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DOE OSTI2022

A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order phase-field fracture models have gained wide adoption given their ability to capture the formation of complex fracture patterns, e.g. via crack merging and branching, and their suitability for implementation within the context of the conventional finite element method. Higher-order phase-field models have also been proposed to increase the regularity of the exact solution and thus increase the spatial convergence rate of its numerical approximation. However, they require special numerical techniques to enforce the necessary continuity of the phase field solution. In this paper, we derive a fourth-order phase-field model of fracture in two independent ways; namely, from Hamilton’s principle and from a higher-order micromechanics-based approach. The latter approach is novel, and provides a physical interpretation of the higher-order terms in the model. In addition, we propose a continuous/discontinuous Galerkin (C/DG) method for use in computing the approximate phase-field solution. This method employs Lagrange polynomial shape functions to guarantee -continuity of the solution at inter-element boundaries, and enforces the required regularity with the aid of additional variational and interior penalty terms in the weak form. Finally, the phase-field equation is coupled with the momentum balance equation to model dynamic fracture problems in hyper-elastic materials. Two benchmark problems are presented to compare the numerical behavior of the C/DG method with mixed finite element methods.

42 ENGINEERING↗

DOE OSTI2020

Baroclinic Residual Circulation and Mass Transport Due to Internal Tides

Baroclinic (BC) tidal residual circulation due to internal tides is investigated around islands over a shallow ridge using a numerical ocean model. Internal tides enhance vertical mixing over shallow slopes, leading to horizontal density gradients that drive BC residual circulation along the main thermocline. For a strongly stratified summer case, the vertical diffusivity estimated by the Mellor and Yamada turbulence closure model exceeds 1 × 10 -2 m 2 s -1 , and the velocity of BC residual circulations reaches 0.2 m s -1 . The magnitude of BC residual circulation is larger than that of barotropic residual tidal circulation, implying that BC residual circulation due to internal tides plays an important role in coastal ocean circulation. Furthermore, BC residual flow accounts for an equal percentage (5%) of the total tidal kinetic energy as the barotropic residual flow under summer stratification conditions. Results from a coupled sediment resuspension and transport model show the growth of intermediate nepheloid layers formed by strong bottom shear stress and BC residual flow. The residual component contributes largely (23% of the total in summer) to the total suspended sediment flux. Seasonal variability is explored, with weaker winter stratification leading to reduced mixing, and thus weaker BC residual circulation and sediment flux. Lastly, the magnitude of the BC residual circulation is also shown to be proportional to the square of the tidal amplitude.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Asymmetry between deuterium and tritium turbulent particle flows

The asymmetry between deuterium (D) and tritium (T) turbulent particle fluxes in mixed D–T plasmas is studied with numerical simulations of nonlinear gyrokinetic turbulence in ion temperature gradient-dominated and trapped electron mode-dominated regimes. At 50–50 D–T concentration, the asymmetry, or flow separation, between D and T fluxes is such that the tritium is better confined than the deuterium in both regimes. To supplement the nonlinear simulations, an analytic quasilinear theory of the particle flux symmetry breaking is developed and is valid for general electron dynamics. Furthermore, this theory correctly predicts the numerically computed deviation in the ion density fraction (from 50–50), or ion density gradient (from the electron gradient), required to restore equal deuterium and tritium fluxes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

PARTICLE RESOLVED DNS STUDY OF TURBULENCE EFFECTS ON HYPORHEIC MIXING IN RANDOMLY PACKED SEDIMENT BEDS

Pore-resolved direct numerical simulations (DNS) are used to investigate the interactions between stream-water flow turbulence and groundwater flow through a porous sediment bed in the hyporheic zone. Two permeability Reynolds numbers (2.56 and 5.17), representative of aquatic systems and representing ratio of permeability to viscous length scales, were simulated to understand its influence on the momentum exchange at the sediment-water interface (SWI). A doubleaveraging methodology is used to compute the Reynolds stresses, form-induced stresses, and pressure fluctuations. It is observed that both shear layer and turbulent shear stress penetration increases with ReK. Reynolds and form-induced bed-normal stresses increase with ReK. The peak values of the form-induced stresses for the lower (2.56) and higher (5.17) ReK happen within the top layer of the sediment bed. The sum of turbulent and form-induced pressure fluctuations, analyzed at their respective zero-displacement planes, are statistically similar and can be well approximated by a t location-scale distribution fit providing with a model that could potentially be used to impose boundary conditions at the SWI in reach scale simulations.

