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DOE OSTI2021

A Computational Information Criterion for Particle-Tracking with Sparse or Noisy Data

Traditional probabilistic methods for the simulation of advection-diffusion equations (ADEs) often overlook the entropic contribution of the discretization, e.g., the number of particles, within associated numerical methods. Many times, the gain in accuracy of a highly discretized numerical model is outweighed by its associated computational costs or the noise within the data. Herein, we address the question of how many particles are needed in a simulation to best approximate and estimate parameters in one-dimensional advective-diffusive transport. To do so, we use the well-known Akaike Information Criterion (AIC) and a recently-developed correction called the Computational Information Criterion (COMIC) to guide the model selection process. Random-walk and mass-transfer particle tracking methods are employed to solve the model equations at various levels of discretization. Numerical results demonstrate that the COMIC provides an optimal number of particles that can describe a more efficient model in terms of parameter estimation and model prediction compared to the model selected by the AIC even when the data is sparse or noisy, the sampling volume is not uniform throughout the physical domain, or the error distribution of the data is non-IID Gaussian.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Interface-aware Methods for Diffusion Equations [Slides]

In this talk, we will present interface-aware methods for diffusion equation. The focus is on the necessity of interface-aware, mixed cells, interface reconstruction, discontinuity of material diffusion coefficients, order of accuracy in time, property for large time steps, and simpler interface-aware methods. Numerical examples are provided to demonstrate the features on these aspects of the methods

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Fluctuating hydrodynamics and the Rayleigh–Plateau instability

The Rayleigh–Plateau instability occurs when surface tension makes a fluid column become unstable to small perturbations. At nanometer scales, thermal fluctuations are comparable to interfacial energy densities. Consequently, at these scales, thermal fluctuations play a significant role in the dynamics of the instability. These microscopic effects have previously been investigated numerically using particle-based simulations, such as molecular dynamics (MD), and stochastic partial differential equation–based hydrodynamic models, such as stochastic lubrication theory. In this paper, we present an incompressible fluctuating hydrodynamics model with a diffuse-interface formulation for binary fluid mixtures designed for the study of stochastic interfacial phenomena. An efficient numerical algorithm is outlined and validated in numerical simulations of stable equilibrium interfaces. We present results from simulations of the Rayleigh–Plateau instability for long cylinders pinching into droplets for Ohnesorge numbers of Oh = 0.5 and 5.0. Both stochastic and perturbed deterministic simulations are analyzed and ensemble results show significant differences in the temporal evolution of the minimum radius near pinching. Short cylinders, with lengths less than their circumference, were also investigated. As previously observed in MD simulations, we find that thermal fluctuations cause these to pinch in cases where a perturbed cylinder would be stable deterministically. Finally, we show that the fluctuating hydrodynamics model can be applied to study a broader range of surface tension–driven phenomena.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Probabilistic estimation of depth-resolved profiles of soil thermal diffusivity from temperature time series

Abstract. Improving the quantification of soil thermal and physical properties is key to achieving a better understanding and prediction of soil hydro-biogeochemical processes and their responses to changes in atmospheric forcing. Obtaining such information at numerous locations and/or over time with conventional soil sampling is challenging. The increasing availability of low-cost, vertically resolved temperature sensor arrays offers promise for improving the estimation of soil thermal properties from temperature time series, and the possible indirect estimation of physical properties. Still, the reliability and limitations of such an approach need to be assessed. In the present study, we develop a parameter estimation approach based on a combination of thermal modeling, sliding time windows, Bayesian inference, and Markov chain Monte Carlo simulation to estimate thermal diffusivity and its uncertainty over time, at numerous locations and at an unprecedented vertical spatial resolution (i.e., down to 5 to 10 cm vertical resolution) from soil temperature time series. We provide the necessary framework to assess under which environmental conditions (soil temperature gradient, fluctuations, and trend), temperature sensor characteristics (bias and level of noise), and deployment geometries (sensor number and position) soil thermal diffusivity can be reliably inferred. We validate the method with synthetic experiments and field studies. The synthetic experiments show that in the presence of median diurnal fluctuations ≥ 1.5 ∘C at 5 cm below the ground surface, temperature gradients > 2 ∘C m−1, and a sliding time window of at least 4 d the proposed method provides reliable depth-resolved thermal diffusivity estimates with percentage errors ≤ 10 % and posterior relative standard deviations ≤ 5 % up to 1 m depth. Reliable thermal diffusivity under such environmental conditions also requires temperature sensors to be spaced precisely (with accuracy to a few millimeters), with a level of noise ≤ 0.02 ∘C, and with a bias defined by a standard deviation ≤ 0.01 ∘C. Finally, the application of the developed approach to field data indicates significant repeatability in results and similarity with independent measurements, as well as promise in using a sliding time window to estimate temporal changes in soil thermal diffusivity, as needed to potentially capture changes in bulk density or water content.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

