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Results for “Smoothed boundary method”

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 OSTI2023

A Minkowski difference-based advancing front packing technique for generating convex noncircular particles in complex domains

In this work, a Minkowski difference-based advancing front approach is proposed to generate convex and non-circular particles in a predefined computational domain. Two specific algorithms are developed to handle the contact conformity of generated particles with the boundaries of the computational domain. The first, called the open form, is used to handle the smooth contact of generated particles with (external) boundaries, while the other, called the closed form, is proposed to handle the internal boundaries of a computational domain with a complex cavity. The Gilbert-Johnson-Keerthi (GJK) method is used to efficiently solve the contact detection between the newly generated particle at the front and existing particles. Furthermore, the problem of one-sided particle lifting, which can cause some defects in the packing structure in existing advancing front methods during packing generation, is highlighted and an effective solution is developed. Several examples of increasing complexity are used to demonstrate the efficiency and applicability of the proposed packing generation approach. The numerical results show that the generated packing is not only more uniform, but also achieves a higher packing density than existing advancing front methods.

42 ENGINEERING↗
DOE OSTI2023

Recipes for when physics fails: recovering robust learning of physics informed neural networks

Abstract Physics-informed neural networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be sensitive to errors in training data and overfit itself in dynamically propagating these errors over the domain of the solution of the PDE. It also shows how physical regularizations based on continuity criteria and conservation laws fail to address this issue and rather introduce problems of their own causing the deep network to converge to a physics-obeying local minimum instead of the global minimum. We introduce Gaussian process (GP) based smoothing that recovers the performance of a PINN and promises a robust architecture against noise/errors in measurements. Additionally, we illustrate an inexpensive method of quantifying the evolution of uncertainty based on the variance estimation of GPs on boundary data. Robust PINN performance is also shown to be achievable by choice of sparse sets of inducing points based on sparsely induced GPs. We demonstrate the performance of our proposed methods and compare the results from existing benchmark models in literature for time-dependent Schrödinger and Burgers’ equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Comparison of machine learning and electrical resistivity arrays to inverse modeling for locating and characterizing subsurface targets

Here, this study evaluates the performance of multiple machine learning (ML) algorithms and electrical resistivity (ER) arrays for inversion with comparison to a conventional Gauss-Newton numerical inversion method. Four different ML models and four arrays were used for the estimation of only six variables for locating and characterizing hypothetical subsurface targets. The combination of dipole-dipole with Multilayer Perceptron Neural Network (MLP-NN) had the highest accuracy. Evaluation showed that both MLP-NN and Gauss-Newton methods performed well for estimating the matrix resistivity while target resistivity accuracy was lower, and MLP-NN produced sharper contrast at target boundaries for the field and hypothetical data. Both methods exhibited comparable target characterization performance, whereas MLP-NN had increased accuracy compared to Gauss-Newton in prediction of target width and height, which was attributed to numerical smoothing present in the Gauss-Newton approach. MLP-NN was also applied to a field dataset acquired at U.S. DOE Hanford site.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

IGA-MPM: The Isogeometric Material Point Method

In this work, we propose the use of Isogeometric Analysis (IGA) within the context of the Material Point Method (MPM), and refer to the approach as IGA-MPM. We use the idea of IGA, and its instantiation based on Non-Uniform Rational B-Splines (NURBS), to build higher-order accurate and smooth approximation for MPM. Higher-order smoothness yields a continuous representation of the strain rate, and, as a result, prevents jumps in the stress and other history variables as the material points cross the element boundaries. Furthermore, NURBS can exactly represent all conic sections and the corresponding symmetries in the solution, which may be important in some applications. Several numerical examples of increasing complexity are presented, and show the ability of IGA-MPM to eliminate the well known cell-crossing instability of the conventional MPM. In addition, the examples presented demonstrate improved accuracy, convergence, and symmetry preservation of IGA-MPM compared to the conventional MPM, both for rectilinear and curved geometries.

