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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 OSTI2016

Conforming and nonconforming virtual element methods for elliptic problems

Here we present, in a unified framework, new conforming and nonconforming virtual element methods for general second-order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and nonsymmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal H 1 - and L 2 -error estimates, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the two methods is shown to be comparable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

The effects of turbulence on the flame structure and NO formation of ammonia turbulent premixed combustion at various equivalence ratios

Ammonia is carbon-free and is regarded as a potential fuel to address global warming issues. Here, in this work, three-dimensional direct numerical simulations (DNS) of ammonia/air turbulent premixed flames were performed to explore the influence of turbulence and equivalence ratio on the flame structure and NO formation characteristics. Two equivalence ratios were considered, i.e. Φ=0.9 and Φ=1.1. The general flame structures were presented and species distributions were examined. The NO mass fraction was found to be the highest in the product for the lean case and in the reaction zone for the rich case. The conditional mean values of species mass fractions and reaction rates were compared with those of the unstrained and strained laminar premixed flames to explore how well the laminar flame structures can approach those of the turbulent flame. The budget analysis of the species transport equations showed that turbulent diffusion plays an important role in species transport. The turbulent diffusivity D T was estimated using the gradient hypothesis based on the DNS data. Various laminar flame simulations with different diffusivities were carried out. It was shown that the conditional means of the DNS agree well with those of the laminar flames including D T in the transport property calculation. The global and local NO formation characteristics were investigated. It was found that the mean NO production conditioned on the progress variable is lower compared with the corresponding laminar flame in the rich case. However, the relative contributions from various NO pathways are rarely affected by turbulence. The NO mass fraction is higher in negative curvature regions compared with positive curvature regions of the flame surface for the rich case, which is due to the preferential diffusion of H 2 and other radicals and the enhanced NO pathways in negatively curved regions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

A high-order finite difference method for moving immersed domain boundaries and material interfaces

Here, we present a high-order sharp treatment of immersed moving domain boundaries and material interfaces, and apply it to the advection-diffusion equation in two and three dimensions. The spatial discretization combines dimension-split finite difference schemes with an immersed boundary treatment based on a weighted least-squares reconstruction of the solution, providing stable discretizations with up to sixth order accuracy for diffusion terms and third order accuracy for advection terms. The temporal discretization relies on a novel strategy for maintaining high-order temporal accuracy in problems with moving boundaries that minimizes implementation complexity and allows arbitrary explicit or diagonally-implicit Runge-Kutta schemes. The approach is broadly compatible with popular PDE-specialized Runge-Kutta time integrators, including low-storage, strong stability preserving, and diagonally implicit schemes. Through numerical experiments we demonstrate that the full discretization maintains high-order spatial and temporal accuracy in the presence of complex 3D geometries and for a range of boundary conditions, including Dirichlet, Neumann, and flux conditions with large jumps in coefficients.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Evolution of planar fractures in limestone: The role of flow rate, mineral heterogeneity and local transport processes

In this study, the processes that affect the evolution of fracture geometry and reactive transport in limestone fractures were evaluated using an integrated experimental and modeling approach. Flow-through experiments were performed to investigate the alteration of three artificially made planar limestone fractures, which were exposed to HCl-acidified water flow (pH 3.8 ± 0.1) at three different rates. Reactive infiltration instability developed in the fractures because of small fracture aperture variations and naturally occurring heterogeneity in the rock, i.e., the presence of clay spots of higher porosity. The dissolution regime changed from conical to dominant and ramified wormhole with increasing flow rate, i.e., Péclet number. Maps of fracture aperture obtained from X-ray micro-tomography imaging, together with measurements of permeability and analyses of fluid chemistry, provided experimental constraints for modeling. Numerical simulations were performed using a 2.5D continuum reactive transport model to examine the development of flow patterns and the reactivity and permeability evolution over time, and to interrogate the impacts of fluid reactivity, mineral heterogeneity and diffusive boundary layer. The modeling results showed that fracture alteration is very sensitive to initial fluid reactivity and mineralogical heterogeneity, in addition to flow rate. Finally, the changes of local transport processes during fracture opening also affected the reactivity of the fractured samples.

58 GEOSCIENCES↗
DOE OSTI2025

Emergent hydrodynamic mode on SU(2) plaquette chains and quantum simulation

We search for emergent hydrodynamic modes in real-time Hamiltonian dynamics of 2+1-dimensional SU(2) lattice gauge theory on a quasi-one-dimensional plaquette chain, by numerically computing symmetric correlation functions of energy densities on lattice sizes of about 20 with the local Hilbert space truncated at 𝑗 max = $\frac{1}{2}$. Because of the Umklapp processes, we only find a mode for energy diffusion. The symmetric correlator exhibits transport peak near zero frequency with a width approximately proportional to momentum squared at small momentum, when the system is fully quantum ergodic, as indicated by the eigenenergy level statistics. This transport peak leads to a power-law 𝑡 −$\frac{1}{2}$ decay of the symmetric correlator at late time, also known as the long-time tail, as well as diffusionlike spreading in position space. We also introduce a quantum algorithm for computing the symmetric correlator on a quantum computer and find it gives results consistent with exact diagonalization when tested on the IBM emulator. Finally we discuss the future prospect of searching for the sound modes.

