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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A Model Predictive Control to Improve Grid Resilience

The following article details a model predictive control (MPC) to improve grid resilience when faced with variable generation resources. This topic is of significant interest to utility power systems where distributed intermittent energy sources will increase significantly and be relied on for electric grid ancillary services. Previous work on MPCs has focused on narrowly targeted control applications such as improving electric vehicle (EV) charging infrastructure or reducing the cost of integrating Energy Storage Systems (ESSs) into the grid. In contrast, this article develops a comprehensive treatment of the construction of an MPC tailored to electric grids and then applies it integration of intermittent energy resources. To accomplish this, the following article includes a description of a reduced order model (ROM) of an electric power grid based on a circuit model, an optimization formulation that describes the MPC, a collocation method for solving linear time-dependent differential algebraic equations (DAEs) that result from the ROM, and an overall strategy for iteratively refining the behavior of the MPC. Next, the algorithm is validated using two separate numerical experiments. First, the algorithm is compared to an existing MPC code and the results are verified by a numerically precise simulation. It is shown that this algorithm produces a control comparable to existing algorithms and the behavior of the control carefully respects the bounds specified. Second, the MPC is applied to a small nine bus system that contains a mix of turbine-spinning-machine-based and intermittent generation in order to demonstrate the algorithm’s utility for resource planning and control of intermittent resources. This study demonstrates how the MPC can be tuned to change the behavior of the control, which can then assist with the integration of intermittent resources into the grid. The emphasis throughout the paper is to provide systematic treatment of the topic and produce a novel nonlinear control compatible design framework applicable to electric grids and the control of variable resources. This differs from the more targeted application-based focus in most presentations.

microgrid↗
DOE OSTI2018

Influence of Emissions and Aqueous Processing on Particles Containing Black Carbon in a Polluted Urban Environment: Insights From a Soot Particle-Aerosol Mass Spectrometer

Inorganic and organic coatings on black carbon (BC) particles can enhance light absorption and affect atmospheric lifetimes of BC-containing particles and thus have significant implications for climate. To study the physical and chemical characteristics of atmospheric BC and BC-associated coatings, a soot particle-aerosol mass spectrometer was deployed during the winter of 2014–2015 in Fresno, a city located in the San Joaquin Valley of California, to selectively analyze BC-containing particles. Comparing soot particle-aerosol mass spectrometer measurements to those from the collocated single-particle soot photometer (SP2) and high-resolution aerosol mass spectrometer, we found that 17% of total submicrometer aerosol mass was associated with BC-containing particles, suggesting that a majority of the fine particles in Fresno contained no BC. Most BC-containing particles appeared to be associated with residential wood burning and vehicular traffic. These particles typically had a bulk-average mass ratio of coating to BC (R coat/rBC ) less than 2. However, during periods of persistent fog larger R coat/rBC values were observed, with the coatings primarily composed of secondary inorganic and organic components that likely resulted from aqueous-phase processing. Specifically, compared to periods with less fog, the BC coating increased in concentration and contained a larger fraction of nitrate and oxidized organic matter. The size distributions of BC and associated organic coating were generally centered around 300 nm in vacuum aerodynamic diameter. However, during foggy periods BC had an additional peak at ~400 nm and organics and nitrate displayed a prominent mode in the accumulation size range.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

A minimally invasive, efficient method for propagation of full-field uncertainty in solid dynamics

In this work, we present a minimally invasive method for forward propagation of material property uncertainty to full-field quantities of interest in solid dynamics. Full-field uncertainty quantification enables the design of complex systems where quantities of interest, such as failure points, are not known a priori. The method, motivated by the well-known probability density function (PDF) propagation method of turbulence modeling, uses an ensemble of solutions to provide the joint PDF of desired quantities at every point in the domain. A small subset of the ensemble is computed exactly, and the remainder of the samples are computed with approximation of the evolution equations based on those exact solutions. Although the proposed method has commonalities with traditional interpolatory stochastic collocation methods applied directly to quantities of interest, it is distinct and exploits the parameter dependence and smoothness of the driving term of the evolution equations. The implementation is model independent, storage and communication efficient, and straightforward. We demonstrate its efficiency, accuracy, scaling with dimension of the parameter space, and convergence in distribution with two problems: a quasi-one-dimensional bar impact, and a two material notched plate impact. For the bar impact problem, we provide an analytical solution to PDF of the solution fields for method validation. With the notched plate problem, we also demonstrate good parallel efficiency and scaling of the method.