42 ENGINEERING↗
DOE OSTI2022

First-passage time statistics on surfaces of general shape: Surface PDE solvers using Generalized Moving Least Squares (GMLS)

Here, we develop numerical methods for computing statistics of stochastic processes on surfaces of general shape with drift-diffusion dynamics d X t = a (X t ) dt + b(X t ) d W t . We formulate descriptions of Brownian motion and general drift-diffusion processes on surfaces. We consider statistics of the form u (x) = E x [$∫^{τ}_{0}$ g (X t ) dt ] + E x [ f (X τ )] for a domain Ω and the exit stopping time τ = inf t { t >0 | X i Ω}, where f , g are general smooth functions. For computing these statistics, we develop high-order Generalized Moving Least Squares (GMLS) solvers for associated surface PDE boundary-value problems based on Backward- Kolmogorov equations. We focus particularly on the mean First Passage Times (FPTs) given by the case f = 0, g = 1 where u (x) = E x [τ]. We perform studies for a variety of shapes showing our methods converge with high-order accuracy both in capturing the geometry and the surface PDE solutions. We then perform studies showing how statistics are influenced by the surface geometry, drift dynamics, and spatially dependent diffusivities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Scaled boundary cubature scheme for numerical integration over planar regions with affine and curved boundaries

This paper introduces the scaled boundary cubature (SBC) scheme for accurate and efficient integration of functions over polygons and two-dimensional regions bounded by parametric curves. Over two-dimensional domains, the SBC method reduces integration over a region bounded by m curves to integration over m regions (referred to as curved triangular regions), where each region is bounded by two line segments and a curve. With proper (counterclockwise) orientation of the boundary curves, the scheme is applicable to convex and nonconvex domains. Additionally, for star-convex domains, a tensor-product cubature rule with positive weights and integration points in the interior of the domain is obtained. If the integrand is homogeneous, we show that this new method reduces to the homogeneous numerical integration scheme; however, the SBC scheme is more versatile since it is equally applicable to both homogeneous and non-homogeneous functions. This paper also introduces several methods for smoothing integrands with point singularities and near-singularities. When these methods are used, highly efficient integration of weakly singular functions is realized. Finally, the SBC method is applied to a number of benchmark problems, which reveal its broad applicability and superior performance (in terms of time to generate a rule and accuracy per cubature point) when compared to existing methods for integration.

42 ENGINEERING↗
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 OSTI2026

Electropolishing-induced topographic defects in niobium: Insights and Implications for SRF

Electropolishing (EP) is the premier surface preparation method for high-Q, high-gradient superconducting RF cavities made of Nb. This leaves behind an apparently smooth surface, yet the achievable peak magnetic fields fall well below the superheating field of Nb, in most cases. In this work, the ultimate surface finish of EP was investigated by studying its effect on highly polished Nb samples. EP introduces high slope angle sloped-steps at grain boundaries. The magnetic field enhancement and superheating field suppression factors associated with such a geometry are calculated in the London theory. Despite the by-eye smoothness of electropolished Nb, such defects compromise the stability of the low-loss Meissner state, likely limiting the achievable peak accelerating fields in superconducting RF cavities. Finally, the impact of surface roughness on impurity diffusion is investigated which can link surface roughness to the effectiveness of heat treatments like low-temperature baking or nitrogen infusion in the vortex nucleation or hydride hypotheses. Surface roughness tends to decrease the effective dose of impurities as a result of the expansion of impurities into regions with greater internal angle. The effective dose of impurities can be protected by minimizing slope angles and step heights, ensuring uniformity.

