend to discrete spatial discretizations. Here, in this work, we provide the first superconvergence estimate in the fully discrete setting with a finite number of spatial discretization points N, and show that it holds with an error constant uniform in N. The proof is based on the two-parameter symbol class, which, to our knowledge, is applied for the first time in algorithm analysis. The key idea is to establish a semiclassical framework by identifying two parameters through the discretization number and the time step size rescaled by the operator norm, such that the semiclassical uniformity guarantees the uniformity of both. This approach may have broader applications in numerical analysis beyond the specific context of this work.

Borns-Weil, Yonah [University of California, Berke↗
DOE OSTI2021

Tomographic X-ray particle tracking velocimetry

We investigate the feasibility of in-laboratory tomographic X-ray particle tracking velocimetry (TXPTV) and consider creeping flows with nearly density matched flow tracers. Specifically, in these proof-of-concept experiments we examined a Poiseuille flow, flow through porous media and a multiphase flow with a Taylor bubble. For a full 360° computed tomography (CT) scan we show that the specially selected 60 micron tracer particles could be imaged in less than 3 seconds with a signal-to-noise ratio between the tracers and the fluid of 2.5, sufficient to achieve proper volumetric segmentation at each time step. In the pipe flow, continuous Lagrangian particle trajectories were obtained, after which all the standard techniques used for PTV or PIV (taken at visible wave lengths) could also be employed for TXPTV data. And, with TXPTV we can examine flows inaccessible with visible wave lengths due to opaque media or numerous refractive interfaces. In the case of opaque porous media we were able to observe material accumulation and pore clogging, and for flow with Taylor bubble we can trace the particles and hence obtain velocities in the liquid film between the wall and bubble, with thickness of liquid film itself also simultaneously obtained from the volumetric reconstruction after segmentation. While improvements in scan speed are anticipated due to continuing improvements in CT system components, we show that for the flows examined even the presently available CT systems could yield quantitative flow data with the primary limitation being the quality of available flow tracers.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS

Here, we present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff–Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell’s mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith’s theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires C 1 -continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-α method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton–Raphson scheme. Finally, the interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.

42 ENGINEERING↗
DOE OSTI2026

A stiff order condition theory for Runge–Kutta methods applied to semilinear ODEs

Classical convergence theory of Runge–Kutta methods assumes that the time step is small relative to the Lipschitz constant of the ordinary differential equation (ODE). For stiff problems, that assumption is often violated, and a problematic degradation in accuracy, known as order reduction, can arise. Methods with high stage order, e.g., Gauss–Legendre and Radau, are known to avoid order reduction, but they must be fully implicit. For the broad class of semilinear ODEs, which consist of a stiff linear term and non-stiff nonlinear term, we show that weaker conditions suffice. Here, our new semilinear order conditions are formulated in terms of orthogonality relations and can be enumerated by rooted trees. Finally, we prove global error bounds that hold uniformly with respect to stiffness of the linear term.

Mathematics and Computing↗
DOE OSTI2020

Microscale mechanical modeling of deformable geomaterials with dynamic contacts based on the numerical manifold method

Abstract Micromechanical modeling of geomaterials is challenging because of the complex geometry of discontinuities and potentially large number of deformable material bodies that contact each other dynamically. In this study, we have developed a numerical approach for micromechanical analysis of deformable geomaterials with dynamic contacts. In our approach, we detect contacts among multiple blocks with arbitrary shapes, enforce different contact constraints for three different contact states of separated, bonded, and sliding, and iterate within each time step to ensure convergence of contact states. With these features, we are able to simulate the dynamic contact evolution at the microscale for realistic geomaterials having arbitrary shapes of grains and interfaces. We demonstrate the capability with several examples, including a rough fracture with different geometric surface asperity characteristics, settling of clay aggregates, compaction of a loosely packed sand, and failure of an intact marble sample. With our model, we are able to accurately analyze (1) large displacements and/or deformation, (2) the process of high stress accumulated at contact areas, (3) the failure of a mineral cemented rock samples under high stress, and (4) post-failure fragmentation. The analysis highlights the importance of accurately capturing (1) the sequential evolution of geomaterials responding to stress as motion, deformation, and high stress; (2) large geometric features outside the norms (such as large asperities and sharp corners) as such features can dominate the micromechanical behavior; and (3) different mechanical behavior between loosely packed and tightly packed granular systems.

