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At least 415 records · Page 23
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 OSTI2020

A matrix-free approach for finite-strain hyperelastic problems using geometric multigrid

This paper investigates matrix-free algorithms for problems in quasi-static finite-strain hyperelasticity. Iterative solvers with matrix-free operator evaluation have emerged as an attractive alternative to sparse matrices in the fluid dynamics and wave propagation communities because they significantly reduce the memory traffic, the limiting factor in classical finite element solvers. Specifically, we study different matrix-free realizations of the finite element tangent operator and determine whether generalized methods of incorporating complex constitutive behavior might be feasible. Furthermore, in order to improve the convergence behavior of iterative solvers, we also propose a method by which to construct level tangent operators and employ them to define a geometric multigrid preconditioner. Additionally, the performance of the matrix-free operator and the geometric multigrid preconditioner is compared to the matrix-based implementation with an algebraic multigrid (AMG) preconditioner on a single node for a representative numerical example of a heterogeneous hyperelastic material in two and three dimensions. We find that matrix-free methods for finite-strain solid mechanics are very promising, outperforming linear matrix-based schemes by two to five times, and that it is possible to develop numerically efficient implementations that are independent of the hyperelastic constitutive law.

42 ENGINEERING↗
DOE OSTI2020

Thermal Model Heat Rate Predictions of the AGR-5/6/7 Experiment

Several fuel and material irradiation experiments have been planned for the U.S. Department of Energy Advanced Gas Reactor Fuel Development and Qualification Program, which supports the development and qualification of tristructural isotropic (TRISO) coated particle fuel for use in high-temperature gas-cooled reactors. The goals of these experiments are to provide irradiation performance data to support fuel process development, qualify fuel for normal operating conditions, support development of fuel performance models and codes, and provide irradiated fuel and materials for post-irradiation examination and safety testing. Originally planned and named as separate fuel experiments, but subsequently combined into a single test train. AGR-5/6/7 will test low-enriched uranium oxycarbide (UCO – a heterogeneous mixture of uranium oxide and uranium carbide) TRISO fuel. The AGR-5/6 portion of the experiment will provide data to support qualification of the selected reference fuel design, while the AGR-7 portion will serve as a margin test, irradiating the fuel beyond normal operating conditions. During irradiation, the temperature in each capsule is controlled by varying the helium / neon gas mixture flowing through the capsule until the desired thermocouple temperature is reached. Further adjustments can be made by changing the lobe power and the neutron filter. Three neutron filters are available to use as the experiment burns up the fissionable fuel. A thermal finite element model has been created for the five capsules comprising the AGR-5/6/7 experiment. Heat rates from a physics analysis are imported into the model along with fast neutron fluence. Graphite shrinkage due to the fast neutron fluence is incorporated into the model. Gas gaps change as a function of fast neutron fluence. Radiation heat transfer is a major contributor in this model. This is a large model with more than 1 million finite element brick elements. More than 150 different parts are modeled in the finite element model and communicate with each other from a heat transfer sense. More than 50 thermocouples are used in the experiment and are compared to actual measurements. The experiment is composed of five separate stainless steel capsules all welded together. This paper presents a method used to predict the gas mixture in the event that all of the thermocouples fail in a particular capsule. Curve fitting of heat rates from previous cycles and projecting them into the future is the basis of the method.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Investigation of finite-volume methods to capture shocks and turbulence spectra in compressible flows

The aim of the present paper is to provide a comparison between several finite-volume methods of different numerical accuracy: the second-order Godunov method with PPM interpolation and the high-order finite-volume WENO method. In this work, the results show that while on a smooth problem the high-order method performs better than the second-order one, when the solution contains a shock all the methods collapse to first-order accuracy. In the context of the decay of compressible homogeneous isotropic turbulence with shocklets, the actual overall order of accuracy of the methods reduces to second-order, despite the use of fifth-order reconstruction schemes at cell interfaces. Most important, results in terms of turbulent spectra are similar regardless of the numerical methods employed, except that the PPM method fails to provide an accurate representation in the high-frequency range of the spectra. It is found that this specific issue comes from the slope-limiting procedure and a novel hybrid PPM/WENO method is developed that has the ability to capture the turbulent spectra with the accuracy of a high-order method, but at the cost of the second-order Godunov method. Overall, it is shown that virtually the same physical solution can be obtained much faster by refining a simulation with the second-order method and carefully chosen numerical procedures, rather than running a coarse high-order simulation. Our results demonstrate the importance of evaluating the accuracy of a numerical method in terms of its actual spectral dissipation and dispersion properties on mixed smooth/shock cases, rather than by the theoretical formal order of convergence rate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Non-equilibrium effective field theory and second sound