Lechner, Eric [Thomas Jefferson National Accelerat↗
DOE OSTI2026

Electropolishing-induced topographic defects in niobium: insights and implications for superconducting radio frequency applications

Electropolishing (EP) is the premier surface preparation method for high-Q, high-gradient superconducting RF cavities made of Nb. This leaves behind an apparently smooth surface, yet the achievable peak magnetic fields fall well below the superheating field of Nb, in most cases. Here, in this work, the ultimate surface finish of EP was investigated by studying its effect on highly polished Nb samples. EP introduces high slope angle sloped-steps at grain boundaries. The magnetic field enhancement and superheating field suppression factors associated with such a geometry are calculated in the London theory. Despite the by-eye smoothness of electropolished Nb, such defects compromise the stability of the low-loss Meissner state, likely limiting the achievable peak accelerating fields in superconducting RF cavities. Finally, the impact of surface roughness on impurity diffusion is investigated which can link surface roughness to the effectiveness of heat treatments like low-temperature baking or nitrogen infusion in the vortex nucleation or hydride hypotheses. Surface roughness tends to decrease the effective dose of impurities as a result of the expansion of impurities into regions with greater internal angle. The effective dose of impurities can be protected by minimizing slope angles and step heights, ensuring uniformity.

Hryhorenko, Oleksandr [Thomas Jefferson National A↗
DOE OSTI2021

Source term method for binary neutron stars initial data

The initial condition problem for a binary neutron star system requires a Poisson equation solver for the velocity potential with a Neumann-like boundary condition on the surface of the star. Difficulties that arise in this boundary value problem are: (a) the boundary is not known a priori, but constitutes part of the solution of the problem; (b) various terms become singular at the boundary. In this work, we present a new method to solve the fluid Poisson equation for irrotational/spinning binary neutron stars. The advantage of the new method is that it does not require complex fluid surface fitted coordinates and it can be implemented in a Cartesian grid, which is a standard choice in numerical relativity calculations. This is accomplished by employing the source term method proposed by Towers, where the boundary condition is treated as a jump condition and is incorporated as additional source terms in the Poisson equation, which is then solved iteratively. The issue of singular terms caused by vanishing density on the surface is resolved with an additional separation that shifts the computation boundary to the interior of the star. We present two-dimensional tests to show the convergence of the source term method, and we further apply this solver to a realistic three-dimensional binary neutron star problem. By comparing our solution with the one coming from the initial data solver cocal, we demonstrate agreement to approximately 1%. We report our method can be used in other problems with non-smooth solutions like in magnetized neutron stars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Grain boundary solute segregation across the 5D space of crystallographic character

Solute segregation in materials with grain boundaries (GBs) has emerged as a popular method to thermodynamically stabilize nanocrystalline structures. However, the impact of varied GB crystallographic character on solute segregation has never been thoroughly examined. Here, this work examines Co solute segregation in a dataset of 7272 Al bicrystal GBs that span the 5D space of GB crystallographic character. Considerable attention is paid to verification of the calculations in the diverse and large set of GBs. In addition, the results of this work are favorably validated against similar bicrystal and polycrystal simulations. As with other work, we show that Co atoms exhibit strong segregation to sites in Al GBs and that segregation correlates strongly with GB energy and GB excess volume. Segregation varies smoothly in the 5D crystallographic space but has a complex landscape without an obvious functional form.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Vortex splitting in two-dimensional fluids and non-neutral electron plasmas with smooth vorticity profiles

Initially, elliptical, quasi-two-dimensional (2D) fluid vortices can split into multiple pieces if the aspect ratio is sufficiently large due to the growth and saturation of perturbations known as Love modes on the vortex edge. Presented here are experiments and numerical simulations, showing that the aspect ratio threshold for vortex splitting is significantly higher for vortices with realistic, smooth edges than that predicted by a simple “vortex patch” model, where the vorticity is treated as piecewise constant inside a deformable boundary. The experiments are conducted by exploiting the E × B drift dynamics of collisionless, pure electron plasmas in a Penning–Malmberg trap, which closely model 2D vortex dynamics due to an isomorphism between the Drift–Poisson equations describing the plasmas and the Euler equations describing ideal fluids. The simulations use a particle-in-cell method to model the evolution of a set of point vortices. The aspect ratio splitting threshold ranges up to about twice as large as the vortex patch prediction and depends on the edge vorticity gradient. This is thought to be due to spatial Landau damping, which decreases the vortex aspect ratio over time and, thus, stabilizes the Love modes. Near the threshold, asymmetric splitting events are observed in which one of the split products contains much less circulation than the other. These results are relevant to a wide range of quasi-2D fluid systems, including geophysical fluids, astrophysical disks, and drift-wave eddies in tokamak plasmas.

