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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Weak boundary conditions for Lagrangian shock hydrodynamics: A high-order finite element implementation on curved boundaries

Here, we propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations using high-order finite elements on curved boundaries. Specifically, the variational formulation is appropriately modified to enforce free-slip wall boundary conditions, without perturbing the structure of the function spaces used to represent the solution, with a considerable simplification with respect to traditional approaches. Total energy is conserved and the resulting mass matrices are constant in time. The robustness and accuracy of the proposed method are validated with an extensive set of tests involving nontrivial curved boundaries.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A thin-walled composite beam model for light-weighted structures interacting with fluids

A thin-walled beam model is proposed for structures of variable cross-section, which can be either open or closed and includes multicellular cross-sections with either isotropic or orthotropic materials. The proposed model does not require any priori definition of cross-sectional warping which instead results from the solution of the problem. To achieve that a special deformation pattern is superimposed on the bending deformation described by Euler–Bernoulli beam theory. All sectional properties are automatically incorporated in the analysis as a result of the usual variational formulation of the system of equations. The proposed model is specifically designed to simulate the dynamics of wind/hydrokinetic turbine blade with low computational cost, especially in fluid–structure interaction (FSI) simulation. A number of test cases have been carried out to validate the proposed structural model which show good agreement between the results obtained her e and the solutions available in literature. Finally, FSI simulation of a hydrokinetic blade under field condition is carried out to illustrate the capability of the current thin-walled beam model in practice.

42 ENGINEERING↗
DOE OSTI2024

Performance of large-scale 6 Li-doped pulse-shape discriminating plastic scintillators

A 6 Li-doped plastic scintillator with pulse-shape discrimination capabilities, commercially identified as EJ -299-50, has been developed and produced at the kilogram-scale. A total of 44 bars of dimensions 5.5 cm x 5.5 cm x 50 cm of this material have been characterized. Optical properties like light output and effective attenuation length have been found to be comparable to 6 Li-doped liquid scintillators. Further, the scintillator EJ -299-50 shows good neutron detection capabilities with an effective efficiency for capture on 6 Li of approximately 85%. Stability tests performed on two formulation variations showed no intrinsic degradation in the material or optical properties during several months of observations.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Lagrangian and Dirac constraints for the ideal incompressible fluid and magnetohydrodynamics

The incompressibility constraint for fluid flow was imposed by Lagrange in the so-called Lagrangian variable description using his method of multipliers in the Lagrangian (variational) formulation. An alternative is the imposition of incompressibility in the Eulerian variable description by a generalization of Dirac’s constraint method using noncanonical Poisson brackets. Here it is shown how to impose the incompressibility constraint using Dirac’s method in terms of both the canonical Poisson brackets in the Lagrangian variable description and the noncanonical Poisson brackets in the Eulerian description, allowing for the advection of density. Both cases give the dynamics of infinite-dimensional geodesic flow on the group of volume preserving diffeomorphisms and explicit expressions for this dynamics in terms of the constraints and original variables is given. Since Lagrangian and Eulerian conservation laws are not identical, comparison of the various methods is made.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

The collisional particle-in-cell method for the Vlasov–Maxwell–Landau equations

We introduce an extension of the particle-in-cell method that captures the Landau collisional effects in the Vlasov–Maxwell–Landau equations. The method arises from a regularisation of the variational formulation of the Landau equation, leading to a discretisation of the collision operator that conserves mass, charge, momentum and energy, while increasing the (regularised) entropy. The collisional effects appear as a fully deterministic effective force, thus the method does not require any transport–collision splitting. The scheme can be used in arbitrary dimension, and for a general interaction, including the Coulomb case. We validate the scheme on scenarios such as the Landau damping, the two-stream instability and the Weibel instability, demonstrating its effectiveness in the numerical simulation of plasma.

Bailo, Rafael (ORCID:0000000180183799)↗
DOE OSTI2025

Extended Galerkin Neural Network Approximation of Singular Variational Problems with Error Control

We present extended Galerkin neural networks, a variational framework for approximating general boundary value problems (BVPs) with error control. The main contributions of this work are (1) a rigorous theory guiding the construction of new weighted least squares variational formulations suitable for use in neural network approximation of general BVPs, and (2) an “extended” feedforward network architecture which incorporates and is even capable of learning singular solution structures, thus greatly improving approximability of singular solutions. Furthermore, numerical results are presented for several problems, including steady Stokes flow around reentrant corners and in convex corners with Moffatt eddies in order to demonstrate efficacy of the method.