We investigate the phenomenon of second sound in various states of matter from the perspective of non-equilibrium effective field theory (EFT). In particular, for each state of matter considered, we find that at least two (though sometimes multiple) qualitatively different EFTs exist at finite temperature such that there is always at least one EFT with a propagating second-sound wave and at least one with no such second-sound wave. To aid in the construction of these EFTs, we use the method of cosets developed for non-equilibrium systems. It turns out that the difference between the EFTs with and without second-sound modes can be understood as arising from different choices of a new kind of inverse Higgs constraint. Finally, we demonstrate that it is possible to bypass the need for new inverse Higgs constraints by formulating EFTs on a new kind of manifold that is like the usual fluid worldvolume, but with reduced gauge symmetries.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Data-assisted combustion simulations with dynamic submodel assignment using random forests

This investigation outlines a data-assisted approach that employs random forest classifiers for local and dynamic submodel assignment in turbulent-combustion simulations. This method is demonstrated in simulations of a single-element GOX/GCH4 rocket combustor; a priori as well as a posteriori assessments are conducted to (i) evaluate the accuracy and adjustability of the classifier for targeting different quantities of interest (QoIs), and (ii) assess improvements, resulting from the data-assisted combustion model assignment, in predicting target QoIs during simulation runtime. Results from the a priori study show that random forests, trained with local flow properties as input variables and combustion model errors as training labels, assign three different combustion models – finite-rate chemistry (FRC), flamelet progress variable (FPV) model, and inert mixing (IM) – with reasonable classification performance even when targeting multiple QoIs. Applications in a posteriori studies demonstrate improved predictions from data-assisted simulations, in temperature and CO mass fraction, when compared with monolithic FPV calculations. An additional a posteriori data-assisted simulation of a modified configuration demonstrates that the present approach can be successfully applied to different configurations, as long as thermophysical behavior can be represented by the training data. Furthermore, these results demonstrate that this data-driven framework holds promise for dynamic combustion submodel assignments in reacting flow simulations.

42 ENGINEERING↗
DOE OSTI2022

Trions in twisted bilayer graphene

The strong-coupling phase diagram of magic-angle twisted bilayer graphene (TBG) predicts a series of exact one-particle charge ±1 gapped excitations on top of the integer-filled ferromagnetic ground states. Finite-size exact diagonalization studies showed that these are the lowest charge ±1 excitations in the system (for 10 nm screening length), with the exception of charge +1 at filling -1 in the chiral limit. In the current paper we show that this “trion bound state,” a 3-particle, charge 1 excitation of the insulating ferromagnetic ground state of the projected Hamiltonian of TBG, is the lowest charge +1 overall excitation at ν =-1, and also for some large (≈20 nm) screening lengths at ν =-2 in the chiral limit and with very small binding energy. At other fillings, we show that trion bound states do exist, but only for momentum ranges that do not cover the entire moiré Brillouin zone. The trion bound states (at different momenta) exist for finite parameter range w 0 /w 1 but they all disappear in the continuum far below the realistic values of w 0 /w 1 = 0.8. Thus we find the conditions for the existence of the trion bound state, a good variational wave function for it, and investigate its behavior for different screening lengths, at all integer fillings, on both the electron and hole sides.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Enriched immersed finite element and isogeometric analysis: algorithms and data structures

Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their implementation remains a major challenge due to, among other things, the need to apply nontrivial stabilization schemes and generate custom quadrature rules. This article introduces the robust and computationally efficient algorithms and data structures comprising an immersed finite element preprocessing framework. The input to the preprocessor consists of a background mesh and one or more geometries defined on its domain. The output is structured into groups of elements with custom quadrature rules formatted such that common finite element assembly routines may be used without or with only minimal modifications. The key to the preprocessing framework is the construction of material topology information, concurrently with the generation of a quadrature rule, which is then used to perform enrichment and generate stabilization rules. While the algorithmic framework applies to a wide range of immersed finite element methods using different types of meshes, integration, and stabilization schemes, the preprocessor is presented within the context of the extended isogeometric analysis. This method utilizes a structured B-spline mesh, a generalized Heaviside enrichment strategy considering the material layout within individual basis functions’ supports, and face-oriented ghost stabilization. Using a set of examples, the effectiveness of the enrichment and stabilization strategies is demonstrated alongside the preprocessor’s robustness in geometric edge cases. Additionally, the performance and parallel scalability of the implementation are evaluated.