Hamiltonian systems↗
DOE OSTI2020

Fast and Universal Kohn-Sham Density Functional Theory Algorithm for Warm Dense Matter to Hot Dense Plasma

Understanding many processes, e.g., fusion experiments, planetary interiors, and dwarf stars, depends strongly on microscopic physics modeling of warm dense matter and hot dense plasma. This complex state of matter consists of a transient mixture of degenerate and nearly free electrons, molecules, and ions. This regime challenges both experiment and analytical modeling, necessitating predictive ab initio atomistic computation, typically based on quantum mechanical Kohn-Sham density functional theory (KS-DFT). However, cubic computational scaling with temperature and system size prohibits the use of DFT through much of the warm dense matter regime. A recently developed stochastic approach to KS-DFT can be used at high temperatures, with the exact same accuracy as the deterministic approach, but the stochastic error can converge slowly and it remains expensive for intermediate temperatures (< 50 eV). Here we have developed a universal mixed stochastic-deterministic algorithm for DFT at any temperature. This approach leverages the physics of KS-DFT to seamlessly integrate the best aspects of these different approaches. We demonstrate that this method significantly accelerated self-consistent field calculations for temperatures from 3 to 50 eV, while producing stable molecular dynamics and accurate diffusion coefficients.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

2017 Status report-Tritium aging studies on stainless steel: Effect of hydrogen, tritium and decay helium on the fracture-toughness properties of stem, cup and block forgings

The materials of construction of tritium reservoirs are forged stainless steels. During service, the structural properties of the stainless steel change over time because of the diffusion of tritium into the reservoir wall and its radioactive decay to helium-3. This aging effect can cause cracks to initiate and grow which could result in a tritium leak or delayed failure of a tritium reservoir. Numerous factors affect the tendency for crack formation and propagation and are being investigated in this program. The goal of the research is to provide relevant fracture mechanics data that can be used by the design agencies in their assessments of tritium reservoir structural integrity. In this status report, new experimental results are presented on the effects of tritium and decay helium on the cracking properties of specimens taken from actual tritium reservoir forgings instead of the experimental forgings of past programs. The properties measured are more representative of actual reservoir properties because the microstructure of the specimens tested are more like that of the actual tritium reservoirs. The program was designed to measure the effects of material variables on tritium compatibility and includes two stainless steels (Type 304L and 316L stainless steel), multiple yield strengths (360-500 MPa), and multiple forging shapes (Stem, Cup, and Block).

36 MATERIALS SCIENCE↗
DOE OSTI2016

GALACTIC COSMIC-RAY INTENSITY MODULATION BY COROTATING INTERACTION REGION STREAM INTERFACES AT 1 au

We present a new model that couples galactic cosmic-ray (GCR) propagation with magnetic turbulence transport and the MHD background evolution in the heliosphere. The model is applied to the problem of the formation of corotating interaction regions (CIRs) during the last solar minimum from the period between 2007 and 2009. The numerical model simultaneously calculates the large-scale supersonic solar wind properties and its small-scale turbulent content from 0.3 au to the termination shock. Cosmic rays are then transported through the background, and thus computed, with diffusion coefficients derived from the solar wind turbulent properties, using a stochastic Parker approach. Our results demonstrate that GCR variations depend on the ratio of diffusion coefficients in the fast and slow solar winds. Stream interfaces inside the CIRs always lead to depressions of the GCR intensity. On the other hand, heliospheric current sheet (HCS) crossings do not appreciably affect GCR intensities in the model, which is consistent with the two observations under quiet solar wind conditions. Therefore, variations in diffusion coefficients associated with CIR stream interfaces are more important for GCR propagation than the drift effects of the HCS during a negative solar minimum.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