a posteriori error estimate↗
DOE OSTI2023

Mitigating the noise of DESI mocks using analytic control variates

In order to address fundamental questions related to the expansion history of the Universe and its primordial nature with the next generation of galaxy experiments, we need to model reliably large-scale structure observables such as the correlation function and the power spectrum. Cosmological N-body simulations provide a reference through which we can test our models, but their output suffers from sample variance on large scales. Fortunately, this is the regime where accurate analytic approximations exist. To reduce the variance, which is key to making optimal use of these simulations, we can leverage the accuracy and precision of such analytic descriptions using Control Variates (CV). The power of control variates stems from utilizing inexpensive but highly correlated surrogates of the statistics one wishes to measure. The stronger the correlation between the surrogate and the statistic of interest, the larger the variance reduction delivered by the method. We apply two control variate formulations to mock catalogs generated in anticipation of upcoming data from the Dark Energy Spectroscopic Instrument (DESI) to test the robustness of its analysis pipeline. Our CV-reduced measurements offer a factor of 5-10 improvement in the measurement error compared with the raw measurements. We explore the relevant properties of the galaxy samples that dictate this reduction and comment on the improvements we find on some of the derived quantities relevant to Baryon Acoustic Oscillation (BAO) analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

An Immersed Finite Element Lagrangian-Eulerian Code-Coupling Framework

This report presents an assessment of immersed Eulerian-Lagrangian code-coupling techniques suitable for use in a broad range of mechanics applications. The coupling algorithm is based on an immersed finite element method that considers the Lagrangian and Eulerian overlap regions in the overall variational formulation. In this report the basic formulation details are presented followed by various aspects of the code-coupling algorithm using OpenIFEM as the Lagrangian/coupling framework. A series of representative test cases that illustrate the code-coupling algorithm are discussed. The current work provides an in-depth investigation into the immersed finite element method for the purposes of providing a rigorous coupling technique that is minimally invasive in the respective Eulerian and Lagrangian codes. A number of extensions to the base immersed finite element method have been examined. These extension include nodal and quadrature-based indicator functions, a Lagrangian volume-fraction calculation in regions of overlap, and the use of penalty constraints between the Lagrangian and Eulerian domains. A unique MPI-based coupling strategy that retains the independent MPI structure of each code has been demonstrated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A variational multiscale immersed meshfree method for heterogeneous materials

Abstract We introduce an immersed meshfree formulation for modeling heterogeneous materials with flexible non-body-fitted discretizations, approximations, and quadrature rules. The interfacial compatibility condition is imposed by a volumetric constraint, which avoids a tedious contour integral for complex material geometry. The proposed immersed approach is formulated under a variational multiscale based formulation, termed the variational multiscale immersed method (VMIM). Under this framework, the solution approximation on either the foreground or the background can be decoupled into coarse-scale and fine-scale in the variational equations, where the fine-scale approximation represents a correction to the residual of the coarse-scale equations. The resulting fine-scale solution leads to a residual-based stabilization in the VMIM discrete equations. The employment of reproducing kernel (RK) approximation for the coarse- and fine-scale variables allows arbitrary order of continuity in the approximation, which is particularly advantageous for modeling heterogeneous materials. The effectiveness of VMIM is demonstrated with several numerical examples, showing accuracy, stability, and discretization efficiency of the proposed method.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Comparative investigation of iterative solutions of the all-frequency stable formulation and its vector-potential-only variation

An all-frequency stable formulation has been proposed and applied to solve low-frequency and multiscale electromagnetic problems to avoid the low-frequency breakdown catastrophe of the traditional vector wave equation. Based on the potential representation of the fields, this formulation involves vector and scalar potentials, as well as an auxiliary potential to enforce the gauge condition. In this paper, such a formulation is first simplified to involve vector potential only. Their iterative solutions are then sought by using an incomplete LU preconditioner and an iterative solver. The iterative performance of both formulations are investigated in a comparative study.

