A Partitioned Method for Reduced OrderModel-Finite Element Model (ROM-FEM)and ROM-ROM Couplings with SeparateReduced Bases for Interior and InterfaceVariables
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de Castro, Amy Grace↗
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Results for “interior methods”
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High-order dimensionally-split Cartesian embedded boundary method for non-dissipative schemes
Centered finite-difference schemes are commonly used for high-fidelity turbulent flow simulations in canonical configurations because of their non-dissipative property and computational efficiency. However, their use in flow simulations over complex geometries is limited by the requirements of a structured grid and a stable boundary treatment in the absence of artificial (numerical) dissipation. Cartesian embedded boundary (EB) approaches provide an efficient structured-grid framework to apply difference schemes over complex domains. However, they are often restricted to low orders of accuracy because of numerical instabilities at the embedded boundaries and the issues of small-cell problem that are difficult to address with high-order accuracy. The present work discusses a systematic approach to obtain high-order EB methods with non-dissipative centered schemes in the interior. This approach, based on satisfying the primary and secondary conservation conditions, is employed to derive EB schemes that are up to sixth-order accurate in the interior and fourth-order accurate globally for hyperbolic, parabolic as well as incompletely parabolic problems. The proposed finite-difference discretization is, by construction, dimensionally split and addresses the small-cell problem without any cell/geometry transformations, thus, highly simplifying implementation in a flow solver. Various linear and non-linear numerical tests are performed to evaluate the stability and the accuracy of the proposed EB schemes.
97 MATHEMATICS AND COMPUTING↗
Infrared intrusion detection system (IRIDS)
A system and method for intrusion detection includes an imager directed towards an object in an interior space. The imager is in data communication with a computer. The computer is arranged to process digital three-dimensional image data received from the imager and programmed to execute a change detection algorithm in response to the processed three-dimensional data to determine movement of the object. The computer generates an alarm output in response to detecting movement of the object above a predetermined threshold. The method includes providing an imager directed towards an object in an interior space; receiving Time of Flight signals by the imager; processing digital three-dimensional image data received from the imager; and executing a change detection algorithm in response to the processed three-dimensional data to determine movement of the object.
Russell, John L.↗
A discontinuous piecewise polynomial generalized moving least squares scheme for robust finite element analysis on arbitrary grids
A variational approach is developed with a meshless discretization to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. Here, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality, which we call discontinuous piecewise polynomial generalized moving least squares (DPP-GMLS). At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework, providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5 x improvement in accuracy and allows for taking an 8 x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method.
97 MATHEMATICS AND COMPUTING↗
Resource loading system and method for use in atmosphere containment scenarios
The invention provides a system for preventing fluid exchange between the interior and exterior of containment enclosures such as process-, hazard-, and research-enclosure systems generally, gloveboxes, containment systems, isolation systems, confinement systems, cleanrooms, negative air systems, and positive air system areas while simultaneously providing material transfer into and out of the enclosures. The invention also provides a method for transporting material into or out of a containment structure.
Dilday, Jr., Daniel R.↗
Generative AI models for learning flow maps of stochastic dynamical systems in bounded domains
Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary interactions. Despite the success of machine learning-based methods in learning SDEs, existing learning methods are not applicable to SDEs in bounded domains because they cannot accurately capture the particle exit dynamics. We present a unified hybrid data-driven approach that combines a conditional diffusion model with an exit prediction neural network to capture both interior stochastic dynamics and boundary exit phenomena. Our ML model consists of two major components: a neural network that learns exit probabilities using binary cross-entropy loss with rigorous convergence guarantees, and a training-free diffusion model that generates state transitions for non-exiting particles using closed-form score functions. The two components are integrated through a probabilistic sampling algorithm that determines particle exit at each time step and generates appropriate state transitions. Here, the performance of the proposed approach is demonstrated via three test cases: a one-dimensional simplified problem for theoretical verification, a two-dimensional advection-diffusion problem in a bounded domain, and a three-dimensional problem of interest to magnetically confined fusion plasmas.