HYDRODYNAMICAL INTERACTION OF MILDLY RELATIVISTIC EJECTA WITH AN AMBIENT MEDIUM

The hydrodynamical interaction of spherical ejecta freely expanding at mildly relativistic speeds into an ambient cold medium is studied in semianalytical and numerical ways to investigate how ejecta produced in energetic stellar explosions dissipate their kinetic energy through the interaction with the surrounding medium. We especially focus on the case in which the circumstellar medium (CSM) is well represented by a steady wind at a constant mass-loss rate, having been ejected from the stellar surface prior to the explosion. As a result of the hydrodynamical interaction, the ejecta and CSM are swept by the reverse and forward shocks, leading to the formation of a geometrically thin shell. We present a semianalytical model describing the dynamical evolution of the shell and compare the results with numerical simulations. The shell can give rise to bright emission as it gradually becomes transparent to photons. We develop an emission model for the expected emission from the optically thick shell, in which photons in the shell gradually diffuse out to the interstellar space. Then we investigate the possibility that radiation powered by the hydrodynamical interaction is the origin of an underluminous class of gamma-ray bursts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Emulating a System Dynamics Model with Agent-Based Models: A Methodological Case Study in Simulation of Diabetes Progression

An agent-based simulation model hierarchy emulating disease states and behaviors critical to progression of diabetes type 2 was designed and implemented in the DEVS framework. The models are translations of basic elements of an established system dynamics model of diabetes. In this model hierarchy, which mimics diabetes progression over an aggregated U.S. population, was dis-aggregated and reconstructed bottom-up at the individual (agent) level. Four levels of model complexity were defined in order to systematically evaluate which parameters are needed to mimic outputs of the system dynamics model. Moreover, the four estimated models attempted to replicate stock counts representing disease states in the system dynamics model, while estimating impacts of an elderliness factor, obesity factor and health-related behavioral parameters. Health-related behavior was modeled as a simple realization of the Theory of Planned Behavior, a joint function of individual attitude and diffusion of social norms that spread over each agent s social network. Although the most complex agent-based simulation model contained 31 adjustable parameters, all models were considerably less complex than the system dynamics model which required numerous time series inputs to make its predictions. In all three elaborations of the baseline model provided significantly improved fits to the output of the system dynamics model. The performances of the baseline agent-based model and its extensions illustrate a promising approach to translate complex system dynamics models into agent-based model alternatives that are both conceptually simpler and capable of capturing main effects of complex local agent-agent interactions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

ACCELERATION OF THERMAL PROTONS BY GENERIC PHENOMENOLOGICAL MECHANISMS

We investigate heating and acceleration of protons from a thermal gas with a generic diffusion and acceleration model, and subject to Coulomb scattering and energy loss, as was done by Petrosian and East for electrons. As protons gain energy their loss to electrons becomes important. Thus, we need to solve the coupled proton–electron kinetic equation. We numerically solve the coupled Fokker–Planck equations and compute the time evolution of the spectra of both particles. We show that this can lead to a quasi-thermal component plus a high-energy nonthermal tail. We determine the evolution of the nonthermal tail and the quasi-thermal component. The results may be used to explore the possibility of inverse bremsstrahlung radiation as a source of hard X-ray emissions from hot sources such as solar flares, accretion disk coronas, and the intracluster medium of galaxy clusters. We find that the emergence of nonthermal protons is accompanied by excessive heating of the entire plasma, unless the turbulence needed for scattering and acceleration is steeper than Kolmogorov and the acceleration parameters, the duration of the acceleration, and/or the initial distributions are significantly fine-tuned. These results severely constrain the feasibility of the nonthermal inverse bremsstrahlung process producing hard X-ray emissions. However, the nonthermal tail may be the seed particles for further re-acceleration to relativistic energies, say by a shock. In the Appendix we present some tests of the integrity of the algorithm used and present a new formula for the energy loss rate due to inelastic proton–proton interactions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Enabling fast charging of lithium-ion batteries through secondary-/dual- pore network: Part II - numerical model

To increase the market share of electric vehicles, it is desirable to reduce the battery charge times, which are significantly limited by poor electrolyte transport. A high rate charging is achievable by using expensive and low energy density cells with thin electrodes. For higher energy density cells, new electrolytes with improved conductivity and diffusivity and/or electrodes with advanced architecture are required to boost the electrolyte transport, leading to a more uniform utilization of active materials. In our previous work, an analytical model was developed to investigate the effect of secondary pore network (SPN) on electrolyte transport and the configuration of SPN was optimized by enforcing equal characteristic diffusion times in through-plane and in-plane directions. Here, to evaluate the effect of SPN on the fast-charging capability of lithium-ion batteries, a 2D physics-based electrochemical model is developed with SPN in either one or both electrodes. Additionally, the effect of SPN on cell energy density and lithium plating is investigated for cells with different loadings and electrode porosities. Combining SPN with elevated charging temperatures, the model predicts that the volumetric discharge energy density of a 3 mA h/cm2 cell can reach 270 Wh/L after a 6C constant-current charging.