Karra, Shashank↗

DOE OSTI2024

High-Fidelity Simulation of the Light-to-Dense Stratification Transient in the HiRJET Facility

Density stratification in a large enclosure is a crucial phenomenon to heat transfer and sustainable passive heat removal of a sodium fast reactor during reactivity transients. However, engineering turbulence models were identified to have unsatisfactory performance in predicting propagation of a stratified front. Yet, the scarcity of high-resolution data for stratification hampers the development of models. To explor e applications of leveraging direct numerical simulation (DNS) data to support turbulence model development, this work conducted DNS using NekRS to study a long stratification transient in the High-Resolution Jet (HiRJET) experimental facility. Here, this work considers an experiment run where light fluid is injected into a tank containing a denser fluid with a relative density difference of 1.5%. Formation of the stratified layer is identified as impingement of the buoyant jet promoting mixing of the two fluids. Based on the transient statistics, transport of the concentration can be characterized by regions with dominating effects of turbulent mixing, buoyant dissipation, and molecular diffusion, respectively, as moving away from the elevation of jet impingement. Concentration near the stratified front also exhibits oscillation at Brunt-Väisälä frequency. Preliminary validation of the simulation showed encouraging agreement of the concentration distribution with the reference experiment.

buoyant mixing↗

DOE OSTI2022

Robust trajectory-constrained frequency control for microgrids considering model linearization error

Grid supportive modes integrated within inverter-based resources can improve the frequency response of renewable-rich microgrids. The synthesis of grid supportive modes to guarantee frequency trajectory constraints under a predefined disturbance set is challenging but essential. To tackle this challenge, a numerical optimal control (NOC)-based control synthesis methodology is proposed. Without loss of generality, a wind-diesel fed microgrid is studied, where we aim to design grid supportive functions in the wind turbine. In the control design, linearized models are used, and the linearization-induced errors are quantitatively analyzed by reachability and interval arithmetics and represented in the form of interval uncertainties. Then, the NOC problem can be formulated into a robust mixed-integer linear program. The control structure is strategically configured into two levels to realize online deployment. The proposed control is verified on the modified 33-node microgrid with a full-order three-phase nonlinear model in Simulink. In conclusion, the simulation results show the effectiveness of the proposed control paradigm and the necessity of considering linearization-induced uncertainty.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Improving the representation of isopycnal mixing in E3SM (Final Report)

The DOE-supported Energy Exascale Earth System Model (E3SM) is a major attempt by the Department of Energy to develop a new Earth System Model using unstructured grids, which allow for the model to concentrate resolution where it is most needed and avoid numerical artifacts experienced by previous Earth System Models (ESMs) using regular grids in which the lateral resolution becomes extremely fine as the resolution shrinks at the poles. This effort required rewriting many of the algorithms previously developed for regular grids. One algorithm that was problematic in the first version of E3SM was the representation of mixing due to turbulent ocean eddies with scales smaller than the model grid. These mesoscale eddies are the primary way by which tracers are stirred along density surfaces in the ocean interior. In particular, the process of isopycnal mixing exchanges fresher, more oxygenated waters from polar regions with saltier, nutrient-rich and oxygen poor waters from tropical regions. Previous work in our group has shown that this mechanism is vitally important for bringing oxygen into poorly ventilated tropical regions (Gnanadesikan et al., 2012, 2013) and plays a significant role in determining the uptake of anthropogenic carbon dioxide (Gnanadesikan et al., 2015). However, in E3SMv1 this process was turned off, as turning it on caused the model to become unstable. Additionally, the rate of isopycnal mixing is directly proportional to a mixing coefficient $A_{Redi}$ whose value varies from less than 400 m 2 /s to 2000 m 2 /s across contemporary climate models. The main thrusts of this proposal therefore were to: 1.) Improve the numerics of isopycnal mixing in E3SM; 2.) Identify ways in which climate models are sensitive to the isopycnal mixing coefficient; and 3.) Develop better representations of the isopycnal mixing coefficient.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Transport in Stochastic Media with Random Chord Length Distributions