The Flux-Differencing Discontinuous Galerkin Method Applied to an Idealized Fully Compressible Nonhydrostatic Dry Atmosphere

Dynamical cores used to study the circulation of the atmosphere employ various numerical methods ranging from finite-volume, spectral element, global spectral, and hybrid methods. In this work, we explore the use of Flux-Differencing Discontinuous Galerkin (FDDG) methods to simulate a fully compressible dry atmosphere at various resolutions. We show that the method offers a judicious compromise between high-order accuracy and stability for large-eddy simulations and simulations of the atmospheric general circulation. In particular, filters, divergence damping, diffusion, hyperdiffusion, or sponge-layers are not required to ensure stability; only the numerical dissipation naturally afforded by FDDG is necessary. We apply the method to the simulation of dry convection in an atmospheric boundary layer and in a global atmospheric dynamical core in the standard benchmark of Held and Suarez

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Bridging Scales to Model Reactive Diffusive Transport in Porous Media

Published by ECS. Two novel scale-bridging algorithms to model reaction-diffusion transport in porous media are presented. The algorithms are based on direct numerical simulations and couple the information of a micro-scale model, which accounts for the large field of view provided by micro X-ray computed tomography (X-ray CT), and a nano-scale model, which locally resolves transport in the fine structure extracted from nano X-ray CT. The micro-scale model is discretized in the through-plane direction into a 1D grid, where effective properties and internal boundaries are determined based on the results from the nano-scale model. The validated algorithms are used to examine transport of oxygen in precious group metal-free electrodes considering both zero- and first-order kinetics. Unlike conventional methods, the results show that the effective diffusivity is not a passive property but increases in regions where the reaction-rate coefficient is large. The proposed algorithms account for the multiscale coupling of reaction-diffusion transport and material microstructure, thus improving the predictions compared to conventional methods.

42 ENGINEERING↗

DOE OSTI2024

Reaction-diffusion modeling provides insights into biophysical carbon-concentrating mechanisms in land plants

Carbon-concentrating mechanisms (CCMs) have evolved numerous times in photosynthetic organisms. They elevate the concentration of CO 2 around the carbon-fixing enzyme rubisco, thereby increasing CO 2 assimilatory flux and reducing photorespiration. Biophysical CCMs, like the pyrenoid-based CCM (PCCM) of Chlamydomonas reinhardtii or carboxysome systems of cyanobacteria, are common in aquatic photosynthetic microbes, but in land plants appear only among the hornworts. To predict the likely efficiency of biophysical CCMs in C 3 plants, we used spatially resolved reaction-diffusion models to predict rubisco saturation and light use efficiency. We found that the energy efficiency of adding individual CCM components to a C 3 land plant is highly dependent on the permeability of lipid membranes to CO 2 , with values in the range reported in the literature that are higher than those used in previous modeling studies resulting in low light use efficiency. Adding a complete PCCM into the leaf cells of a C 3 land plant was predicted to boost net CO 2 fixation, but at higher energetic costs than those incurred by photorespiratory losses without a CCM. Two notable exceptions were when substomatal CO 2 levels are as low as those found in land plants that already use biochemical CCMs and when gas exchange is limited, such as with hornworts, making the use of a biophysical CCM necessary to achieve net positive CO 2 fixation under atmospheric CO 2 levels. This provides an explanation for the uniqueness of hornworts' CCM among land plants and the evolution of pyrenoids multiple times.

Kaste, Joshua A. M.↗

DOE OSTI2024

The Method of Finite Averages: A rigorous upscaling methodology for heterogeneous porous media

