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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems

In the hyperbolic community, discontinuous Galerkin (DG) approaches are mainly applied when finite element methods are considered. As the name suggested, the DG framework allows a discontinuity at the element interfaces, which seems for many researchers a favorable property in case of hyperbolic balance laws. On the contrary, continuous Galerkin methods appear to be unsuitable for hyperbolic problems and there exists still the perception that continuous Galerkin methods are notoriously unstable. To remedy this issue, stabilization terms are usually added and various formulations can be found in the literature. However, this perception is not true and the stabilization terms are unnecessary, in general. In this paper, we deal with this problem, but present a different approach. We use the boundary conditions to stabilize the scheme following a procedure that are frequently used in the finite difference community. Here, the main idea is to impose the boundary conditions weakly and specific boundary operators are constructed such that they guarantee stability. This approach has already been used in the discontinuous Galerkin framework, but here we apply it with a continuous Galerkin scheme. No internal dissipation is needed even if unstructured grids are used. Further, we point out that we do not need exact integration, it suffices if the quadrature rule and the norm in the differential operator are the same, such that the summation-by-parts property is fulfilled meaning that a discrete Gauss Theorem is valid. This contradicts the perception in the hyperbolic community that stability issues for pure Galerkin scheme exist. In numerical simulations, we verify our theoretical analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Projection-Based Model Reduction for Coupled Conduction—Enclosure Radiation Systems

We report a projection-based reduced order model (pROM) methodology has been developed for transient heat transfer problems involving coupled conduction and enclosure radiation. The approach was demonstrated on two test problems of varying complexity. The reduced order models demonstrated substantial speedups (up to 185×) relative to the full order model with good accuracy (less than 3% L ∞ error). An attractive feature of pROMs is that there is a natural error indicator for the ROM solution: the final residual norm at each time-step of the converged ROM solution. Using example test cases, we discuss how to interpret this error indicator to assess the accuracy of the ROM solution. The approach shows promise for many-query applications, such as uncertainty quantification and optimization. The reduced computational cost of the ROM relative to the full-order model (FOM) can enable the analysis of larger and more complex systems as well as the exploration of larger parameter spaces.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A Semi-Analytical Solution Approach for Solving Constant-Coefficient First-Order Partial Differential Equations

Simulation and control of many dynamic systems involve solving partial differential equations (PDE). This letter proposes a semi-analytical solution (SAS) approach for fast and high-quality solution of first-order PDEs. The region of interest of the studied PDE is divided into a grid, and an SAS is derived for each grid cell in the form of the multivariate polynomials, of which the coefficients are identified using initial value and boundary value conditions. The solutions are solved in a “time-stepping” manner, i.e. within one time step, the coefficients of the SAS are identified and the initial value of the next time step is evaluated. This approach achieves a significantly larger grid cell than the widely used finite difference method, and thus enhances the computational efficiency significantly. Furthermore, the simulation result on the natural gas pipeline model demonstrates the advantages of SAS in accuracy and computational efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Parallel Cut-Cell Algorithm for the Free-Boundary Grad--Shafranov Problem

A parallel cut-cell algorithm is described to solve the free-boundary problem of the Grad--Shafranov equation. The algorithm reformulates the free-boundary problem in an irregular bounded domain and its important aspects include a searching algorithm for the magnetic axis and separatrix, a surface integral along the irregular boundary to determine the boundary values, an approach to optimize the coil current based on a targeting plasma shape, Picard iterations with Aitken's acceleration for the resulting nonlinear problem, and a Cartesian grid embedded boundary method to handle the complex geometry. Here the algorithm is implemented in parallel using a standard domain-decomposition approach and a good parallel scaling is observed. Numerical results verify the accuracy and efficiency of the free-boundary Grad--Shafranov solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Objective and algorithm considerations when optimizing the number and placement of turbines in a wind power plant

Abstract. Optimizing turbine layout is a challenging problem that has been extensively researched in the literature. However, optimizing the number of turbines within a given boundary has not been studied as extensively and is a difficult problem because it introduces discrete design variables and a discontinuous design space. An essential step in performing wind power plant layout optimization is to define the objective function, or value, that is used to express what is valuable to a wind power plant developer, such as annual energy production, cost of energy, or profit. In this paper, we demonstrate the importance of selecting the appropriate objective function when optimizing a wind power plant in a land-constrained site. We optimized several different wind power plants with different wind resources and boundary sizes. Results show that the optimal number of turbines varies drastically depending on the objective function. For a simple, one-dimensional, land-based scenario, we found that a wind power plant optimized for minimal cost of energy produced just 72 % of the profit compared to the wind power plant optimized for maximum profit, which corresponded to a loss of about USD 2 million each year. This paper also compares the performance of several different optimization algorithms, including a novel repeated-sweep algorithm that we developed. We found that the performance of each algorithm depended on the number of design variables in the problem as well as the objective function.