Physics↗
DOE OSTI2020

Confining Liquids inside Carbon Nanotubes: Accelerated Molecular Dynamics with Spliced, Soft-Core Potentials and Simulated Annealing

Understanding emergent phenomena of fluids under physical confinement requires the development of advanced tools for rapid and accurate simulation of their physiochemical properties. Simulating liquid molecules commensurate in size with the nanoscale enclosures that confine them is a key challenge. In this work, we demonstrate an accelerated molecular dynamics simulation technique that combines soft-core potentials (SCP) and simulated annealing (SA) to analyze confined liquids. This integrated SCP/SA method relies on a new spliced soft-core potential (SSCP), which enables tunable accuracy with respect to the target hard-core potential (HCP). SCP/SA enables the packing of enclosures with bulk material in a controlled, thermodynamically consistent manner. The enhanced SSCP accuracy is a critical feature of SCP/SA, enabling a smooth transition between the SCP and the HCP at a desired SCP hardness. We applied SCP/SA to the problem of filling a carbon nanotube (CNT) in periodic boundary conditions with a popular ionic liquid (IL), 1- butyl-3-methylimidazolium hexafluorophosphate $[\text{BMIM}^+][\text{PF}^–_6]$. We performed a series of triplicate simulations on systems with varying CNT diameter and charge to demonstrate SCP/SA’s versatility. Beyond this IL/CNT system, the SCP/SA simulation framework has a broad range of potential applications, not limited to nanoscale enclosures and interfaces, including both solid-state and biological systems.

36 MATERIALS SCIENCE↗
DOE OSTI2025

On optimal control of hybrid dynamical systems using complementarity constraints

Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate them using non-smooth and non-convex complementarity constraints as a mathematical program with complementarity constraints (MPCC). We utilize a moving finite element based strategy to discretize the differential equation system to accurately locate the unknown switching points at the finite element boundary and achieve high-order accuracy at intermediate non-collocation points. We propose a globalization approach to solve the discretized MPCC problem using a mixed NLP/MILP-based strategy to converge to a non-spurious first-order optimal solution. The method is tested on three dynamic optimization examples, including a gas–liquid tank model and an optimal control problem with a sliding mode solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Warm boundary-layer cloud properties and cloud susceptibilities product at the ARM ENA observatory

Cloud liquid water path, albedo, and cloud fraction susceptibilities for marine warm boundary-layer clouds are quantified using the Meteosat retrieved cloud microphysical properties at the ARM Eastern North Atlantic (ENA) observatory in the Azores. The Meteosat cloud retrievals are based on the methods applied by the Clouds and the Earth’s Radiant Energy System (CERES) project, which are specifically tailored to support the ARM user facility over the ARM ground-based observation sites (enavisstpx2dm11minnisX1.c1). Cloud susceptibility is quantified as the slope between cloud properties and Nd within a 1-degree-by-1-degree grid box at each satellite time step using a least-square regression. To reduce uncertainties associated with the adiabatic assumption in the Nd retrieval, for each cloud object, we exclude cloudy pixels at the cloud edge, defined as those adjacent to cloud-free pixels. To minimize influence of cloud heterogeneity and co-variability on the retrieved cloud susceptibility, cloud properties are averaged to 0.25-degree resolution using the 3-km pixel-level retrieval, and the 1-degree cloud susceptibilities are estimated using the smoothed data. Cloud type classification is applied to distinct cloud object, labeling all contiguous cloudy pixels. Marine warm boundary-layer clouds are defined as clouds with 90% of cloud tops below 3km, and Meteosat retrieved cloud phase as liquid.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Evaluating Terrain as a Turbulence Generation Method

