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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 757 records · Page 42
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

A method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems

An efficient numerical method for solving the partial differential equation (PDE) governing the flexible manipulator control dynamics is presented. A finite-dimensional model of the equation is obtained through discretization in both time and space coordinates by using finite-difference approximations to the PDE. An expert program written in the Macsyma symbolic language is utilized in order to embed the boundary conditions into the program, accounting for a mass carried at the tip of the manipulator. The advantages of the proposed algorithm are many, including the ability to (1) include any distributed actuation term in the partial differential equation, (2) provide distributed sensing of the beam displacement, (3) easily modify the boundary conditions through an expert program, and (4) modify the structure for running under a multiprocessor environment.

Tzes, Anthony P.↗
NASA NTRS1992

A comparison of artificial compressibility and fractional step methods for incompressible flow computations

We have applied and compared the efficiency and accuracy of two commonly used numerical methods for the solution of Navier-Stokes equations. The artificial compressibility method augments the continuity equation with a transient pressure term and allows one to solve the modified equations as a coupled system. Due to its implicit nature, one can have the luxury of taking a large temporal integration step at the expense of higher memory requirement and larger operation counts per step. Meanwhile, the fractional step method splits the Navier-Stokes equations into a sequence of differential operators and integrates them in multiple steps. The memory requirement and operation count per time step are low, however, the restriction on the size of time marching step is more severe. To explore the strengths and weaknesses of these two methods, we used them for the computation of a two-dimensional driven cavity flow with Reynolds number of 100 and 1000, respectively. Three grid sizes, 41 x 41, 81 x 81, and 161 x 161 were used. The computations were considered after the L2-norm of the change of the dependent variables in two consecutive time steps has fallen below 10(exp -5).

Chan, Daniel C.↗
DOE OSTI2021

Physics-Informed Neural Network Method for Forward and Backward Advection-Dispersion Equations

Advection-dispersion equations (ADEs) are commonly used to describe transport phenomena in porous media. Even though mature discretization-based numerical methods for ADEs exist, some challenges still remain, especially when it comes to solving advection-dominated forward ADEs and diffusion-dominated backward ADEs. The latter problem usually arises in the source identification context and leads to numerically unstable grid-based solutions that require a form of regularization or should be treated as an inverse problem that is computationally more expensive because it requires solving the forward problem multiple times. In this study, we propose a discretization-free approach based on the physics-informed neural network (PINN) method for solving coupled ADE and Darcy flow equations with space-dependent hydraulic conductivity. In this approach, the hydraulic conductivity, hydraulic head, and concentration fields are approximated with deep neural networks (DNNs). We assume that the conductivity field is given by its values on a grid, and we use these values to train the conductivity DNN. The head and concentration DNNs are trained by minimizing the residuals of the flow equation and ADE and using the initial and boundary conditions as additional constraints. The PINN method is applied to one- and two-dimensional forward ADE problems, where its performance for various P\'{e}clet numbers ($Pe$) is compared with the analytical and numerical solutions. We find that the PINN method is accurate with errors of less than 1\% and outperforms some conventional discretization-based methods for $Pe$ larger that 100. Next, we demonstrate that the PINN method remains accurate for the backward ADEs, with the relative errors in most cases staying under 5\% compared to the reference concentration field. Finally, we show that when available, the concentration measurements can be easily incorporated in the PINN method and significantly improve (by more than 50\% in the considered cases) the accuracy of the PINN solution of the backward ADE.

He, Qizhi↗
NASA NTRS1985

An efficient numerical algorithm for transverse impact problems

Transverse impact problems in which the elastic and plastic indentation effects are considered, involve a nonlinear integral equation for the contact force, which, in practice, is usually solved by an iterative scheme with small increments in time. In this paper, a numerical method is proposed wherein the iterations of the nonlinear problem are separated from the structural response computations. This makes the numerical procedures much simpler and also efficient. The proposed method is applied to some impact problems for which solutions are available, and they are found to be in good agreement. The effect of the magnitude of time increment on the results is also discussed.

Sankar, B. V.↗
DOE OSTI2022

Explainable Bayesian Neural Network for Probabilistic Transient Stability Analysis Considering Wind Energy

While several data-driven models have been developed for transient stability assessment, how to consider the uncertainties from load and renewable generations and provide interpretation of data-driven assessment results are still open. This paper proposes an explainable Bayesian Neural Network (BNN) for probabilistic transient stability assessment (TSA). By extracting the uncertainties from loads and wind farms, the BNN model can make a reliable prediction and quantify the prediction uncertainties. We also develop the Gradient Shap algorithm to make the global and local explanations for the probabilistic TSA model, a significant advantage over existing black-box data-driven methods. Numerical results on the modified IEEE 39-bus system show that the proposed method outperforms the existing methods in terms of prediction accuracy and uncertainty quantification capabilities. The explainability of the proposed method allows system operators to design preventive controls for enhancing system stability.