17 WIND ENERGY↗
DOE OSTI2021

Ocean Energy Systems Wave Energy Modeling Task 10.4: Numerical Modeling of a Fixed Oscillating Water Column

This paper reports on an ongoing international effort to establish guidelines for numerical modeling of wave energy converters, initiated by the International Energy Agency Technology Collaboration Program for Ocean Energy Systems. Initial results for point absorbers were presented in previous work, and here we present results for a breakwater-mounted Oscillating Water Column (OWC) device. The experimental model is at scale 1:4 relative to a full-scale installation in a water depth of 12.8 m. The power-extracting air turbine is modeled by an orifice plate of 1–2% of the internal chamber surface area. Measurements of chamber surface elevation, air flow through the orifice, and pressure difference across the orifice are compared with numerical calculations using both weakly-nonlinear potential flow theory and computational fluid dynamics. Both compressible- and incompressible-flow models are considered, and the effects of air compressibility are found to have a significant influence on the motion of the internal chamber surface. Recommendations are made for reducing uncertainties in future experimental campaigns, which are critical to enable firm conclusions to be drawn about the relative accuracy of the numerical models. It is well-known that boundary element method solutions of the linear potential flow problem (e.g., WAMIT) are singular at infinite frequency when panels are placed directly on the free surface. This is problematic for time-domain solutions where the value of the added mass matrix at infinite frequency is critical, especially for OWC chambers, which are modeled by zero-mass elements on the free surface. A straightforward rational procedure is described to replace ad-hoc solutions to this problem that have been proposed in the literature.

16 TIDAL AND WAVE POWER↗
DOE OSTI2021

Higher-order particle representation for particle-in-cell simulations

In this paper we present an alternative approach to the representation of simulation particles for unstructured electrostatic and electromagnetic PIC simulations. In our modified PIC algorithm we represent particles as having a smooth shape function limited by some specified finite radius, r 0 . A unique feature of our approach is the representation of this shape by surrounding simulation particles with a set of virtual particles with delta shape, with fixed offsets and weights derived from Gaussian quadrature rules and the value of r 0 . As the virtual particles are purely computational, they provide the additional benefit of increasing the arithmetic intensity of traditionally memory bound particle kernels. The modified algorithm is implemented within Sandia National Laboratories' unstructured EMPIRE-PIC code, for electrostatic and electromagnetic simulations, using periodic boundary conditions. We show results for a representative set of benchmark problems, including electron orbit, a transverse electromagnetic wave propagating through a plasma, numerical heating, and a plasma slab expansion. In this work, good error reduction across all of the chosen problems is achieved as the particles are made progressively smoother, with the optimal particle radius appearing to be problem-dependent.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Fast Active-Set Thresholding Method for Nonnegative Least Squares

Nonnegative Least Squares (NNLS) is a fundamental constrained optimization problem encountered in many applications such as image deblurring, signal processing, nonnegative matrix factorization, magnetic microscopy, and hyperspectral imaging. Active-set based methods are a common class of algorithms for solving NNLS which identify the optimal variable set of the NNLS solution. They do so by iteratively solving a series of unconstrained least squares problems, identifying which variables violate the nonnegativity constraints, and then swapping variables in/out of consideration until the optimal set of variables is found. Several variations improving upon this method exist in the literature. In this work, we propose an active-set swap heuristic which further improves upon existing active-set based methods for NNLS. Our optimizations are based upon adding multiple variables to the passive set within a threshold of the smallest gradient value and removing variables within a similar threshold of the closest boundary constraint. We leverage these optimizations to yield a Fast Active-Set Thresholding NNLS (FAST-NNLS) algorithm which significantly outperforms the existing state-of-the-art NNLS algorithms for a wide range of problems. Rigorous convergence guarantees are proven for the proposed method. We demonstrate the effectiveness of our proposed method on multiple synthetic datasets and two realworld text analysis applications. In doing so, we present the most comprehensive NNLS solver comparison in the literature to date.