Computer implementation↗
DOE OSTI2021

Physics-Informed Machine Learning Models for Predicting the Progress of Reactive-Mixing

This paper presents a physics-informed machine learning (ML) framework to construct reduced-order models (ROMs) for reactive-transport quantities of interest (QoIs) based on high-fidelity numerical simu-lations. QoIs include species decay, product yield, and degree of mixing. The ROMs for QoIs are applied to quantify and understand how the chemical species evolve over time. First, high-resolution datasets for constructing ROMs are generated by solving anisotropic reaction-di?usion equations using a non-negative finite element formulation for di?erent input parameters. The reactive-mixing model input parameters are: time-scale associated with flipping of velocity, spatial-scale controlling small/large vortex structures of velocity, perturbation parameter of the vortex-based velocity, anisotropic dispersion strength/contrast, and molecular diffusion. Second, random forests, F-test, and mutual information criterion are used to evaluate the importance of model inputs/features with respect to QoIs. We observed that anisotropic dispersion strength/contrast is the most important feature and time-scale associated with flipping of velocity is the least important feature. Third, Support Vector Machines (SVM) and Support Vector Regression (SVR) are used to construct ROMs based on the model inputs. The constructed SVR-ROMs are then used to predict scaling of QoIs. We also present estimates and inequalities on the QoIs, which inform that the species decay, mix, and produce in an exponential fashion. These inequalities also inform that a radial basis function is the most suitable kernel for the SVM/SVR models for QoIs. It is observed that R2-score for SVR-ROMs on unseen data is greater than 0.9, implying that the SVR-ROMs are able to predict the reaction-diffusion system state reasonably well. Finally, in terms of the computational cost, the proposed SVM-ROMs are O(107) times faster than running a high-fidelity finite element simulation for evaluating QoIs. This makes the proposed ML-based ROMs attractive for reactive-transport sensing and real-time monitoring applications as they are significantly faster yet reasonably accurate.

Mudunuru, Maruti K.↗
DOE OSTI2026

Omega-Limit Sets and Input-To-State Stability in Power Grids with Switching Equilibria

This paper studies a power transmission system with both conventional generators (CGs) and distributed energy assets (DEAs) providing frequency control. We consider an operating condition with demand aggregating two dynamic components: one that switches between different values on a finite set, and one that varies smoothly over time. Such dynamic operating conditions may result from protection scheme activations, external cyber-attacks, or due to the integration of dynamic loads, such as data centers. Mathematically, the dynamics of the resulting system are captured by a system that switches between a finite number of vector fields - or modes -, with each mode having a distinct equilibrium point induced by the demand aggregation. To analyze the stability properties of the resulting switching system, we leverage tools from hybrid dynamic inclusions and the concept of ..omega.. -limit sets from sets. Specifically, we characterize a compact set that is semi-globally practically asymptotically stable under the assumption that the switching frequency and load variation rate are sufficiently slow. For arbitrarily fast variations of the load, we use a level-set argument with multiple Lyapunov functions to establish input-to-state stability of a larger set and with respect to the rate of change of the loads. The theoretical results are illustrated via numerical simulations on the IEEE 39-bus test system.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Comment on Improved CO 2 Hydrogenation on Ni–ZnO/MCM-41 Catalysts with Cooperative Ni and ZnO Sites

A recent publication from Murthy et al.1 describes experiments in which they proposed the hypothesis that a bifunctional catalyst consisting of adlineated,2 nanometer-sized domains of Ni and ZnO, confined within the pores of MCM-41, hydrogenates carbon dioxide adsorbed on the ZnO using hydrogen atoms produced by the Ni-catalyzed dissociation of H2. The reanalysis of their data presented below suggests that the reaction rates they employed to test their hypothesis, when properly normalized, show little to no effect of bifunctionality. This closer inspection of their data raises the possibility that the observed effects may instead arise from experimental artifacts (e.g., different levels of conversion, finite rates of mass transport) or morphological correlations that were not considered by the authors.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Release dynamics of nanodiamonds created by laser-driven shock-compression of polyethylene terephthalate