42 ENGINEERING↗
DOE OSTI2022

Adaptive experimental design for multi-fidelity surrogate modeling of multi-disciplinary systems

We present an adaptive algorithm for constructing surrogate models of multi-disciplinary systems composed of a set of coupled components. With this goal we introduce “coupling” variables with a priori unknown distributions that allow surrogates of each component to be built independently. Once built, the surrogates of the components are combined to form an integrated-surrogate that can be used to predict system-level quantities of interest at a fraction of the cost of the original model. The error in the integrated-surrogate is greedily minimized using an experimental design procedure that allocates the amount of training data, used to construct each component-surrogate, based on the contribution of those surrogates to the error of the integrated-surrogate. Here, the multi-fidelity procedure presented is a generalization of multi-index stochastic collocation that can leverage ensembles of models of varying cost and accuracy, for one or more components, to reduce the computational cost of constructing the integrated-surrogate. Extensive numerical results demonstrate that, for a fixed computational budget, our algorithm is able to produce surrogates that are orders of magnitude more accurate than methods that treat the integrated system as a black-box.

42 ENGINEERING↗
DOE OSTI2023

Dirichlet-type absorbing boundary conditions for peridynamic scalar waves in two-dimensional viscous media

Construction of absorbing boundary conditions (ABCs) for nonlocal models is generally challenging, primarily due to the fact that nonlocal operators are commonly associated with volume constrained boundary conditions. Moreover, application of Fourier and Laplace transforms, which are essential for the majority of available methods for ABCs, to nonlocal models is complicated. In this paper, we propose a simple method to construct accurate ABCs for peridynamic scalar wave-type problems in viscous media. The proposed ABCs are constructed in the time and space domains and are of Dirichlet type. Consequently, their implementation is relatively simple, since no derivatives of the wave field are required. The proposed ABCs are derived at the continuum level, from a semi-analytical solution of the exterior domain using harmonic exponential basis functions in space and time (plane-wave modes). The numerical implementation is done using a meshfree collocation approach employed within a boundary layer adjacent to the interior domain boundary. The modes satisfy the peridynamic numerical dispersion relation, resulting in a compatible solution of the interior region (near-field) with that of the exterior region (far-field). The accuracy and stability of the proposed ABCs are demonstrated with several numerical examples in two-dimensional unbounded domains.

42 ENGINEERING↗
DOE OSTI2019

Absorbing boundary condition (ABC) and perfectly matched layer (PML) in numerical beam propagation: a comparison

The absorbing boundary condition (ABC) and the perfectly matched layer (PML) are employed to suppress the numerical reflections in wave propagation methods. The PML has earlier been shown to fail at the grazing angle propagation of beam. The ABC is preferred over the PML where refractive index is not an analytic function. We have explored the performance of the ABC in reflection-less absorption of non-paraxial propagation of beams and have compared it against the PML. We have considered an example of the propagation of Gaussian beams through a homogeneous medium terminated with ABC or PML. We have used the collocation method for propagation. We have found that both the boundary conditions are comparable in performance. The ABC performed relatively better than the PML for beams at smaller angles. However, the performance of the PML is better than that of the ABC at larger tilt angles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A state estimation approach based on stochastic expansions

This paper presents a new approach for state estimation problems. It is based on the representation of random variables using stochastic functions. Its main idea is to expand the state variables in terms of the noise variables of the system, and then estimate the unnoisy value of the state variables by taking the mean value of the stochastic expansion. Moreover, it was shown that in some situations, the proposed approach may be adapted to the determination of the probability distribution of the state noise. For the determination of the coefficients of the expansions, we present three approaches: moment matching (MM), collocation (COL) and variational (VAR). In the numerical analysis section, three examples are analyzed including a discrete linear system, the Influenza in a boarding school and the state estimation problem in the Hodgkin–Huxley’s model. In all these examples, the proposed approach was able to estimate the values of the state variables with precision, i.e., with very low RMS values.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A computationally efficient method for tempered fractional differential equations with application