Cobb, Benjamin [Georgia Institute of Technology]↗
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↗
DOE OSTI2023

A comparison of eight optimization methods applied to a wind farm layout optimization problem

Abstract. Selecting a wind farm layout optimization method is difficult. Comparisons between optimization methods in different papers can be uncertain due to the difficulty of exactly reproducing the objective function. Comparisons by just a few authors in one paper can be uncertain if the authors do not have experience using each algorithm. In this work we provide an algorithm comparison for a wind farm layout optimization case study between eight optimization methods applied, or directed, by researchers who developed those algorithms or who had other experience using them. We provided the objective function to each researcher to avoid ambiguity about relative performance due to a difference in objective function. While these comparisons are not perfect, we try to treat each algorithm more fairly by having researchers with experience using each algorithm apply each algorithm and by having a common objective function provided for analysis. The case study is from the International Energy Association (IEA) Wind Task 37, based on the Borssele III and IV wind farms with 81 turbines. Of particular interest in this case study is the presence of disconnected boundary regions and concave boundary features. The optimization methods studied represent a wide range of approaches, including gradient-free, gradient-based, and hybrid methods; discrete and continuous problem formulations; single-run and multi-start approaches; and mathematical and heuristic algorithms. We provide descriptions and references (where applicable) for each optimization method, as well as lists of pros and cons, to help readers determine an appropriate method for their use case. All the optimization methods perform similarly, with optimized wake loss values between 15.48 % and 15.70 % as compared to 17.28 % for the unoptimized provided layout. Each of the layouts found were different, but all layouts exhibited similar characteristics. Strong similarities across all the layouts include tightly packing wind turbines along the outer borders, loosely spacing turbines in the internal regions, and allocating similar numbers of turbines to each discrete boundary region. The best layout by annual energy production (AEP) was found using a new sequential allocation method, discrete exploration-based optimization (DEBO). Based on the results in this study, it appears that using an optimization algorithm can significantly improve wind farm performance, but there are many optimization methods that can perform well on the wind farm layout optimization problem, given that they are applied correctly.

17 WIND ENERGY↗
DOE OSTI2024

Multilevel Monte Carlo methods for the Grad-Shafranov free boundary problem

The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad-Shafranov equation. The presence of uncertainty in the model parameters introduces the need to quantify the variability in the predictions. This is often done by computing a large number of model solutions on a computational grid for an ensemble of parameter values and then obtaining estimates for the statistical properties of solutions. In this study, we explore the savings that can be obtained using multilevel Monte Carlo methods, which reduce costs by performing the bulk of the computations on a sequence of spatial grids that are coarser than the one that would typically be used for a simple Monte Carlo simulation. We examine this approach using both a set of uniformly refined grids and a set of adaptively refined grids guided by a discrete error estimator. Numerical experiments show that multilevel methods dramatically reduce the cost of simulation, with cost reductions typically on the order of 60 or more and possibly as large as 200. Furthermore, adaptive griding results in more accurate computation of geometric quantities such as x-points associated with the model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Updates to Nek5000: RANS wall functions, NRC support, and documentation

As a key part of the U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation program (NEAMS), the next generation of tools for nuclear reactor design are being developed. A primary metric for success of this program is the adoption of those tools by industry stakeholders. To help meet this metric for Nek5000, development efforts this year have focused on the expansion of the available Reynolds-averaged Navier-Stokes (RANS) turbulence models to include wall function models, continued support of the U.S. Nuclear Regulatory Commission in simulating a hydrogen mitigation benchmark experiment, and expansion of the Nek5000 documentation to enhance the code’s usability. The implementation of wall functions is intended to significantly decrease time to-solution for a wide range of problems and it has been identified as an important feature by stakeholders across the nuclear community. The initial implementation of standard and pressure corrected wall functions has been tested in Nek5000 on the classical problems of channel flow and a backward facing step. It has also been tested on a 2D molten salt fast reactor core and a T-junction. The recommended formulation of choosing y + = 30 as a boundary value combined with a Neumann-Neumann formulation of the boundary condition for k and τ produces the most consistent results compared to a wall resolved approach. The collaboration with the NRC is a continuing exercise that has been ongoing for multiple years. This year we have concluded investigations into appropriate inlet conditions, showing that fully developed turbulent conditions are adequate for the full PANDA domain. We have also concluded simulations for an unobstructed jet and are now refocusing to the original obstructed jet case. The expansion of the code documentation has also been an ongoing effort over the past few years to address feedback from the various stakeholders. The documentation now more fully covers many of the available features and closes identified SQA gaps. Finally we report on three training sessions that were offered over the past year in an effort to expand the Nek5000 user base.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Designing interagency responses to wicked problems: A viable system model board game

