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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Efficient co-solution of time step size and independent state in simulations of fluid-driven fracture propagation with embedded meshes

Here we present an efficient time-continuation scheme for fluid-driven fracture propagation problems in the extended finite element method framework. The approach applies a monolithic solution strategy to a fully coupled and implicit approximation of hydro-mechanical systems in conjunction with simultaneous linear elastic propagation of multiple fractures. At the end of each time step, the process ensures that the weakest fracture tip is in an equilibrium propagation regime. Furthermore, the solution process provides an initialization procedure for the newly created fracture spaces and an a priori estimate of the stress intensity factor growth rate, improving simulation robustness, and efficiency. The solution process is validated using the Kristianovich-Geertsma-de Klerk analytical solution under the toughness- and viscosity-dominated regimes. It is also extended to and demonstrated on problems with multiple fractures undergoing simultaneous propagation with stress shadow interactions. Numerical examples demonstrate that the solution process can reduce the required computational cost by one order of magnitude compared to other existing methods.

42 ENGINEERING↗
NASA NTRS1989

Parallel multi-time step integration on a transputer system

An algorithm which allows different nodes of the finite element mesh to be integrated with different time steps is presented for second order finite element systems. The implementation of this algorithm on a system of transputer processors is discussed and a numerical example is used to evaluate the efficiency of the algorithm.

Smolinski, P.↗
NASA NTRS1989

Explicit-explicit subcycling with non-integer time step ratios for structural dynamic systems

An explicit-explicit subcycling procedure for the finite element analysis of structural dynamics is developed. This procedure has relaxed the usual constraint of requiring integer time step ratios for adjacent nodal groups. This allows for greater advantage to be taken of local stability criteria, and thus improves the efficiency of the explicit time integrator. Example problems are included to demonstrate the accuracy and stability of the method.

Neal, Mark O.↗
NASA NTRS1984

Obtaining Runge-Kutta Solutions Between Time Steps

New interpolation method used with existing Runge-Kutta algorithms. Algorithm evaluates solution at intermediate point within integration step. Only few additional computations required to produce intermediate solution data. Runge-Kutta method provides accurate solution with larger time steps than allowable in other methods.

Horn, M. K.↗
DOE OSTI2025

On High-Order/Low-Order and Micro-Macro Methods for Implicit Time-Stepping of the BGK Model

In this paper, a high-order/low-order (HOLO) method is combined with a micro-macro (MM) decomposition to accelerate iterative solvers in fully implicit time-stepping of the Bhatnagar–Gross–Krook (BGK) equation for gas dynamics. The MM formulation represents a kinetic distribution as the sum of a local Maxwellian and a perturbation. In highly collisional regimes, the perturbation away from initial and boundary layers is small and can be compressed to reduce the overall storage cost of the distribution. The convergence behavior of the MM methods, the usual HOLO method, and the standard source iteration method is analyzed on a linear BGK model. Both the HOLO and MM methods are implemented using a discontinuous Galerkin (DG) discretization in phase space, which naturally preserves the consistency between high- and low-order models required by the HOLO approach. Furthermore, the accuracy and performance of these methods are compared on the Sod shock tube problem and a sudden wall heating boundary layer problem. Overall, the results demonstrate the robustness of the MM and HOLO approaches and illustrate the compression benefits enabled by the MM formulation when the kinetic distribution is near equilibrium.

BGK model↗
NASA NTRS1991

Suggestions for CAP-TSD mesh and time-step input parameters

Suggestions for some of the input parameters used in the CAP-TSD (Computational Aeroelasticity Program-Transonic Small Disturbance) computer code are presented. These parameters include those associated with the mesh design and time step. The guidelines are based principally on experience with a one-dimensional model problem used to study wave propagation in the vertical direction.

Bland, Samuel R.↗
NASA NTRS1997

Accurate Monotonicity - Preserving Schemes With Runge-Kutta Time Stepping

A new class of high-order monotonicity-preserving schemes for the numerical solution of conservation laws is presented. The interface value in these schemes is obtained by limiting a higher-order polynominal reconstruction. The limiting is designed to preserve accuracy near extrema and to work well with Runge-Kutta time stepping. Computational efficiency is enhanced by a simple test that determines whether the limiting procedure is needed. For linear advection in one dimension, these schemes are shown as well as the Euler equations also confirm their high accuracy, good shock resolution, and computational efficiency.