Thermal radiation transport computations in binary Markovian random mixtures rely almost exclusively on the Levermore-Pomraning (LP) model which is obtained by applying a heuristic closure to the ensemble averaged random medium transport equation. The validity of this model has been extensively tested by comparing numerical results over a broad parameter range (material types and mixing parameters) against benchmark solutions in planar geometry. The conditions under which the LP-model provides useful results and when it breaks down are now well established, but work to date has been largely restricted to homogeneous mixing statistics, i.e., the mean chord lengths of both materials are taken to be spatially constant. In recent work, this limitation was relaxed by allowing the mean chord lengths and, in a consistent fashion, the volume fractions in the LP-model to vary spatially and in a follow-up investigation benchmark solutions were obtained by ensemble averaging results over material realizations sampled from a nonhomogeneous Poisson process (NHPP). Numerical experiments in rod geometry with specifically linear and quadratic spatial dependence of chord lengths showed that the material averaged radiation intensities vary nonmonotonically with depth into the medium, in stark contrast to solutions obtained assuming uniform chord lengths. Moreover, depending on the local optical thickness and strength of scattering, the LP-model results showed locally more nuanced deviations from the benchmark solutions than was the case with constant chord lengths. These limited numerical investigations highlight the nontrivial qualitative and quantitative consequences of nonhomogeneous mixing statistics, in particular that closure approximations may not be uniformly valid or invalid over the problem domain.

42 ENGINEERING↗

DOE OSTI2021

Rayleigh–Taylor and Richtmyer–Meshkov instabilities: A journey through scales

Hydrodynamic instabilities such as Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities usually appear in conjunction with the Kelvin–Helmholtz (KH) instability and are found in many natural phenomena and engineering applications. They frequently result in turbulent mixing, which has a major impact on the overall flow development and other effective material properties. This can either be a desired outcome, an unwelcome side effect, or just an unavoidable consequence, but must in all cases be characterized in any model. The RT instability occurs at an interface between different fluids, when the light fluid is accelerated into the heavy. The RM instability may be considered a special case of the RT instability, when the acceleration provided is impulsive in nature such as that resulting from a shock wave. Here in this pedagogical review, we provide an extensive survey of the applications and examples where such instabilities play a central role. First, fundamental aspects of the instabilities are reviewed including the underlying flow physics at different stages of development, followed by an overview of analytical models describing the linear, nonlinear and fully turbulent stages. RT and RM instabilities pose special challenges to numerical modeling, due to the requirement that the sharp interface separating the fluids be captured with fidelity. These challenges are discussed at length here, followed by a summary of the significant progress in recent years in addressing them. Examples of the pivotal roles played by the instabilities in applications are given in the context of solar prominences, ionospheric flows in space, supernovae, inertial fusion and pulsed-power experiments, pulsed detonation engines and Scramjets. Progress in our understanding of special cases of RT/RM instabilities is reviewed, including the effects of material strength, chemical reactions, magnetic fields, as well as the roles the instabilities play in ejecta formation and transport, and explosively expanding flows. The article is addressed to a broad audience, but with particular attention to graduate students and researchers who are interested in the state-of-the-art in our understanding of the instabilities and the unique issues they present in the applications in which they are prominent.