Bayesian Neural Network↗
DOE OSTI2024

Interface-aware Methods for Diffusion Equations [Slides]

In this talk, we will present interface-aware methods for diffusion equation. The focus is on the necessity of interface-aware, mixed cells, interface reconstruction, discontinuity of material diffusion coefficients, order of accuracy in time, property for large time steps, and simpler interface-aware methods. Numerical examples are provided to demonstrate the features on these aspects of the methods

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1982

Reliability of the finite element method for calculating free edge stresses in composite laminates

The interlaminar normal stress distributions along the interface between the +45 deg and -45 deg plies of a graphite/epoxy laminate, obtained by various investigators, were found to disagree in both magnitude and sign. The reliability of the displacement-formulated finite element method in analyzing the edge-stress problem of a composite laminate is investigated. The history of the edge-stress problem is reviewed, and two well-known elasticity problems, one involving a stress discontinuity and one a singularity, are analyzed. The finite element analysis in these problems yields accurate stress distributions everywhere except in two elements closest to the stress discontinuity or singularity. Stress distributions for a + or -45 deg ply laminate near the singularity were similar to those of the two elasticity problems, demonstrating the methods, accuracy for calculating interlaminar stresses in composite laminates. The disagreement between the numerical methods was attributed to the unsymmetric stress tensor at singularity.

Whitcomb, J. D.↗
NASA NTRS1987

A method of calculating the total flow from a given sea surface topography

Using a simple dynamical model of a wind-driven ocean circulation of the Stommel type, and an analytical basis developed to objectively analyze the sea surface height residuals from an altimeter and, in the process, to determine the total flow instead of just the near surface geostrophic component associated with the given sea surface topography. The method is based on first deriving the solution to the forced problem for a given wind stress required to develop a hypothetical true or perfect data field and to establishing the basis for the objective analysis. The stream function and the surface height field for the forced problem are developed in terms of certain characteristic functions with the same expansion coefficients for both fields. These characteristic functions are simply the solutions for a homogeneous elliptic equation for the stream function and the solutions of an inhomogeneous balance equation for the height field. For the objective analysis, using a sample of randomly selected height values from the true data field, the height field characteristic functions are used to fit the given topography in a least squares sense. The resulting expansion coefficients then permit the synthesis of the total flow field via the stream function characteristic modes and the solution is perfectly well behaved even along the equator. The method of solution is easily adaptable to realistic ocean basis by straight forward numerical methods. The analytical basis of the theory and the results for an ideal rectangular basin on a beta plane are described.

Rao, Desiraju B.↗
NASA NTRS1990

Application of the probabilistic approximate analysis method to a turbopump blade analysis

An eigenvalue analysis of a typical space propulsion system turbopump blade is presented using an approximate probabilistic analysis methodology. The methodology was developed originally to investigate the feasibility of computing probabilistic structural response using closed-form approximate models. This paper extends the methodology to structures for which simple closed-form solutions do not exist. The finite element method will be used for this demonstration, but the concepts apply to any numerical method. The results agree with detailed analysis results and indicate the usefulness of using a probabilistic approximate analysis in determining efficient solution strategies.

Thacker, B. H.↗
NASA NTRS1993

Virtual-pulse time integral methodology: A new explicit approach for computational dynamics - Theoretical developments for general nonlinear structural dynamics

The present paper describes a new explicit virtual-pulse time integral methodology for nonlinear structural dynamics problems. The purpose of the paper is to provide the theoretical basis of the methodology and to demonstrate applicability of the proposed formulations to nonlinear dynamic structures. Different from the existing numerical methods such as direct time integrations or mode superposition techniques, the proposed methodology offers new perspectives and methodology of development, and possesses several unique and attractive computational characteristics. The methodology is tested and compared with the implicit Newmark method (trapezoidal rule) through a nonlinear softening and hardening spring dynamic models. The numerical results indicate that the proposed explicit virtual-pulse time integral methodology is an excellent alternative for solving general nonlinear dynamic problems.

Chen, Xiaoqin↗
DOE OSTI2021

A Computational Information Criterion for Particle-Tracking with Sparse or Noisy Data

Traditional probabilistic methods for the simulation of advection-diffusion equations (ADEs) often overlook the entropic contribution of the discretization, e.g., the number of particles, within associated numerical methods. Many times, the gain in accuracy of a highly discretized numerical model is outweighed by its associated computational costs or the noise within the data. Herein, we address the question of how many particles are needed in a simulation to best approximate and estimate parameters in one-dimensional advective-diffusive transport. To do so, we use the well-known Akaike Information Criterion (AIC) and a recently-developed correction called the Computational Information Criterion (COMIC) to guide the model selection process. Random-walk and mass-transfer particle tracking methods are employed to solve the model equations at various levels of discretization. Numerical results demonstrate that the COMIC provides an optimal number of particles that can describe a more efficient model in terms of parameter estimation and model prediction compared to the model selected by the AIC even when the data is sparse or noisy, the sampling volume is not uniform throughout the physical domain, or the error distribution of the data is non-IID Gaussian.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Physics-based adaptivity of a spectral method for the Vlasov–Poisson equations based on the asymmetrically-weighted Hermite expansion in velocity space