This paper investigates the numerical approximation of the tempered fractional integral by using the Sinc-collocation scheme. The algorithm is extended to solve a class of tempered fractional differential equations that converges to the solution with exponential rate. Several numerical examples compare the numerical approximations with the exact solutions. The behavioral responses of the lumped capacitance model with tempered fractional order for transient conduction are investigated. The efficiency and accuracy of the proposed scheme are analyzed in the perspective of the L{sub 2}-norm error and convergence order.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Numerical approach based on fractional-order Lagrange polynomials for solving a class of fractional differential equations

In this study, we propose a new set of fractional functions based on the Lagrange polynomials to solve a class of fractional differential equations. Fractional differential equations are the best tools for modelling natural phenomenon that are elaborated by fractional calculus. Therefore, we need an accurate and efficient technique for solving them. The main purpose of this article is to generalize new functions based on Lagrange polynomials to the fractional calculus. At first, we present a new representation of Lagrange polynomials and in continue, we propose a new set of fractional-order functions which are called fractional-order Lagrange polynomials (FLPs). Besides, a general formulation for operational matrices of fractional integration and derivative of FLPs on arbitrary nodal points are extracted. These matrices are obtained using Laplace transform. The initial value problems is reduced to the system of algebraic equations using the operational matrix of fractional integration and collocation method. Also, we find the upper bound of error vector for the fractional integration operational matrix and we indicate convergence of approximations of FLPs. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On spectral methods for solving variable-order fractional integro-differential equations

This paper applies the shifted Jacobi–Gauss collocation (SJ–G-C) method for solving variable-order fractional integro-differential equations (VO-FIDE) with initial conditions. The Riemann–Liouville fractional derivative, D{sup ν(x)}, and integral, I{sup ν(x)}, of variable order are combined, and the SJ–G-C applied to produce a system of algebraic equations. Numerical experiments demonstrate the applicability and reliability of the algorithm when compared with current methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A semi-discrete scheme for solving fourth-order partial integro-differential equation with a weakly singular kernel using Legendre wavelets method

In this paper, a semi-discrete scheme is presented for solving fourth-order partial integro-differential equations with a weakly singular kernel. The second-order backward difference formula is used to discretize the temporal derivatives. After discretizing the temporal derivatives, the considered problems are converted into a set of ordinary differential equations which are solved by using Legendre wavelets collocation method. The stability and convergence properties related to the time discretization are discussed and theoretically proven. Several numerical examples are included to demonstrate the accuracy and efficiency of the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A multigrid waveform relaxation method for solving the poroelasticity equations

In this work, a multigrid waveform relaxation method is proposed for solving a collocated finite difference discretization of the linear Biot’s model. This gives rise to the first space–time multigrid solver for poroelasticity equations in the literature. The waveform relaxation iteration is based on a point-wise Vanka smoother that couples the pressure variable at a grid-point with the displacements around it. A semi-algebraic mode analysis is proposed to theoretically analyze the convergence of the multigrid waveform relaxation algorithm. This analysis is novel since it combines the semi-algebraic analysis, suitable for parabolic problems, with the non-standard analysis for overlapping smoothers. The practical utility of the method is illustrated through several numerical experiments in one and two dimensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Discrete Hahn polynomials for numerical solution of two-dimensional variable-order fractional Rayleigh–Stokes problem

The main aim of this paper is to find the numerical solutions of 2D Rayleigh–Stokes problem with the variable-order fractional derivatives in the Riemann–Liouville sense. The presented method is based on collocation procedure in combination with the new operational matrix of the variable-order fractional derivatives, in the Caputo sense, for the discrete Hahn polynomials. The main advantage of the proposed method is obtaining a global approximation for spatial and temporal discretizations, and it reduced the problem to an algebraic system, which is easier to solve. Also, the profit of approximating a continuous function by Hahn polynomials is that for computing the coefficients of the expansion, we only have to compute a summation and the calculation of coefficients is exact. The error bound for the approximate solution is estimated. Finally, we evaluate results of the presented method with other numerical methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Compatible meshfree discretization of surface PDEs