Suresh, A.↗
DOE OSTI2020

Data for publication Wan et al. (2020, JAMES), Improving time-step convergence in an atmosphere model with simplified physics: the impacts of closure assumption and process coupling

This dataset contains simple condensation mdoel output and CAM4 model output that were used to produce figures in the following paper: Wan, H., Woodward, C. S., Zhang, S., Vogl, C. J., Stinis, P., Gardner, D. J., Rasch, P. J., Zeng, X., Larson, V. E., and Singh, B. (2020): Improving time-step convergence in an atmosphere model with simplified physics: the impacts of closure assumption and process coupling, Journal of Advances in Modeling Earth Systems, https://doi.org/10.1029/2019MS001982

54 ENVIRONMENTAL SCIENCES↗
NASA NTRSDate not supplied

Effect of Time-Step Duration and Other Parameters on Ice Accretion

This work addresses the ice prediction cases studies for the 1st AIAA Ice Prediction Workshop generated using a mix of commercial and in-house tools. All predictions are compared with those by LEWICE. Results from both 2D NACA 23012 airfoil cases and 3D NACA 0012 swept wing cases have been included. It is observed that the computational tools have a much better correlation with experimental data for rime icing conditions. For glaze icing conditions, the ice horns are not accurately predicted. The impact of parameters such as surface temperature, heat transfer coefficient, and time-step for flow and droplet field re-computation is explored.

Icing, Rotorcraft↗
DOE OSTI2023

TransformerG2G: Adaptive time-stepping for learning temporal graph embeddings using transformers

Dynamic graph embedding has emerged as a very effective technique for addressing diverse temporal graph analytic tasks (i.e., link prediction, node classification, recommender systems, anomaly detection, and graph generation) in various applications. Such temporal graphs exhibit heterogeneous transient dynamics, varying time intervals, and highly evolving node features throughout their evolution. Hence, incorporating long-range dependencies from the historical graph context plays a crucial role in accurately learning their temporal dynamics. In this paper, we develop a graph embedding model with uncertainty quantification, TransformerG2G, by exploiting the advanced transformer encoder to first learn intermediate node representations from its current state (t) and previous context (over timestamps [t–1,t–l], l is the length of context). Moreover, we employ two projection layers to generate lower-dimensional multivariate Gaussian distributions as each node's latent embedding at timestamp t. We consider diverse benchmarks with varying levels of "novelty" as measured by the TEA (Temporal Edge Appearance) plots. Here, our experiments demonstrate that the proposed TransformerG2G model outperforms conventional multi-step methods and our prior work (DynG2G) in terms of both link prediction accuracy and computational efficiency, especially for high degree of novelty. Furthermore, the learned time-dependent attention weights across multiple graph snapshots reveal the development of an automatic adaptive time stepping enabled by the transformer. Importantly, by examining the attention weights, we can uncover temporal dependencies, identify influential elements, and gain insights into the complex interactions within the graph structure. For example, we identified a strong correlation between attention weights and node degree at the various stages of the graph topology evolution.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

An expert system for setting time steps in dynamic finite element programs

An expert system, ETUDES - Expert Time integration control Using Deep and Surface Knowledge System, which addresses the determination of the timestep for time integration of linear structural dynamic equations is described. This timestep may also be applicable for a moderately nonlinear simulation of the same structure. The program also determines whether an explicit or implicit method is most efficient for the particular simulation. A production rule programming system written in OPS5 is used for the implementation of this prototype expert system. Issues relating to the expert system architecture for this application, such as knowledge representation and structure, as well as domain knowledge are discussed. The prototype is evaluated by measuring its performance in various benchmark model problems.