Mekonnen, Minyechil↗
DOE OSTI2020

On the Derivation of Quasi-Newton Formulas for Optimization in Function Spaces

Newton’s method is usually preferred when solving optimization problems due to its superior convergence properties compared to gradient-based or derivative-free optimization algorithms. However, deriving and computing second-order derivatives needed by Newton’s method often is not trivial and, in some cases, not possible. In such cases quasi-Newton algorithms are a great alternative. In this paper, we provide a new derivation of well-known quasi-Newton formulas in an infinite-dimensional Hilbert space setting. Furthermore, it is known that quasi-Newton update formulas are solutions to certain variational problems over the space of symmetric matrices. In this paper, we formulate similar variational problems over the space of bounded symmetric operators in Hilbert spaces. By changing the constraints of the variational problem we obtain updates (for the Hessian and Hessian inverse) not only for the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method but also for Davidon–Fletcher–Powell (DFP), Symmetric Rank One (SR1), and Powell-Symmetric-Broyden (PSB). In addition, for an inverse problem governed by a partial differential equation (PDE), we derive DFP and BFGS “structured” secant formulas that explicitly use the derivative of the regularization and only approximates the second derivative of the misfit term. We show numerical results that demonstrate the desired mesh-independence property and superior performance of the resulting quasi-Newton methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

The second-generation Shifted Boundary Method and its numerical analysis

Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we present enhanced variational SBM formulations for the Poisson and Stokes problems with improved flexibility and robustness. These simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations. First, we show that these new SBM implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive. Second, we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at Dirichlet boundaries, therefore avoiding the calibration of an additional stabilization parameter. Finally, we prove enhanced L 2 -estimates without the cumbersome assumption – of earlier proofs – that the surrogate domain is convex. Instead we rely on a conventional assumption that the boundary of the true domain is smooth, which can also be replaced by requiring convexity of the true domain. The aforementioned improvements open the way to a more general and efficient implementation of the Shifted Boundary Method, particularly in complex three-dimensional geometries. We complement these theoretical developments with numerical experiments in two and three dimensions.

42 ENGINEERING↗
DOE OSTI2024

Variation-Resilient FeFET-Based In-Memory Computing Leveraging Probabilistic Deep Learning

Reliability issues stemming from device level nonidealities of nonvolatile emerging technologies like ferroelectric field-effect transistors (FeFETs), especially at scaled dimensions, cause substantial degradation in the accuracy of in-memory crossbar-based AI systems. Here, in this work, we present a variation-aware design technique to characterize the device level variations and to mitigate their impact on hardware accuracy employing a Bayesian neural network (BNN) approach. An effective conductance variation model is derived from the experimental measurements of cycle-to-cycle (C2C) and device-to-device (D2D) variations performed on FeFET devices fabricated using 28 nm high-k metal gate technology. The variations were found to be a function of different conductance states within the given programming range, which sharply contrasts earlier efforts where a fixed variation dispersion was considered for all conductance values. Such variation characteristics formulated for three different device sizes at different read voltages were provided as prior variation information to the BNN to yield a more exact and reliable inference. Near-ideal accuracy for shallow networks (MLP5 and LeNet models) on the MNIST dataset and limited accuracy decline by ~3.8%–16.1% for deeper AlexNet models on CIFAR10 dataset under a wide range of variations corresponding to different device sizes and read voltages, demonstrates the efficacy of our proposed device-algorithm co-design technique.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Enriched immersed boundary method (EIBM) for interface-coupled multi-physics and applications to convective conjugate heat transfer

It is challenging to develop numerical methods that simultaneously maintain accuracy of resolving boundary conditions and mesh flexibility to handle the interface in interface-coupled multi-physics problems involving large property discontinuity. On the one hand, boundary-fitted methods possess high accuracy in capturing the interfacial phenomenon but involve complicated volumetric mesh generation, mesh-motion, and even re-meshing procedures. On the other hand, immersed boundary methods (IBM) provide mesh flexibility but sometimes suffer from inferior interface representations, leading to poor enforcement of boundary conditions. This paper presents an enriched immersed boundary method (EIBM) to overcome this challenge and demonstrates its efficacy in conjugate heat transfer, a representative example in interface-coupled multi-physics systems that have implications for many industrial processes. Further, the core technique of the method is to enhance IBM’s accuracy of the fluid–solid interface by enriching the degrees of freedom of the cut elements to enforce temperature and flux compatibilities and resolve all the physical unknowns on the background mesh to simplify the volumetric mesh generation. We implement the EIBM under the framework of a variational multiscale formulation for coupled Navier–Stokes and thermodynamics equations. The enriched DoFs enable better enforcement of temperature and flux compatibilities with large conductivity ratios across the fluid–solid interface. At the same time, the immersed nature of the proposed method still attains mesh flexibility. The EIBM’s accuracy is thoroughly evaluated through a set of examples, ranging from benchmark problems with analytical solutions to real-world cooling processes of a moving metallic structure with complex geometry.