25 ENERGY STORAGE↗
DOE OSTI2017

The Effects of Magnetic Fields on the Dynamics of Radiation Pressure–dominated Massive Star Envelopes

We use three-dimensional radiation magnetohydrodynamic simulations to study the effects of magnetic fields on the energy transport and structure of radiation pressure–dominated main sequence massive star envelopes at the region of the iron opacity peak. We focus on the regime where the local thermal timescale is shorter than the dynamical timescale, corresponding to inefficient convective energy transport. We begin with initially weak magnetic fields relative to the thermal pressure, from 100 to 1000 G in differing geometries. The unstable density inversion amplifies the magnetic field, increasing the magnetic energy density to values close to equipartition with the turbulent kinetic energy density. By providing pressure support, the magnetic field's presence significantly increases the density fluctuations in the turbulent envelope, thereby enhancing the radiative energy transport by allowing photons to diffuse out through low-density regions. Magnetic buoyancy brings small-scale magnetic fields to the photosphere and increases the vertical energy transport, with the energy advection velocity proportional to the Alfvén velocity, although in all cases we study, photon diffusion still dominates the energy transport. The increased radiative and advective energy transport causes the stellar envelope to shrink by several scale heights. We also find larger turbulent velocity fluctuations compared with the purely hydrodynamic case, reaching $\approx 100\,{{\rm{km}}{\rm{s}}}^{-1}$ at the stellar photosphere. The photosphere also shows vertical oscillations with similar averaged velocities and periods of a few hours. The increased turbulent velocity and oscillations will have strong impacts on the line broadening and periodic signals in massive stars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Overlapping Schwarz Methods Are Not Anisotropy‐Robust Multigrid Smoothers

We analyze overlapping multiplicative Schwarz methods as smoothers in the geometric multigrid solution of two-dimensional anisotropic diffusion problems. For diffusion equations, it is well known that the smoothing properties of point-wise smoothers, such as Gauss Seidel, rapidly deteriorate as the strength of anisotropy increases. On the other hand, global smoothers based on line smoothing are known to generally provide good smoothing for diffusion problems, independent of the anisotropy strength. Here, a natural question is whether global methods are really necessary to achieve good smoothing in such problems, or whether it can be obtained with locally overlapping block smoothers using sufficiently large blocks and overlap. Through local Fourier analysis and careful numerical experimentation, we show that global methods are indeed necessary to achieve anisotropy-robust smoothing. Specifically, for any fixed block size bounded sufficiently far away from the global domain size, we find that the smoothing properties of overlapping multiplicative Schwarz rapidly deteriorate with increasing anisotropy, irrespective of the amount of overlap between blocks. Moreover, our results indicate that anisotropy-robust smoothing requires blocks of diameter 𝒪⁡(𝜖 −1/2 ) for anisotropy ratio 𝜖 ∈(0,1] .

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Convergence analysis of two-node CMFD method for two-group neutron diffusion eigenvalue problem

In this paper, the nonlinear coarse-mesh finite difference method with two-node local problem (CMFD2N) is proven to be unconditionally stable for neutron diffusion eigenvalue problems. The explicit current correction factor (CCF) is derived based on the two-node analytic nodal method (ANM2N), and a Fourier stability analysis is applied to the linearized algorithm. It is shown that the analytic convergence rate obtained by the Fourier analysis compares very well with the numerically measured convergence rate. It is also shown that the theoretical convergence rate is only governed by the converged second harmonic buckling and the mesh size. It is also noted that the convergence rate of the CCF of the CMFD2N algorithm is dependent on the mesh size, but not on the total problem size. This is contrary to expectation for eigenvalue problem. The novel points of this paper are the analytical derivation of the convergence rate of the CMFD2N algorithm for eigenvalue problem, and the convergence analysis based on the analytic derivations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Rayleigh-Darcy convection with hydrodynamic dispersion

We investigate the effect of hydrodynamic dispersion on convection in porous media by performing direct numerical simulations (DNS) in a two-dimensional Rayleigh-Darcy domain. Scaling analysis of the governing equations shows that the dynamics of this system are not only controlled by the classical Rayleigh-Darcy number based on molecular diffusion, Ra m , and the domain aspect ratio, but also controlled by two other dimensionless parameters: the dispersive Rayleigh number Ra d =H/α t and the dispersivity ratio r=α l /α t , where H is the domain height and αt and αl are the transverse and longitudinal dispersivities, respectively. For Δ=Ra d /Ra m >O(1), the influence from the mechanical dispersion is minor; for Δ≲0.02, however, the flow pattern is determined by Rad while the convective flux is F~c(Ra d )Ra m for large Ram. Our DNS results also show that the increase of mechanical dispersion, i.e., decreasing Rad, will coarsen the convective pattern by increasing the plume spacing. Moreover, the inherent anisotropy of mechanical dispersion breaks the columnar structure of the megaplumes at large Ra m , if Ra d <5000. This results in a fan-flow geometry that reduces the convective flux.

42 ENGINEERING↗