Bounded domains↗
The shape of convection in 2D and 3D global simulations of stellar interiors
Context. Theoretical descriptions of convective overshooting in stellar interiors often rely on a basic one-dimensional parameterization of the flow called the filling factor for convection. Several different definitions of the filling factor have been developed for this purpose, based on: (1) the percentage of the volume, (2) the mass flux, and (3) the convective flux that moves through the boundary. Aims. We examine these definitions of the filling factor with the goal of establishing their ability to explain differences between 2D and 3D global simulations of stellar interiors that include fully compressible hydrodynamics and realistic microphysics for stars. Methods. We study convection and overshooting in pairs of identical two-dimensional (2D) and three-dimensional (3D) global simulations of stars produced with MUSIC , a fully compressible, time-implicit hydrodynamics code. We examine pairs of simulations for (1) a 3 M ⊙ red giant star near the first dredge-up point, (2) a 1 M ⊙ pre-main-sequence star with a large convection zone, (3) the current sun, and (4) a 20 M ⊙ main-sequence star with a large convective core. Results. Our calculations of the filling factor based on the volume percentage and the mass flux indicate asymmetrical convection near the surface for each star with an outer convection zone. However, near the convective boundary, convective flows achieve inward-outward symmetry for each star that we study; for 2D and 3D simulations, these filling factors are indistinguishable. A filling factor based on the convective flux is contaminated by boundary-layer-like flows, making a theoretical interpretation difficult. We present two possible new alternatives to these frequently used definitions of a filling factor, which instead compare flows at two different radial points. The first alternative is the penetration parameter of Anders et al. (2022, ApJ, 926, 169). The second alternative is a new statistic that we call the plume interaction parameter. We demonstrate that both of these parameters captures systematic differences between 2D and 3D simulations around the convective boundary.
79 ASTRONOMY AND ASTROPHYSICS↗
Improvements to the Powder Processing of near-Final Shape alnico Magnets
Alnico permanent magnets (PMs), a recent PM system of interest as an attractive rare earth-free PM alternative, have advantageous high operating temperature and magnetic saturation with the potential for utilization in electric machines, e.g. interior-PM motors found in electric vehicles, if current directional solidification methods can be replaced by a true mass production approach. Recently, two unique alnico compositions, termed Full-Co and Co-lean, with improved coercivity, were gas atomized, compression molded, and vacuum sintered (4h at 1240°C) to high densities of 97.8% and 99.3%, respectively. However, the Co-lean remained fine grained isotropic magnets and the Full-Co grains were not textured, lowering magnetic strength in spite of attempts to grow large textured grains by a stress-biased solid state grain alignment method to convert them to high energy anisotropic magnets. It was hypothesized that oxidation during de-binding in air left many prior particle boundary oxides within the sintered microstructure that hindered grain growth and texturing during the stress-biased texturing procedure and prevented the desired abnormal grain growth (AGG). Here we explored a vacuum de-binding step that was linked (in-place) to vacuum sintering and found that the Co-lean exhibited faster uniform grain growth that doubled the average grain size (40 μm to 80 μm). Linked vacuum de-binding and sintering of Full-Co produced some AGG after only 1 h of 1240°C sintering. A new direction for promoting AGG (and stress-biased texturing) in alnico is being explored that utilizes a fundamental analysis of systems with second phase particles that either inhibit or boost grain growth. This effort explores the influence of vacuum de-binding linked to a series of lower sintering temperatures at a fixed time (4h) to see if oxide particle size and volume fraction can be changed to promote AGG conditions in alnico. Surprising qualitative results indicate that AGG may be promoted for vacuum sintering at less than 1200°C.
Rinko, Emily↗
Observation of negative surface and interface energies of quantum dots
Surface energy is a fundamental property of materials and is particularly important in describing nanomaterials where atoms or molecules at the surface constitute a large fraction of the material. Traditionally, surface energy is considered to be a positive quantity, where atoms or molecules at the surface are less thermodynamically stable than their counterparts in the interior of the material because they have fewer bonds or interactions at the surface. Using calorimetric methods, we show that the surface energy is negative in some prototypical colloidal semiconductor nanocrystals, or quantum dots with organic ligand coatings. This implies that the surface atoms are more thermodynamically stable than those on the interior due to the strong bonds between these atoms and surfactant molecules, or ligands, that coat their surface. In addition, we extend this work to core/shell indium phosphide/zinc sulfide nanocrystals and show that the interfacial energy between these materials is highly thermodynamically favorable in spite of their large lattice mismatch. This work challenges many of the assumptions that have guided thinking about colloidal nanomaterial thermodynamics, investigates the fundamental stability of many technologically relevant colloidal nanomaterials, and paves the way for future experimental and theoretical work on nanocrystal thermodynamics.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Turbine component and methods of making and cooling a turbine component
A turbine component includes a root and an airfoil extending from the root to a tip opposite the root. The airfoil forms a leading edge and a trailing edge portion extending to a trailing edge. A plurality of axial cooling channels in the trailing edge portion of the airfoil are arranged to permit axial flow of a cooling fluid from an interior of the turbine component at the trailing edge portion to an exterior of the turbine component at the trailing edge portion. A method of making a turbine component includes forming an airfoil having a trailing edge portion with axial cooling channels. The axial cooling channels are arranged to permit axial flow of a cooling fluid from an interior to an exterior of the turbine component at the trailing edge portion. A method of cooling a turbine component is also disclosed.