We propose a spectral method for the 1D-1V Vlasov–Poisson system where the discretization in velocity space is based on asymmetrically-weighted Hermite functions, dynamically adapted via a scaling α and shifting u of the velocity variable. Specifically, at each time instant an adaptivity criterion selects new values of α and u based on the numerical solution of the discrete Vlasov–Poisson system obtained at that time step. Once the new values of the Hermite parameters α and u are fixed, the Hermite expansion is updated and the discrete system is further evolved for the next time step. The procedure is applied iteratively over the desired temporal interval. The key aspects of the adaptive algorithm are: the map between approximation spaces associated with different values of the Hermite parameters that preserves total mass, momentum and energy; and the adaptivity criterion to update α and u based on physics considerations relating the Hermite parameters to the average velocity and temperature of each plasma species. For the discretization of the spatial coordinate, we rely on Fourier functions and use the implicit midpoint rule for time stepping. The resulting numerical method possesses intrinsically the property of fluid-kinetic coupling, where the low-order terms of the expansion are akin to the fluid moments of a macroscopic description of the plasma, while kinetic physics is retained by adding more spectral terms. Moreover, the scheme features conservation of total mass, momentum and energy associated in the discrete, for periodic boundary conditions. A set of numerical experiments confirms that the adaptive method outperforms the non-adaptive one in terms of accuracy and stability of the numerical solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Determining topological order from infinite projected entangled pair states

In this work, we present a method of extracting information about the topological order from the ground state of a strongly correlated two-dimensional system computed with the infinite projected entangled pair state (iPEPS). For topologically ordered systems, the iPEPS wrapped on a torus becomes a superposition of degenerate, locally indistinguishable ground states. Projectors in the form of infinite matrix product operators onto states with well-defined anyon flux are used to compute topological S and T matrices (encoding mutual and self-statistics of emergent anyons). The algorithm is shown to be robust against a perturbation driving string-net toric code across a phase transition to a ferromagnetic phase. Our approach provides accurate results near quantum phase transition, where the correlation length is prohibitively large for other numerical methods. Moreover, we used numerically optimized iPEPS describing the ground state of the Kitaev honeycomb model in the toric code phase and obtained topological data in excellent agreement with theoretical prediction.

36 MATERIALS SCIENCE↗
NASA NTRS1992

Optimal matrix approximants in structural identification

Problems of model correlation and system identification are central in the design, analysis, and control of large space structures. Of the numerous methods that have been proposed, many are based on finding minimal adjustments to a model matrix sufficient to introduce some desirable quality into that matrix. In this work, several of these methods are reviewed, placed in a modern framework, and linked to other previously known ideas in computational linear algebra and optimization. This new framework provides a point of departure for a number of new methods which are introduced here. Significant among these is a method for stiffness matrix adjustment which preserves the sparsity pattern of an original matrix, requires comparatively modest computational resources, and allows robust handling of noisy modal data. Numerical examples are included to illustrate the methods presented herein.

Beattie, C. A.↗
NASA NTRS1998

Spurious Numerical Oscillations in Numerical Simulation of Supersonic Flows Using Shock Capturing Schemes

The numerical simulation of transitional and turbulent processes in hypersonic boundary layers often involves a physical process of a shock-disturbance wave interaction in complex two-dimensional and three-dimensional flow fields. For such simulations, it is required that there be a high order of accuracy in capturing both the shock and the small disturbances. The purpose of this paper is to evaluate the viability of using high order shock capturing schemes to track small disturbances in a multi-dimensional steady hypersonic flow. The numerical methods that are to be studied are the Total Variation Diminishing (TVD) scheme, and Essentially Non-Oscillatory (ENO) scheme. This paper shows that the presence of numerical oscillations in the flow field solution may drastically hinder any attempt at tracking the propagation of any physical disturbances. It has been found that the numerical oscillations that exist for shock capturing methods may be significant enough to pollute a flow field containing small physical disturbances. The effects of the refinement of the grid do not reduce the oscillations, but rather they decrease the wavelength of the oscillations. It is shown that by aligning the shock with the grid, the amplitude of these spurious oscillations may be greatly reduced.

Lee, Theodore K.↗
NASA NTRS1993

Three-dimensional magnetotail equilibria by numerical relaxation techniques

Consideration is given to a numerical method to iteratively approach 3D magnetostatic force equilibria, with modeling emphasis on the development of a suitable model of the earth's magnetotail, including a portion of the inner magnetosphere, i.e., on models which violate the 'tail approximation' commonly employed in analytical models. The numerical approach is compared to methods developed for laboratory plasma physics. The method is applied to the magnetotail outside of 10 R(E), using Tsyganenko's (1987) model for the quiet magnetosphere as an initial condition. The changes of the magnetic field necessary to yield an equilibrium configuration and the resulting distribution of the self-consistently derived pressure are discussed. It is shown that a self-consistent magnetotail equilibrium based on a close approximation to Tsyganenko's requires a region 1 type current system, which is not present in the initial configuration.

Hesse, Michael↗
NASA NTRS1987

Parallel Algorithm Solves Coupled Differential Equations

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

Hayashi, A.↗