42 ENGINEERING↗

DOE OSTI2021

Demons in the North Atlantic: Variability of Deep Ocean Ventilation

Abstract Translation of atmospheric forcing variability into the ocean interior via ocean ventilation is an important aspect of transient climate change. On a seasonal timescale in the subtropics, this translation is mediated by a so‐called “Demon” that prevents access to all except late‐winter mixed‐layer water. Here, we use an eddy‐permitting numerical circulation model to investigate a similar process operating on longer (interannual) timescales in the subpolar North Atlantic. We find that variations in atmospheric forcing are mediated in their translation to the ocean interior, with year‐to‐year changes in the late‐winter mixed layer depth being the critical factor. The signature of persistent strong atmospheric forcing driving deep mixed layers is preferentially ventilated to the interior when the forcing is ceased. Susceptibility to this effect depends on the location and density of subduction—with the rate at which newly ventilated water escapes its region of subduction being the crucial factor.

MacGilchrist, G. A.↗

DOE OSTI2026

Locally purified maximally mixed states at scale: Entanglement pruning and symmetries

Locally Purified Density Operators (LPDOs) are state-of-the-art tensor network ansatze candidates that efficiently represent mixed quantum states at scale. However, given their non-uniqueness, their representational complexity is generally sub-optimal in practical computations. Here, in this work we perform a comprehensive numerical and analytical analysis and resolve this issue in the experimentally relevant limit where noise depolarizes the density operator into a maximally mixed state. To resolve the sub-optimality issue, we analyze two numerical tools, one analytic method, and detail the relations between them. The numerical tools used are fidelity-preserving truncations and isometric gauge transformations leveraging Riemannian optimizations over entropic objective functions. In addition, by invoking the injectivity and symmetry constraints of the maximally mixed LPDO, we also present analytical closed-form expressions for the disentangler and discuss their relation to numerical optimizers. Further, away from the maximally mixed state, our simulations highlight how the truncation threshold smoothly interpolate, as a function of depolarization, between established matrix product results and our new results. Our work shows how, by minimizing the resources required to represent key states of practical interest in experiment, the efficiency of tensor network algorithms can be substantially increased. This paves the path for uncovering tensor network’s fundamental scalability limits and latent potential in representing the wide locus of mixed quantum states that are accessible on near-term quantum devices.

Gangapuram, Amit Jamadagni [Oak Ridge National Lab↗

DOE OSTI2025

Impact of neutrino flavor conversions on neutron star merger dynamics, ejecta, nucleosynthesis, and multimessenger signals

We present numerical relativity simulations of binary neutron star mergers incorporating neutrino flavor transformations triggered by fast flavor instability, quantum many-body effects, or potential beyond standard model physics. In both long-lived and short-lived remnant scenarios, neutrino flavor conversions modify species-dependent neutrino luminosities and mean energies, and drive the matter towards more neutron rich conditions. They produce up to more neutron rich ejecta and significantly boost the r-process yields, especially in low-density, near-equatorial outflows. We identify regions unstable to fast flavor instabilities and find that these instabilities persist despite flavor conversions. We further test the sensitivity to the equilibration timescale of the flavor conversions, finding that slower flavor conversions can interact with thermodynamic equilibration, and increase the neutron richness of the ejecta. Flavor conversions may also contribute to stronger gravitational wave and neutrino emissions, pointing to a correlation between neutrino transport and merger dynamics. Furthermore, these results highlight the potential impact of flavor conversions while motivating future work to improve on theoretical understanding of flavor instabilities in global simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

3d N=4 Bootstrap and Mirror Symmetry

We investigate the non-BPS realm of 3d {N} = 4 N = 4 superconformal field theory by uniting the non-perturbative methods of the conformal bootstrap and supersymmetric localization, and utilizing special features of 3d {N} = 4 N = 4 theories such as mirror symmetry and a protected sector described by topological quantum mechanics (TQM). Supersymmetric localization allows for the exact determination of the conformal and flavor central charges, and the latter can be fed into the mini-bootstrap of the TQM to solve for a subset of the OPE data. We examine the implications of the Z_2 Z 2 mirror action for the SCFT single- and mixed-branch crossing equations for the moment map operators, and apply numerical bootstrap to obtain universal constraints on OPE data for given flavor symmetry groups. A key ingredient in applying the bootstrap analysis is the determination of the mixed-branch superconformal blocks. Among other results, we show that the simplest known self-mirror theory with SU(2) \times SU(2) S U ( 2 ) × S U ( 2 ) flavor symmetry saturates our bootstrap bounds, which allows us to extract the non-BPS data and examine the self-mirror Z_2 Z 2 symmetry thereof.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