Government agencies struggle to address wicked problems because they are open-ended, highly interdependent issues that cross agency, stakeholder, jurisdictional, and geopolitical boundaries. While both quantitative modelling and qualitative problem structuring methodologies have been used to support interagency decision making in the past, co-designing an effective interagency organization to collaboratively tackle wicked problems is more challenging. Few approaches have been developed to enable such efforts. This paper explains how the viable system model (VSM) was implemented through a board game, which was employed to co-design an interagency meta-organization that would be capable of more effectively collaborating to jointly address a wicked problem: international organized drug crime and its interface with local gangs in Chicago, USA. The board game was developed to make the VSM easier for the participants to learn, given that the cybernetic language and engineering-influenced diagrams in the original literature can be off-putting to leaders and managers. The board game was used as the final stage of a multi-method, systemic approach, which involved boundary critique and problem structuring as well as deployment of the VSM. The research findings indicate that the VSM board game, used as part of a larger mixed-methods systemic intervention, contributes to building trust in the value of systems thinking amongst the participants, and sets up a rich context for collaboration on multi-agency co-design. The game therefore offers significant promise as part of the co-design of interagency responses to wicked problems because it creates an embodied process for stakeholders to learn about the VSM. It also reduces the work involved in this learning. Thus, the game enables an effective appropriation of the VSM language and criteria.

Business & Economics↗
DOE OSTI2026

Non-conformal interface-cohesive modeling with the shifted boundary method

The accurate simulation of boundary- and interface-dominated problems on complex geometries remains challenging when boundary- or interface-fitted meshes are difficult to generate, particularly for curved boundaries, polycrystalline microstructures, and dense interface networks. The Shifted Boundary Method (SBM) alleviates this meshing burden by shifting the enforcement of boundary conditions from the true boundary to a nearby surrogate boundary and recovering the effect of the true boundary through geometric correction terms, thereby enabling standard finite element spaces on non-boundary-fitted meshes. In this report, we develop a general shiftedboundary and shifted-interface framework within the open-source MOOSE framework. We first present a general SBM implementation for complex geometries on non-boundary-fitted meshes. We then adopt the Shifted Interface Method (SIM) for internal interfaces and develop a unified shifted-interface treatment in which the interface law is enforced on a surrogate interface and the effect of the true interface is recovered through shifted jumps, fluxes, and tractions. This perspective brings scalar thermal-contact and vector-valued cohesive-zone mechanics into a single framework, the latter realized as the Shifted Cohesive Zone Method (SCZM) and coupled with history-dependent constitutive models from NEML2. We further extend the MOOSE mesh infrastructure to support cohesive-zone calculations on distributed meshes. The framework is verified and demonstrated through three progressive studies: Poisson’s equation on a smoothed starshaped domain, a manufactured thermal-contact problem on a non-interface-fitted mesh, and a two-dimensional polycrystalline representative volume element combining crystal plasticity with cohesive grain-boundary interfaces. Across these studies, the shifted formulations reproduce boundary- and interface-fitted reference solutions with high fidelity, indicating that the proposed framework provides an accurate and efficient route to boundary- and interface-dominated simulations on arbitrary geometries without requiring fitted meshes.

Yang, Cheng-Hau↗
DOE OSTI2021

Periodic boundary conditions for arbitrary deformations in molecular dynamics simulations

A generalization of the Lees-Edwards periodic boundary conditions (gLE-PBC) for molecular dynamics (MD) simulations is developed to allow for arbitrary deformations to be applied to the domain. The gLE-PBC domain remains a rectangular cuboid regardless of the applied deformation in contrast with the Lagrangian-rhomboid periodic boundary conditions (LR-PBC) where the domain deforms according to the applied deformation. Furthermore, the kinematics of gLE-PBC are validated against pure shear. The gLE-PBC method for interacting systems is then validated against the LR-PBC method and analytical solutions for a solid under isotropic compression, one-dimensional shearing, three-dimensional extension and shearing and for a liquid under Couette flow. Bulk physical properties extracted from the gLE-PBC simulations agree well with values calculated from equilibrium MD simulations. Three dimensional shearing and a deformation with a full velocity gradient matrix are also simulated, showing the range of problems gLE-PBC can explore.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