Dutta, Sandip↗
Towards a self-consistent model of the convective core boundary in upper main sequence stars: I. 2.5D and 3D simulations
There is strong observational evidence that the convective cores of intermediate-mass and massive main sequence stars are substantially larger than those predicted by standard stellar-evolution models. However, it is unclear what physical processes cause this phenomenon or how to predict the extent and stratification of stellar convective boundary layers. Convective penetration is a thermal-timescale process that is likely to be particularly relevant during the slow evolution on the main sequence. We use our low-Mach-number S EVEN -L EAGUE H YDRO code to study this process in 2.5D and 3D geometries. Starting with a chemically homogeneous model of a 15 M ⊙ zero-age main sequence star, we construct a series of simulations with the luminosity increased and opacity decreased by the same factor, ranging from 10 3 to 10 6 . After reaching thermal equilibrium, all of our models show a clear penetration layer; its thickness becomes statistically constant in time and it is shown to converge upon grid refinement. The penetration layer becomes nearly adiabatic with a steep transition to a radiative stratification in simulations at the lower end of our luminosity range. This structure corresponds to the adiabatic ‘step overshoot’ model often employed in stellar-evolution calculations. The simulations with the highest and lowest luminosity differ by less than a factor of two in the penetration distance. The high computational cost of 3D simulations makes our current 3D data set rather sparse. Depending on how we extrapolate the 3D data to the actual luminosity of the initial stellar model, we obtain penetration distances ranging from 0.09 to 0.44 pressure scale heights, which is broadly compatible with observations.
79 ASTRONOMY AND ASTROPHYSICS↗
Low-Order Preconditioning for the High-Order Finite Element de Rham Complex
Here, we present a unified framework for constructing spectrally equivalent low-order-refined discretizations for the high-order finite element de Rham complex. This theory covers diffusion problems in H 1 , H(curl), and H(div) and is based on combining a low-order discretization posed on a refined mesh with a high-order basis for Nédélec and Raviart–Thomas elements that makes use of the concept of polynomial histopolation (polynomial fitting using prescribed mean values over certain regions). This spectral equivalence, coupled with algebraic multigrid methods constructed using the low-order discretization, results in highly scalable matrix-free preconditioners for high-order finite element problems in the full de Rham complex. Additionally, a new lowest-order (piecewise constant) preconditioner is developed for high-order interior penalty discontinuous Galerkin (DG) discretizations, for which spectral equivalence results and convergence proofs for algebraic multigrid methods are provided. In all cases, the spectral equivalence results are independent of polynomial degree and mesh size; for DG methods, they are also independent of the penalty parameter. These new solvers are flexible and easy to use; any “black-box” preconditioner for low-order problems can be used to create an effective and efficient preconditioner for the corresponding high-order problem. A number of numerical experiments are presented, based on an implementation in the finite element library MFEM. A range of challenging three-dimensional problems are used to corroborate the theoretical properties and demonstrate the flexibility and scalability of the method.
97 MATHEMATICS AND COMPUTING↗
Aerosol-Based Method Seals the Deal for Tighter New Homes
What if an aerosol-based sealing method could tighten new home envelopes more quickly and effectively than traditional sealing methods? The method involves pressurizing an entire building while dispersing an aerosol sealant "fog" to the building interior. As air escapes the building through leaks in the envelope, sealant particles are carried to the leaks where they make contact and stick, sealing the leaks. A standard blower door and connected laptop facilitate the sealing process and provide real-time feedback and a permanent record of the sealing. The technology is thus capable of simultaneously measuring, locating, and automatically sealing leaks in a building. In fact, hundreds of linear feet of narrow leaks can be sealed simultaneously, reducing the time needed for manual inspection and sealing. To investigate the use of this method in new homes, the Center for Energy and Environment and partners worked with builders who performed the technique on 11 homes in California and 15 homes in Minnesota.