Laser-driven dynamic compression experiments of plastic materials have found surprisingly fast formation of nanodiamonds (ND) via X-ray probing. This mechanism is relevant for planetary models, but could also open efficient synthesis routes for tailored NDs. We investigate the release mechanics of compressed NDs by molecular dynamics simulation of the isotropic expansion of finite size diamond from different P-T states. Analysing the structural integrity along different release paths via molecular dynamic simulations, we found substantial disintegration rates upon shock release, increasing with the on-Hugnoiot shock temperature. We also find that recrystallization can occur after the expansion and hence during the release, depending on subsequent cooling mechanisms. Our study suggests higher ND recovery rates from off-Hugoniot states, e.g., via double-shocks, due to faster cooling. Laser-driven shock compression experiments of polyethylene terephthalate (PET) samples with in situ X-ray probing at the simulated conditions found diamond signal that persists up to 11 ns after breakout. In the diffraction pattern, we observed peak shifts, which we attribute to thermal expansion of the NDs and thus a total release of pressure, which indicates the stability of the released NDs.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Vorticity screening by dense layers

We investigate variable density layers in the presence of vortices, by analogy to line charges in the presence of a dielectric slab. We adapt solutions for dielectric layers from the literature to the variable density fluid case, obtaining exact hypergeometric expressions for flow velocities induced everywhere by a vortex in the vicinity of a finite-thickness slab of different densities. The dimensionless Atwood number, which appears naturally in other variable density phenomena, such as the Rayleigh–Taylor instability, reappears here as the natural ordering parameter for the influence of the slab, which acts primarily to screen the influence of vorticity across the slab to a lower effective circulation. The solution takes the form of scaling correction factors that might be applied to computational models or evaluated directly. Extensions, where vorticity is localized within the dense layer itself and amplified outside of it, are considered, as well as some speculative applications such as inertial confinement fusion capsule designs.

42 ENGINEERING↗
DOE OSTI2022

Ultrafast valley polarization of graphene nanorings

Here, we study theoretically electron dynamics of a graphene nanoring placed in the field of an ultrashort optical pulse. We describe the graphene nanoring within an effective model with infinite mass boundary conditions. For an optical pulse with a duration of just a few femtoseconds, the electron dynamics is coherent and is described by a time-dependent Schrödinger equation. If the optical pulse is circularly polarized, then two valleys of graphene are populated differently, resulting in a finite valley polarization of the system after the pulse. Such a valley polarization is a unique property of graphene nanoscale systems, while for a graphene monolayer, a circularly polarized pulse does not produce any valley polarization. The valley polarization of the graphene nanoring depends on parameters of the system, such as inner and outer radii. With the system's size increasing, the valley polarization monotonically decreases, converging to its zero value for the infinite graphene monolayer.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Fourier Analysis-Based Evolutionary Multi-Objective Multiphysics Optimization of Liquid-Cooled Heat Sinks

Optimal heat dissipation in power modules can significantly increase their power density. Removing the generated heat is critical for capturing the benefits of advanced semiconductor materials and improving the reliability of the device operation. This article proposes a design optimization method for liquid-cooled heat sinks that use a Fourier analysis-based tool and an evolutionary optimization algorithm to optimize the heat sink geometry for specified objectives. The optimized heat sink geometry is then compared with state-of-the-art solutions in literature based on finite element analysis of different designs. The proposed methodology can develop complex geometries that outperform the conventional heat sink geometries.

Sahu, Raj↗
DOE OSTI2020

Electronic Scanning Strategies in Adaptive Electrical Capacitance Volume Tomography: Tradeoffs and Prospects

Electrical Capacitance Volume Tomography (ECVT) has been applied for imaging of multiphase flows found in industrial applications. The ill-posed nature of the image reconstruction problem in ECVT and the consequent low resolution can be alleviated by employing electronic scanning enabled by electrode segmentation and reconfiguration during data acquisition. Here we study electronic scanning strategies that mimic physical rotation and shifting of the sensor along its symmetry axis. First, we study the feasibility of electronic scanning by analyzing the capacitance transducer circuit in SPICE. Then, we simulate electronic scanning using the finite element method for different electrode shapes, for which we compare the image reconstruction results and acquisition time. We find a noticeable improvement in image resolution for the scanning cases over conventional ECVT. Lastly, among the scanning cases, we emphasize a particular electrode shape that provides the best image resolution along with the minimal amount of acquisition time.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Zero-pairing and zero-temperature limits of finite-temperature Hartree-Fock-Bogoliubov theory