58 GEOSCIENCES↗
DOE OSTI2022

Stability Analysis of Coupled Advection-Diffusion Models with Bulk Interface Condition

Numerical stability is of critical importance in general circulation models because it affects the design of algorithms, time to solution, and computational costs associated with the simulations, which are very expensive in practice. In this paper we extend the stability analysis for ocean-atmosphere coupling proposed in [Zhang et al., J. Sci. Comput. 84, 44(2020)] to a more realistic model that includes horizontal advection. We analyze various time-stepping strategies. We find that advection has a stabilizing effect in scenarios common to climate models when bulk interface condition and explicit flux coupling are used. We also show that our method can be used to study the stability impact of advection for other interface conditions such as Dirichlet-Neumann conditions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Clustering and Cliques in Preferential Attachment Random Graphs with Edge Insertion

In this paper, we investigate the global clustering coefficient (a.k.a transitivity) and clique number of graphs generated by a preferential attachment random graph model with an additional feature of allowing edge connections between existing vertices. Specifically, at each time step t, either a new vertex is added with probability f(t), or an edge is added between two existing vertices with probability 1 – f(t). We establish concentration inequalities for the global clustering and clique number of the resulting graphs under the assumption that f(t) is a regularly varying function at infinity with index of regular variation –$\gamma$, where $\gamma$ $\in$ [0, 1). Finally, we also demonstrate an inverse relation between these two statistics: the clique number is essentially the reciprocal of the global clustering coefficient.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Atmospheric humidity deficits tell us how soil moisture deficits down-regulate ecosystem evaporation

Knowing how actual evaporation is down-regulated from potential evaporation during periods with soil moisture deficits is one of the greatest challenges towards computing evaporation everywhere on a regular basis. We propose the hypothesis that vegetated landscapes transmit information on soil moisture deficits through its down-regulation of evaporation, which in turn affects the humidification and growth of the planetary boundary layer. To test this hypothesis, here, we examined how the evaporative fraction, defined as the ratio between actual and potential evaporation, corresponds with the soil moisture stress index, defined as the relative humidity with a power law dependence on vapor pressure deficit times a parameter, β. We tested the parameterized soil moisture stress index with direct eddy covariance measurements of actual evaporation and computations of potential evaporation based on meteorological conditions, averaged on monthly time steps. The analysis was conducted on a dataset obtained from 144 FLUXNET sites. These sites spanned much of the world's climates and biomes and contained over 5900 months of observations. Observations of the evaporative fraction fit the model of the soil moisture stress index best for semi-arid and arid ecosystems, and least for the humid and wet ecosystems. Consequently, a significant relationship between measurements of the evaporative fraction and soil moisture stress index held for about one-half of the population of sites. Under this condition, the median value of the parameter, β, was 1.41. To investigate the mechanism of this empirical soil moisture stress index, we diagnosed it with a coupled evaporation-planetary boundary layer model. The soil moisture stress index is strongly related to surface resistance, as defined by inverting Penman-Monteith equation. Consequently, this index provides an independent estimate of surface resistance based on easy to measure mean monthly weather conditions like relative humidity and temperature. Thereby, this soil moisture stress index has potential to be applied to weather, climate and biogeochemical models and the interpretation of satellite derived evaporation products, like the one provided by the ECOSTRESS mission.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Revisiting the definition of field capacity as a functional parameter in a layered agronomic soil profile beneath irrigated maize