Ramirez, Martin R.↗
DOE OSTI2025

Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations

In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac–Frenkel time-dependent variational principle. In recent years, it has attracted a lot of attention due to its wide applicability. Our schemes are inspired by the three-step procedure used in the rank adaptive version of the unconventional robust integrator (the so called BUG integrator) (Ceruti et al. in BIT Numer Math 62(4):1149–1174, 2022) for DLRA. First, a prediction (basis update) step is made computing the approximate column and row spaces at the next time level. Second, a Galerkin evolution step is invoked using an implicit solves for the small core matrix. Finally, a truncation is made according to a prescribed error threshold. Since the DLRA is evolving the differential equation projected on to the tangent space of the low rank manifold, the error estimate of the BUG integrator contains the tangent projection (modeling) error which cannot be easily controlled by mesh refinement. This can cause convergence issue for equations with cross terms. To address this issue, we propose a simple modification, consisting of merging the row and column spaces from the explicit step truncation method together with the BUG spaces in the prediction step. In addition, we propose an adaptive strategy where the BUG spaces are only computed if the residual for the solution obtained from the prediction space by explicit step truncation method, is too large. Here, we prove stability and estimate the local truncation error of the schemes under assumptions. We benchmark the schemes in several tests, such as anisotropic diffusion, solid body rotation and the combination of the two, to show robust convergence properties.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Entropy–Preserving and Entropy–Stable Relaxation IMEX and Multirate Time–Stepping Methods

In this work, we propose entropy-preserving and entropy-stable partitioned Runge–Kutta (RK) methods. In particular, we extend the explicit relaxation Runge–Kutta methods to IMEX–RK methods and a class of explicit second-order multirate methods for stiff problems arising from scale-separable or grid-induced stiffness in a system. The proposed approaches not only mitigate system stiffness but also fully support entropy-preserving and entropy-stability properties at a discrete level. The key idea of the relaxation approach is to adjust the step completion with a relaxation parameter so that the time-adjusted solution satisfies the entropy condition at a discrete level. The relaxation parameter is computed by solving a scalar nonlinear equation at each timestep in general; however, as for a quadratic entropy function, we theoretically derive the explicit form of the relaxation parameter and numerically confirm that the relaxation parameter works the Burgers equation. Several numerical results for ordinary differential equations and the Burgers equation are presented to demonstrate the entropy-conserving/stable behavior of these methods. We also compare the relaxation approach and the incremental direction technique for the Burgers equation with and without a limiter in the presence of shocks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

The ABCflux database: Arctic–boreal CO 2 flux observations and ancillary information aggregated to monthly time steps across terrestrial ecosystems

Past efforts to synthesize and quantify the magnitude and change in carbon dioxide (CO 2 ) fluxes in terrestrial ecosystems across the rapidly warming Arctic–boreal zone (ABZ) have provided valuable information but were limited in their geographical and temporal coverage. Furthermore, these efforts have been based on data aggregated over varying time periods, often with only minimal site ancillary data, thus limiting their potential to be used in large-scale carbon budget assessments. To bridge these gaps, we developed a standardized monthly database of Arctic–boreal CO 2 fluxes (ABCflux) that aggregates in situ measurements of terrestrial net ecosystem CO 2 exchange and its derived partitioned component fluxes: gross primary productivity and ecosystem respiration. The data span from 1989 to 2020 with over 70 supporting variables that describe key site conditions (e.g., vegetation and disturbance type), micrometeorological and environmental measurements (e.g., air and soil temperatures), and flux measurement techniques. Here, we describe these variables, the spatial and temporal distribution of observations, the main strengths and limitations of the database, and the potential research opportunities it enables. In total, ABCflux includes 244 sites and 6309 monthly observations; 136 sites and 2217 monthly observations represent tundra, and 108 sites and 4092 observations represent the boreal biome. The database includes fluxes estimated with chamber (19 % of the monthly observations), snow diffusion (3 %) and eddy covariance (78 %) techniques. The largest number of observations were collected during the climatological summer (June–August; 32 %), and fewer observations were available for autumn (September–October; 25 %), winter (December–February; 18 %), and spring (March–May; 25 %). ABCflux can be used in a wide array of empirical, remote sensing and modeling studies to improve understanding of the regional and temporal variability in CO 2 fluxes and to better estimate the terrestrial ABZ CO 2 budget.

59 BASIC BIOLOGICAL SCIENCES↗