42 ENGINEERING↗
DOE OSTI2024

Bi-fidelity variational auto-encoder for uncertainty quantification

Quantifying the uncertainty of quantities of interest (QoIs) from physical systems is a primary objective in model validation. However, achieving this goal entails balancing the need for computational efficiency with the requirement for numerical accuracy. To address this trade-off, we propose a novel bi-fidelity formulation of variational auto-encoders (BF-VAE) designed to estimate the uncertainty associated with a QoI from low-fidelity (LF) and high-fidelity (HF) samples of the QoI. Here, this model allows for the approximation of the statistics of the HF QoI by leveraging information derived from its LF counterpart. Specifically, we design a bi-fidelity auto-regressive model in the latent space which is integrated within the VAE’s probabilistic encoder–decoder structure. An effective algorithm is proposed to maximize the variational lower bound of the HF log-likelihood in the presence of limited HF data, resulting in the synthesis of HF realizations with a reduced computational cost. Additionally, we introduce the concept of the bi-fidelity information bottleneck (BF-IB) to provide an information-theoretic interpretation of the proposed BF-VAE model. Our numerical results demonstrate that the BF-VAE leads to considerably improved accuracy, as compared to a VAE trained using only HF data, when limited HF data is available.

42 ENGINEERING↗
DOE OSTI2022

Variational multiscale reinforcement learning for discovering reduced order closure models of nonlinear spatiotemporal transport systems

Abstract A central challenge in the computational modeling and simulation of a multitude of science applications is to achieve robust and accurate closures for their coarse-grained representations due to underlying highly nonlinear multiscale interactions. These closure models are common in many nonlinear spatiotemporal systems to account for losses due to reduced order representations, including many transport phenomena in fluids. Previous data-driven closure modeling efforts have mostly focused on supervised learning approaches using high fidelity simulation data. On the other hand, reinforcement learning (RL) is a powerful yet relatively uncharted method in spatiotemporally extended systems. In this study, we put forth a modular dynamic closure modeling and discovery framework to stabilize the Galerkin projection based reduced order models that may arise in many nonlinear spatiotemporal dynamical systems with quadratic nonlinearity. However, a key element in creating a robust RL agent is to introduce a feasible reward function, which can be constituted of any difference metrics between the RL model and high fidelity simulation data. First, we introduce a multi-modal RL to discover mode-dependant closure policies that utilize the high fidelity data in rewarding our RL agent. We then formulate a variational multiscale RL (VMRL) approach to discover closure models without requiring access to the high fidelity data in designing the reward function. Specifically, our chief innovation is to leverage variational multiscale formalism to quantify the difference between modal interactions in Galerkin systems. Our results in simulating the viscous Burgers equation indicate that the proposed VMRL method leads to robust and accurate closure parameterizations, and it may potentially be used to discover scale-aware closure models for complex dynamical systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Integral boundary conditions in phase field models

Modeling the chemical, electric and thermal transport as well as phase transitions and the accompanying mesoscale microstructure evolution within a material in an electronic device setting involves the solution of partial differential equations often with integral boundary conditions. Employing the familiar Poisson equation describing the electric potential evolution in a material exhibiting insulator to metal transitions, we exploit a special property of such an integral boundary condition, and we properly formulate the variational problem and establish its well-posedness. Next, we compare our method with the commonly-used Lagrange multiplier method that can also handle such boundary conditions. Numerical experiments demonstrate that our new method achieves optimal convergence rate in contrast to the conventional Lagrange multiplier method. Furthermore, the linear system derived from our method is symmetric positive definite, and can be efficiently solved by Conjugate Gradient method with algebraic multigrid preconditioning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Goal-oriented a-posteriori estimation of model error as an aid to parameter estimation

In this work, a Bayesian model calibration framework is presented that utilizes goal-oriented a-posterior error estimates in quantities of interest (QoIs) for classes of high-fidelity models characterized by PDEs. It is shown that for a large class of computational models, it is possible to develop a computationally inexpensive procedure for calibrating parameters of high-fidelity models of physical events when the parameters of low-fidelity (surrogate) models are known with acceptable accuracy. The main ingredients in the proposed model calibration scheme are goal-oriented a-posteriori estimates of error in QoIs computed using a so-called lower fidelity model compared to those of an uncalibrated higher fidelity model. The estimates of error in QoIs are used to define likelihood functions in Bayesian inversion analysis. A standard Bayesian approach is employed to compute the posterior distribution of model parameters of high-fidelity models. As applications, parameters in a quasi-linear second-order elliptic boundary-value problem (BVP) are calibrated using a second-order linear elliptic BVP. In a second application, parameters of a tumor growth model involving nonlinear time-dependent PDEs are calibrated using a lower fidelity linear tumor growth model with known parameter values.

A-posterior estimates↗