A subdivision-stabilized B-spline mixed material point method

Subjected to external loadings, polymeric materials, e.g., biological tissues, hydrogels, and elastomers, may undergo extreme, nearly incompressible, (self-)contact deformations. For numerical modeling employing mesh-based techniques such as the finite element method (FEM), these deformations pose significant challenges due to large distortions in the deformed geometry, accuracy issues stemming from volumetric locking effects, and increased computational cost from complex contact searches. As an alternative to mesh-based methods, the material point method (MPM), a continuum-based particle technique, is gaining attention for its ability to handle extreme distortions and capture no-slip contact without added cost. For nearly incompressible material behaviors, while mixed formulations can address locking effects by treating displacements and pressure as independent fields, they can suffer from numerical instabilities close to the incompressibility limit due to the violation of the inf-sup condition, leading to inaccurate nodal pressure solutions. Here we propose an efficient and stable mixed B-spline material point method with highest achievable regularity for quasi-compressible polymeric materials. Using the two-scale relation of B-splines, we introduce a subdivision-stabilization for the two-field mixed MPM and obtain numerically stable, oscillation-free nodal solutions with equal-order interpolations with optimal regularity. Building on the Eulerian-Lagrangian nature of MPM, a previously-converged solution framework is adopted to mitigate issues related to cell-crossing and numerical fracture artifact present in standard MPM. We assess the stability and accuracy of the developed mixed MPM at large deformations for soft materials through the benchmark Cook’s membrane problem. Additionally, we test the robustness of the proposed MPM by modeling several examples, including the compression and indentation of a circular block into a quasi-compressible substrate and the twisting deformation of a rectangular block. The findings demonstrate the MPM’s capabilities for modeling practical soft material applications.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Geologic stress modulates fluid mixing at fracture intersections

Fracture intersections are critical links that enable flow and transport in subsurface fracture networks, and their behavior strongly influences fluid mixing in a network. Although all subsurface fractures are subjected to geological stress, we lack a fundamental understanding of how fracture intersection geometry evolves under stress and how these changes influence fluid mixing. Here, we combine 3D printing, 3D X-ray tomographic imaging, and 3D pore-scale numerical simulations to reveal stress-induced changes in intersection geometry and their impact on mixing. Mixing is found to be strongly affected by partial closure of an intersection under stress. As an intersection closes, the void area for fluid flow and diffusion decreases leading to substantial deviations between conventional mixing models and full pore-scale modeling. To address this, we propose a modified mixing model that accounts for intersection deformation, which is essential for accurate modeling of solute transport and mixing through fracture networks.

15 GEOTHERMAL ENERGY↗

DOE OSTI2020

Simulating combustion of a seven-component surrogate for a gasoline/ethanol blend including soot formation and comparison with experiments

Combustion of a seven-component surrogate for a research grade 87 octane gasoline mixed with 10% ethanol is investigated experimentally and numerically from the perspective of an isolated droplet burning under conditions that promote one-dimensional gas transport. The numerical analysis included a kinetic mechanism comprised of 398 species and 24,814 reactions and a soot model that accounted for nucleation, surface growth, coalescence/aggregation of soot particles, and luminous flame radiation. Measurements of droplet and flame diameters were made for an initial droplet diameter (D o ) of approximately 0.63 mm. The simulations agreed well with the measurements including the location of the soot shell. Preferential vaporization was revealed by simulations of the liquid concentrations in the droplet. Predicted peak soot volume fractions coincided with temperatures between 1300 K and 1400 K as a soot inception temperature. Simulations were also carried out for D o between 0.25 mm and 5 mm to explore the effect of radiation and D o on burning. Below 0.25 mm radiation was negligible and burning rates and flame temperatures converged to a single value. Increasing D o up to 1.8 mm lowered the burning rate with luminous radiation having a strong effect. When radiation was entirely removed from the model the burning rate was nearly constant. Above D o = 2 mm droplets extinguished almost immediately after ignition. The flame temperature decreased with increasing D o while it increased when radiation was omitted. As a result, the simulations show that soot precursors including polyaromatic hydrocarbons were concentrated around the soot shell.