Meshfree discretization of surface partial differential equations is appealing, due to their ability to naturally adapt to deforming motion of the underlying manifold. In this work, we consider an existing scheme proposed by Liang et al. reinterpreted in the context of generalized moving least squares (GMLS), showing that existing numerical analysis from the GMLS literature applies to their scheme. With this interpretation, their approach may then be unified with recent work developing compatible meshfree discretizations for the div-grad problem in R d . Informally, this is analogous to an extension of collocated finite differences to staggered finite difference methods, but in the manifold setting and with unstructured nodal data. In this way, we obtain a compatible meshfree discretization of elliptic problems on manifolds which is naturally stable for problems with material interfaces, without the need to introduce numerical dissipation or local enrichment near the interface. As a result, we provide convergence studies illustrating the high-order convergence and stability of the approach for manufactured solutions and for an adaptation of the classical five-strip benchmark to a cylindrical manifold.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Experimental and Numerical Investigation on Vibration of Sandwich Plates with Honeycomb Cores Based on Radial Basis Function

The vibration characteristic of the sandwich plate with a honeycomb core was investigated by experimental measurements and numerical calculation based on radial basis function (RBF). RBF method was used not only in the meshless approach but also in the post-processing of the experimental data. During the experiment, amplitude-fluctuation electronic speckle pattern interferometry was applied to access the resonant frequencies and the corresponding vibration mode shapes simultaneously. Then RBF method was used to improve the quality of patterns and reconstruct the out-of-plane vibration amplitude after fringe analysis. As for numerical calculation, the modal parameters were numerically predicted using the first-order shear deformation theory. The computation approach was based on collocation with multi-quadric radial basis function. To understand the influence of the thickness of face sheet on dynamic behaviors, three types of specimens with different thickness were tested and analyzed. Of particular interest was that the vibration modes show veering due to the thickness increment. Furthermore, the numerical predicted results were compared with the experimental measurements for the first five modes. They are in good agreement with each other for resonant frequencies, mode shapes and relative out-of-plane amplitudes.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Generalized Modular Representation Framework for the Synthesis of Extractive Separation Systems

In this work, a systematic process synthesis and intensification method is presented for extractive separation based on the Generalized Modular Representation Framework (GMF). GMF employs a mass/heat exchange module-based superstructure representation, incorporating detailed thermodynamic model, to investigate conventional or intensified process options for nonideal azeotropic separation without a pre-postulation of plausible unit/flowsheet configurations. Orthogonal Collocation is also applied to enhance GMF representation to obtain intra-module operation information and module dimensionality estimation while maintaining model size compactness. Furthermore, entrainer selection, process synthesis, design, and intensification are examined within a single mixed-integer nonlinear optimization (MINLP) problem. A case study on the separation of ethanol-water mixture is presented to highlight the potential of the proposed approach in deriving optimal and verifiable extractive separation systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Domain wall motion across microstructural features in polycrystalline ferroelectric films

This paper describes the effect of microstructural features such as grain boundaries and triple points on the pinning of domain wall motion in perovskite Pb(Zr 0.52 Ti 0.48 )O 3 (PZT) films on polycrystalline SrRuO 3 /SrTiO 3 substrates. Here, spatial variability in the collective domain wall dynamics was assessed using non-linearity mapping via Band Excitation Piezoresponse Force Microscopy (BE-PFM). Collocating the non-linearity maps with triple point locations (as visualized by EBSD) allowed for exploration of the effects that local microstructure (e.g., grain boundary) have on domain wall motion. It was found that the extrinsic behavior varied with both the misorientation angle and the proximity to the grain boundary. The width of influence of individual grain boundaries on the motion of domain walls was a function of the character of the grain boundary; random grain boundaries exhibit deeper minima in α d /d 33,initial and larger widths of influence (up to 905 nm) compared to coincident site lattice (CSL) boundaries (up to 572 nm). Additionally, triple points containing larger numbers of random boundaries exhibited non-Rayleigh behavior to greater distances, suggesting that the triple point provides either a deep potential minimum or a region where domain wall motion is unfavorable.

36 MATERIALS SCIENCE↗
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↗