Recently, variational Hartree-Fock-Bogoliubov (HFB) mean-field equations were shown to possess a mathematically well-defined zero-pairing limit, independently of the closed- or open-shell character of the system under consideration. This limit is non-trivial for open-shell systems such that HFB theory does {\it not} reduce to the Hartree-Fock (HF) formalism in all cases. The present work extends this analysis to finite-temperature HFB (FTHFB) theory by investigating the behavior of this more general formalism in the combined zero-temperature and zero-pairing limits. The zero-pairing and zero-temperature limits of the FTHFB statistical density operator constrained to carry an arbitrary (integer) number of particles A on average is worked out analytically and realized numerically using a two-nucleon interaction. While the FTHFB density operator reduces to the projector corresponding to a pure HF Slater determinant for closed-shell nuclei, the FTHFB formalism does not reduce to the HF theory in all cases in the zero-temperature and zero-pairing limits, i.e. for open-shell nuclei. However, the fact that a nucleus can be of open-shell character in these joint limits is necessarily the result of some symmetry restrictions. Whenever it is the case, the non-trivial description obtained for open-shell systems is shown to depend on the order with which both limits are taken, i.e. the two limits do not commute for these systems. When the zero-temperature limit is performed first, the FTHFB density operator is demoted to a projector corresponding to a pure state made out of a linear combination of a finite number of Slater determinants with different (even) numbers of particles. When the zero-pairing limit is performed first, the FTHFB density operator remains a statistical mixture of a finite number of Slater determinants with both even and odd particle numbers. While the entropy (pairing density) is zero in the first (second) case, it does not vanish in the second (first) case in spite of the temperature (pairing) tending towards zero. The difference between both limits can have striking consequences for the (thermal) expectation values of observables. For instance, the particle-number variance does not vanish in either case and has limiting values that differ by a factor of two in both cases. In conclusion, while in the textbook situation associated with closed-shell nuclei Hartree-Fock-Bogoliubov (finite-temperature Hartree-Fock) theory reduces to Hartree-Fock theory in the zero-pairing (zero-temperature) limit, the present analysis demonstrates that a non trivial and unexpected limit is obtained for this formalism in open-shell systems. This result sheds a new light on certain aspects of this otherwise very well-studied many-body formalism.

20 ≤ A ≤ 38↗
DOE OSTI2021

Thermal-Mechanical Elastic-Plastic and Ductile Failure Model Calibrations for 6061-T651 Aluminum Alloy from Plate

Numerical simulations of metallic structures undergoing rapid loading into the plastic range require material models that accurately represent the response. In general, the material response can be seen as having four interrelated parts: the baseline response under slow loading, the effect of strain rate, the conversion of plastic work into heat and the effect of temperature. In essence, the material behaves in a thermal-mechanical manner if the loading is fast enough so when heat is generated by plastic deformation it raises the temperature and therefore influences the mechanical response. In these cases, appropriate models that can capture the aspects listed above are necessary. The matters of interest here are the elastic-plastic response and ductile failure behavior of 6061-T651 aluminum alloy under the conditions described above. The work was accomplished by first designing and conducting a material test program to provide data for the calibration of a modular $J_2$ plasticity model with isotropic hardening as well as a ductile failure model. Both included modules that accounted for temperature and strain rate dependence. The models were coupled with an adiabatic heating module to calculate the temperature rise due to the conversion of plastic work to heat. The test program included uniaxial tension tests conducted at room temperature, 150 and 300 C and at strain rates between 10 –4 and 10 3 1/s as well as four geometries of notched tension specimens and two tests on specimens with shear-dominated deformations. The test data collected allowed the calibration of both the plasticity and the ductile failure models. Most test specimens were extracted from a single piece of plate to maintain consistency. Notched tension tests came from a possibly different plate, but from the same lot. When using the model in structural finite element calculations, element formulations and sizes different from those used to model the test specimens in the calibration are likely to be used. A brief investigation demonstrated that the failure model can be particularly sensitive to the element selection and provided an initial guide to compensate in a specific example.

36 MATERIALS SCIENCE↗