42 ENGINEERING↗

DOE OSTI2025

A GPU Accelerated Mixed‐Precision Finite Difference Informed Random Walker (FDiRW) Solver for Strongly Inhomogeneous Diffusion Problems

In nature, many complex multi‐physics coupling problems exhibit significant diffusivity inhomogeneity, where one process occurs several orders of magnitude faster than others temporally. Simulating rapid diffusion alongside slower processes demands intensive computational resources due to the necessity for small time steps. To address these computational challenges, we have developed an efficient numerical solver named Finite Difference informed Random Walker (FDiRW). In this study, we propose a GPU‐accelerated, mixed‐precision configuration for the FDiRW solver to maximize efficiency through GPU multi‐threaded parallel computation and lower precision computation. Numerical evaluation results reveal that the proposed GPU‐accelerated mixed‐precision FDiRW solver can achieve a 117× speedup over the CPU baseline, while an additional 1.75× speedup is achieved by employing lower precision GPU computation. Notably, for large model sizes, the GPU‐accelerated mixed‐precision FDiRW solver demonstrates strong scaling with the number of nodes used in simulation. When simulating radionuclide absorption processes by porous wasteform particles with a medium‐sized model of 192 × 192 × 192, this approach reduces the total computational time to 10 min, enabling the simulation of larger systems with strongly inhomogeneous diffusivity.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A comparative study of machine learning models for predicting the state of reactive mixing

Mixing phenomena are important mechanisms controlling flow, species transport, and reaction processes in fluids and porous media. Accurate predictions of reactive mixing are critical for many Earth and environmental science problems such as contaminant fate and remediation, macroalgae growth, and plankton biomass evolution. Here, to investigate the evolution of mixing dynamics under different scenarios (e.g., anisotropy, fluctuating velocity fields), a finite-element-based numerical model was built to solve the fast, irreversible bimolecular reaction-diffusion equations to simulate a range of reactive-mixing scenarios. A total of 2,315 simulations were performed using different sets of model input parameters comprising various spatial scales of vortex structures in the velocity field, time-scales associated with velocity oscillations, the perturbation parameter for the vortex-based velocity, anisotropic dispersion contrast (i.e., ratio of longitudinal-to-transverse dispersion), and molecular diffusion. The outputs comprised concentration profiles of reactants and products. The inputs to and outputs from these simulations were concatenated into feature and label matrices, respectively, to train 20 different machine learning (ML) models intended to emulate system behavior. These 20 ML emulators, based on linear methods, Bayesian methods, ensemble learning methods, and multilayer perceptrons (MLPs), were trained to classify the state of mixing and predict three quantities of interest (QoIs) characterizing species production, decay (i.e., average concentration, square of average concentration), and degree of mixing (i.e., variances of species concentration). Unsurprisingly, linear classifiers and regressors failed to reproduce the QoIs; however, ensemble methods (classifiers and regressors) and the MLP model accurately classified the state of reactive mixing and the QoIs. Among ensemble methods, random forest and decision-tree-based AdaBoost faithfully predicted the QoIs. At run time, trained ML emulators produced results times faster than the finite-element simulations. Due to their low computational expense and high accuracy, ensemble and MLP models are excellent emulators for these numerical simulations and great utilities in uncertainty quantification exercises, which can require 1,000s of forward model runs.

97 MATHEMATICS AND COMPUTING↗