The soil water content at the condition of field capacity (θ FC ) is a key parameter in irrigation scheduling and has been suggested to be determined by running a synthetic drainage experiment until the flux rate (q) at the bottom of the soil profile achieves a predefined negligible value (q FC ). We question the impact of q FC on the assessment of field capacity. Moreover, calculating θ FC as the integral mean of the water content profile when q is equal to q FC is strictly valid only for uniform soil profiles. By contrast, this practice is ambiguous and biased for stratified soil profiles due to the soil water content discontinuity at the layer interfaces. In this study, the concept of field capacity was revisited and adapted to practical agronomic heuristics. By resorting to the assessment of root-zone water storage capacity (W), we envision field capacity as a functional hydraulic parameter derived from synthetic irrigation scheduling scenarios to minimize drought stress, drainage, and nitrate leachate below the root zone. A functional analysis was carried out on a 135-cm-thick layered soil profile beneath maize in eastern Nebraska. On-farm irrigation scheduling applications and agricultural practices were recorded for 20 years (2001–2020) at a daily time step. Hydrus-1D was calibrated and validated with direct measurements of the soil water retention curve and soil water content data, respectively, in each soil layer. A set of functional field capacity values was derived from 24 irrigation scheduling scenarios, and the optimal water storage capacity at field capacity (W FC ) was approximately 50 cm (corresponding to about 80% saturation in the soil profile). An average irrigation amount of 217.5 mm distributed over 21 events was obtained by using optimal irrigation scheduling, which was initiated when the matric pressure head took on a value of –700 cm and the irrigation rate was set at 1.0 cm d –1 . This irrigation practice ensured water storage at approximately the same level (ideally at W FC ) by sustaining only evapotranspiration fluxes in the uppermost portion of the root zone and by limiting excessive drainage. This protocol can be transferred to other agricultural fields.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Deep reinforcement learning for class imbalance fault diagnosis of equipment in nuclear power plants

In equipment fault diagnosis in nuclear power plants, there may be far more samples in one class (e.g., a health state) than in another class (e.g., a fault state). The distribution of data in each class is highly skewed. Most machine learning algorithms are suitable for balanced training datasets. When faced with imbalanced samples, these algorithms tend to provide good identification for the majority classes and bias for the minority classes. However, the misclassification of minority classes can lead to high costs. To address the above problem, this paper develops a deep reinforcement learning-based diagnosis method that models fault diagnosis as a sequential decision-making process. At each time step, the agent receives the state of the environment represented by the training samples and then takes a diagnosis action guided by a policy. If the action is correct/incorrect, the agent receives a positive/negative reward. The reward for minority classes is higher than that for majority classes. The agent’s goal is to obtain as many cumulative rewards as possible in the process, i.e., to identify the sample as correctly as possible. Six demonstration scenarios are constructed, depending on the selected fault datasets and the designed model structures. Experiments show that the proposed method achieves a higher weighted-averaged F1 score than the classical supervised learning method in most cases of class imbalance. Finally, the proposed method has potential applications in the field of class imbalance fault diagnosis of equipment in nuclear power plants.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Efficient continuous Energy-Multigroup hybrid depletion scheme using the Shift Monte Carlo code. Part I: Energy condensation sensitivity analysis

Monte Carlo (MC) codes coupled to depletion solvers are increasingly used to provide high fidelity fuel cycle modeling capabilities. Here, these coupled depletion-MC tools produce accurate results in general but can experience nonphysical spatial oscillations when time steps are large or when a system’s dominance ratio approaches unity. Two substepping techniques have been developed previously to remedy and dampen these spatial oscillations without needing to reduce step sizes. The first approach relied on higher-order techniques to account for spectral changes within steps (extrapolation and interpolation techniques). The second approach used the first order perturbation (FOP) theory to account for the change in the one-group spatial flux distribution within steps. This paper develops a hybrid depletion methodology which, in a way, combines how the flux is handled in both substepping techniques. Specifically, the multigroup (MG) MC Shift code is used to update the flux distribution within steps rather than a one-group FOP solver. A fully reflected pincell is investigated, which is not spatially dependent in the MG representation. Thus, the analysis in this paper is an initial demonstration of hybrid depletion. An upcoming companion paper will focus on how the hybrid depletion dampens spatial oscillations. The hybrid depletion approach is verified to be consistent with previous constant extrapolation depletion (CED) methods. This paper finds that the hybrid CED exhibits some error in the eigenvalue and one group constants within macro steps. To address this discrepancy, a simple interpolation scheme (CELI) is investigated. This work found that CELI sufficiently addresses the discrepancy in spectrum for macro steps up to 100 days. Overall, this work demonstrates that the hybrid depletion method can significantly reduce the number of high fidelity MC executions in a MC-coupled depletion with an acceptable eigenvalue error.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