An analysis of the spatio-temporal resolution of the immersed boundary method with direct forcing

The immersed boundary method (IBM) with direct forcing is very popular in the simulation of rigid particulate flows. In the IBM, an interaction force is introduced at the interface between fluid and particle in order to approximate the no-slip boundary condition. The interaction force is calculated through dividing the velocity difference (or error) between fluid and particle at the interface by the time step. Here, a dynamic equation for the velocity difference is derived. Additionally, analyses on the dynamic equation provide a few new findings: (i) The interaction force is the solution of a least-squares error problem, with the direct implication that the Lagrangian marker distribution has no effect on the large scale flow structure once the distribution of Lagrangian markers become saturated along the interface (i.e., each marker remains properly correlated with all its neighbors); (ii) The Lagrangian volume-weight is a relaxation factor to control how fast the velocity error decays to the ideal value of zero; (iii) The optimal choice of the Lagrangian volume-weight is the largest value permissible by a stability condition. A comprehensive convergence analysis with regard to the spatial and temporal resolution is presented for the velocity error and also for the shear-stress and surface pressure. In three simple canonical problems, it is analytically and numerically shown that the IBM results converge to the theoretical solutions obtained with precise imposition of no-slip and no-penetration boundary conditions. It is observed that it is not necessary to match the Lagrangian marker volume-weight to that of the local Eulerian cell volume and in fact this matching leads to lower than optimal computational efficiency. However, it is found that extremely high Eulerian grid resolution and small time step have to be used to obtain high precision simulation results. Especially, the time step should be inversely proportional to the particle Reynolds number for low Reynolds number flows. For high frequency oscillation problems, the grid size needs to be reduced by a factor of the square root of the frequency, and the time step to be reduced by a factor of the frequency. The theoretical findings here can be used to alleviate the technical difficulties in simulating non-spherical particles by not requiring the Lagrangian marker distribution to match the Eulerian grids and also in the implementation of IBM on non-uniform Eulerian grids. The present work also provides simple practical guidance on the choice of temporal and spatial resolution so as to control the simulation error a priori.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Understanding the Roles of Convective Trigger Functions in the Diurnal Cycle of Precipitation in the NCAR CAM5

The wrong diurnal cycle of precipitation is a common weakness of current global climate models (GCMs). To improve the simulation of the diurnal cycle of precipitation and understand what physical processes control it, we test a convective trigger function described in Xie et al. (2019) with additional optimizations in the NCAR Community Atmosphere Model version 5 (CAM5). The revised trigger function consists of three modifications: 1) replacing the Convective Available Potential Energy (CAPE) trigger with a dynamic CAPE (dCAPE) trigger, 2) allowing convection to originate above the top of planetary boundary layer (i.e., the unrestricted air parcel launch level - ULL), and 3) optimizing the entrainment rate and threshold value of the dynamic CAPE generation rate for convection onset based on observations. Results from 1°-resolution simulations show that the revised trigger can alleviate the long-standing GCM problem of too early maximum precipitation during the day and missing the nocturnal precipitation peak that is observed in many regions, including the U.S. southern Great Plains (SGP). The revised trigger also improves the simulation of the propagation of precipitation systems downstream of the Rockies and the Amazon region. A further composite analysis over the SGP unravels the mechanisms through which the revised trigger affects convection. Additional sensitivity tests show that both the peak time and the amplitude of the diurnal cycle of precipitation are sensitive to the entrainment rate and dCAPE threshold values.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Local-nonlocal coupling in Emu/PDMS

A technique called the splice method for coupling local to peridynamic subregions of a body is described. The method relies on ghost nodes, whose values of displacement are interpolated from nearby physical nodes, to make each subregion visible to the other. In each time step, the nodes in each subregion treat the nodes in the other subregion as boundary conditions. Adaptively changing the subregions is possible through the creation and deletion of ghost nodes. Example problems in 2D and 3D illustrate how the method is used to perform multiscale modeling of fracture and impact events within a larger structure.

42 ENGINEERING↗