30 DIRECT ENERGY CONVERSION↗
Lasergate: A windowless gas target for enhanced laser preheat in magnetized liner inertial fusion
At the Z Facility at Sandia National Laboratories, the magnetized liner inertial fusion (MagLIF) program aims to study the inertial confinement fusion in deuterium-filled gas cells by implementing a three-step process on the fuel: premagnetization, laser preheat, and Z-pinch compression. In the laser preheat stage, the Z-Beamlet laser focuses through a thin polyimide window to enter the gas cell and heat the fusion fuel. However, it is known that the presence of the few μm thick window reduces the amount of laser energy that enters the gas and causes window material to mix into the fuel. These effects are detrimental to achieving fusion; therefore, a windowless target is desired. The Lasergate concept is designed to accomplish this by “cutting” the window and allowing the interior gas pressure to push the window material out of the beam path just before the heating laser arrives. In this work, we present the proof-of-principle experiments to evaluate a laser-cutting approach to Lasergate and explore the subsequent window and gas dynamics. Further, an experimental comparison of gas preheat with and without Lasergate gives clear indications of an energy deposition advantage using the Lasergate concept, as well as other observed and hypothesized benefits. While Lasergate was conceived with MagLIF in mind, the method is applicable to any laser or diagnostic application requiring direct line of sight to the interior of gas cell targets.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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↗
Mitigation of Pitting on Nitrogen-Doped Niobium Surfaces through Two-Step Electropolishing
Surface processing of niobium superconducting RF cavities used in particle accelerators is crucial for determining their performance. The nitrogen (N)-doping method, developed at Fermilab, enhances the cavities’ quality factor by doping the cavity’s interior surface with N atoms at 800 °C. After N-doping, electropolishing (EP) is employed to remove the niobium nitride phases and attain the desired concentration of interstitial N atoms. This study explores the effects of EP conditions on N-doped niobium samples. The samples were electropolished at 5 to 40 °C and voltages between 3 and 22 V. Different EP voltage ranges produced two types of pits, classified based on their sizes. Larger pits, linked to higher voltages, are also affected by the reaction rate. Pitting could be reduced at a lower temperature and adequate EP voltage. However, to effectively minimize gas evolution forming large-sized pitting, peeling off the top nitride layer before EP might be beneficial. This was achieved through precise low-voltage etching, forming a two-step EP process. The process involves removing the top 100–200 nm layer at a low voltage, followed by standard EP to remove the required material. This two-step EP process effectively mitigated the pitting risk associated with gas evolution on N-doped surfaces.
43 PARTICLE ACCELERATORS↗
Ultrasonic measurement of temperature distributions in extreme environments: Electrical power plants testing in utility-scale steam generators
Thermal heterogeneities within energy conversion and storage, material processing, nuclear processes, aerospace, and military applications are often inaccessible to characterization by insertion sensors. When sensor deployment is possible, conventional pointwise temperature probes quickly degrade when inserted into harsh environments typical of such processes. We developed spatially-resolved ultrasonic thermometry to noninvasively measure the spatial distributions of thermal properties in such applications, even when sizable thermal gradients are present. Our method divides the path of ultrasonic propagation into segments bound by echogenic features, which create echoes in pulse-echo mode, encoding the information about interior temperature distributions. We use the acquired ultrasonic responses to estimate the internal temperature distributions by solving an inverse problem or concatenating segmental estimates. This work describes the implementation and industrial testing of the developed method at a coal-fired electrical power generation plant. We inserted an echogenically segmented Inconel 625 waveguide into the combustion zone of the utility-scale boiler and continuously acquired ultrasonic data while keeping sensitive components away from the damaging combustion environment. The accuracy of the time-dependent temperature distributions reconstructed from the ultrasonic measurements was comparable to that of thermocouples. The resiliency of ultrasonic thermometry to harsh combustion conditions was far superior to conventional insertion sensors. The measurements obtained during plant operation captured daily steam generation cycles in response to changing customer demand and intermittent contributions of renewable power sources to the power grid. These measurements have revealed new insights into the relationship between the dynamic power generation load and the conditions inside the steam generator. As a result, the successful industrial testing of spatially-resolved ultrasonic thermometry in solids indicates that the developed technology has matured to become an attractive alternative to conventional sensing in solving challenging problems of long-term thermal characterizations in extreme environments.
42 ENGINEERING↗
Parts-Per-Million Carbonate Mineral Quantification with Thermogravimetric Analysis–Mass Spectrometry
Mitigating the deleterious effects of climate change requires the development and implementation of carbon capture and storage technologies. To expand the monitoring, verification, and reporting (MRV) capabilities of geologic carbon mineralization projects, we developed a thermogravimetric analysis–mass spectrometry (TGA–MS) methodology to enable quantification of <100 ppm calcite (CaCO 3 ) in complex samples. We extended TGA–MS calcite calibration curves to enable a higher measurement resolution and lower limits of quantification for evolved CO 2 from a calcite–corundum mixture. We demonstrated <100 ppm carbonate mineral quantification with TGA–MS for the first time, an outcome applicable across earth, environmental, and materials science fields. We applied this carbonate quantification method to a suite of Columbia River Basalt Group (CRBG) well cuttings recovered in 2009 from Pacific Northwest National Laboratory’s Wallula #1 Well. Our execution of this new combined calcite and calcite–corundum calibration curve TGA–MS method on our CRBG sample suite indicated average carbonate contents of 0.050 wt % in flow interiors (caprocks) and 0.400 wt % in interflow zones (reservoirs) in the upper 1250 m of the Wallula #1 Well. Finally, by advancing our knowledge of continental flood basalt-hosted carbonates in the mafic subsurface and reaching new TGA–MS quantification limits for carbonate minerals, we expand MRV capabilities and support the commercial-scale deployment of carbon mineralization projects in the Pacific Northwest United States and beyond.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