When driving microscale large-eddy simulations with mesoscale model solutions, turbulence will take space to develop, known as fetch, on the microscale domain. To reduce fetch, it is common to add perturbations near the boundaries to speed up turbulence development. However, when simulating domains over complex terrain, it is possible that the terrain itself can quickly generate turbulence within the boundary layer. It is shown here that rugged terrain is able to generate turbulence without the assistance of a perturbation strategy; however, the levels of turbulence generated are improved when adding perturbations at the inlet. Flow over smoothed, but not flat, terrain fails to generate adequate turbulence throughout the boundary layer in all tests conducted herein. Sensitivities to the strength of the mean wind speed and boundary layer height are investigated and show that higher wind speeds produce turbulence over terrain features that slower wind speeds do not. Further, by increasing the height of the capping inversion, the effectiveness of topography alone to generate turbulence throughout the depth of the boundary is diminished. In all cases, the inclusion of a perturbation strategy improved simulation performance with respect to turbulence development.

17 WIND ENERGY↗
DOE OSTI2026

Energy-Optimal Vehicle Longitudinal Motion Control via Pontryagin’s Minimum Principle and Ultra-Local Model

Longitudinal vehicle motion control is essential for enhancing performance and optimizing a vehicle’s energy usage. However, it remains a challenging task due to the nonlinear and uncertain nature of vehicle dynamics, along with varying driving conditions. This paper presents a novel ultra-local optimal control approach based on Pontryagin’s Minimum Principle (PMP) that circumvents the need for detailed system identification by employing an ultra-local model. The control objective is to minimize the total energy consumption under boundary conditions while ensuring smooth traction force generation. The proposed approach is evaluated using a high-fidelity vehicle model in three representative scenarios: (i) nominal driving, (ii) a change in tire road friction coefficient (TRFC) from 0.5 to 0.65 and road slope from 0% to 5% during the maneuver, with target velocity unchanged, and (iii) a change in target velocity from 20 m/s to 0 m/s during the maneuver, while maintaining nominal TRFC and slope conditions. The simulation results demonstrate that the proposed method delivers robust performance, effectively balancing consumption and tracking accuracy in all tested scenarios.

Waleed khan, Muhammad [The University of Texas at ↗
DOE OSTI2025

Power Flow Geometry and Approximation

Here, the power flow equations are important in numerous power systems problems of practical interest which consider alternating current power flow (ACPF) physics. Perhaps the most well studied being the alternating current optimal power flow problem (ACOPF), seeking to optimize the operation of an electric power system. Due to their non-linearity, problems which include the power flow equations are typically challenging, particularly in optimization. Interestingly, the set of solutions to the power flow equations forms a smooth manifold. As a result, differential geometry can be used to describe and analyze this set of equations. This approach has proven effective in several engineering applications (e.g., solving ACOPF and analyzing the solution space boundary). Central to the success of this approach is an understanding of the power flow manifold's geometry. In this work, we develop the geometric and topological properties of this manifold using concepts from differential geometry. After demonstrating the convenience of this manifold's representation as a function's graph, computational methods are emphasized: we develop retractions, error bounds for linear approximation, and formulas for evaluating the Riemannian metric (including associated objects such as geodesics and the curvature tensor). Scalar curvature and the second fundamental form play a new role in quantifying the quality of linear approximations, like the popular direct current approximation. All functions are implemented in Julia and available in an online repository. Proofs are included for completeness.

24 POWER TRANSMISSION AND DISTRIBUTION↗