Rigorous upscaling techniques offer accurate and computationally-efficient strategies for modeling the average behaviors of multi-physical, multiscale phenomena in geological porous media. However, such techniques often rely on a variety of methodological assumptions that prohibit their rigorous application to practical systems (e.g., systems involving heterogeneous porous media, system-scale boundary conditions, and fine-scale dynamics that are not diffusion-dominant). In this work, we aim to formulate an upscaling methodology with few methodological assumptions to provide high levels of model generality and foster the utilization of rigorously-derived upscaled models in practice. In particular, we introduce the Method of Finite Averages (MoFA), a novel upscaling methodology for rigorously modeling heterogeneous porous media and system-scale boundary conditions. We then detail MoFA’s implementation for the advective–diffusive transport of a single species and compare the methodology with classic numerical techniques, as well as other rigorous upscaling techniques, to highlight MoFA’s unique combination of rigor and generality. We then validate the derived model while demonstrating its benefits in three numerical experiments. The results suggest that (1.) the applicability and a priori error guarantees of MoFA models do not directly depend on system geometry, (2.) a model’s applicability and error guarantees can be can arbitrarily expanded and reduced, respectively, with further computational expense, and (3.) downscaling with MoFA provides an efficient strategy for generating accurate pore-scale solutions from upscaled results. Ultimately, the results evidence that upscaled models can be rigorously derived for heterogeneous porous media systems and resolved in a fraction of the time it takes to perform the equivalent pore-scale simulations.

58 GEOSCIENCES↗

DOE OSTI2021

Analysis of the Reactive CO 2 Surface Flux in Electrocatalytic Aqueous Flow Reactors

We study how the mass transfer of a chemical species in shear flow is suppressed by the production of a second species that partially reacts away the first species. The second species is produced at the surface with the first species as a reactant. Our work is directly motivated by electrochemical CO 2 reduction in aqueous flow reactors, where OH– molecules generated by the CO evolution reaction react away CO 2 molecules, ultimately inhibiting the mass transfer of CO 2 to the cathode surface. We derive a simple approximation of the Sherwood number, a dimensionless measure of the mass flux into the surface, as a function of the Péclet number, surface Damköhler number, and bulk Damköhler number, and we compare our approximation to numerical solutions of the governing equations. We find that in the diffusion-limited regime, the Sherwood number is well described by the classical Graetz-Lévêque result reduced by a reaction factor due to the competing bulk reaction; with the stoichiometry relevant to electrochemical CO 2 reduction, this reaction factor is 1/2. While the model problem we solve provides insight into how OH– production affects CO 2 mass transfer, experimental systems often involve more complex chemistry. We thus also show how a common buffered electrolyte, KHCO 3 , affects our results.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2022

Spin dynamics and exchange interaction in orthoferrite TbFeO 3 with non-Kramers rare-earth ion

The low-temperature spin dynamics of the orthorhombic TbFeO 3 perovskite has been studied. It has been found that the inelastic neutron scattering (INS) spectrum of the investigated compound contains two modes corresponding to different sublattices. It is shown that the iron subsystem orders antiferromagnetically at T N =632 K and exhibits the high-energy magnon dispersion. The magnetic dynamics of this subsystem has been described within the linear spin wave theory and the in-plane and out-of-plane exchange anisotropy has been demonstrated. The approach proposed previously to describe the magnon dispersion in the TmFeO 3 compound has been used. Three levels of the nondispersive crystal electric field corresponding to Tb 3+ ions have been found in the energy region below 40 meV at about 17, 26, and 35 meV. The behavior of the magnetic correlation length of the terbium subsystem has been determined by studying the diffuse scattering at different temperatures. The evolution of this subsystem has been numerically described within the point charge model. In conclusion, it is shown that the numerical data agree satisfactorily with the experiment and with the general concept of the single-ion approximation applied to the rare-earth subsystem of orthorhombic perovskites.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Stochastic Modeling in a Multimaterial Continuum Mixture Shock Physics Code

Stochastic modelling approaches are presented to capture random effects at multiple time and length scales. Random processes that occur at the microscale produce nondeterministic effects at the macroscale. Here we present three stochastic modeling approaches that describe random processes at microscopic length scales and map these processes to the macroscopic length scale. The first stochastic modeling approach is based upon a particle based numerical technique to solve a Stochastic Differential Equation (SDE) using an arbitrary diffusion process to capture random processes at the microstructural level. The second approach prescribes a Probability Density Function (PDF) for the drift and diffusion of the random variable derived using the forward and backward Kolmogorov equations. This method requires mean and drift evolution PDF transport equations. The third approach is the coupling of multiple random variables which are dependent on each other. The relationship of the PDFs and a coupling function, known as a copula, produces a Joint Probability Density Function (JPDF). These stochastic modeling approaches are implemented into a Multiple Component (MC) shock physics computational code and used to model statistical fracture and reactive flow applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Thermal diffusion, exhaust gas recirculation and blending effects on lean premixed hydrogen flames

Thermodiffusively-unstable lean premixed hydrogen flames are investigated using two-dimensional direct numerical simulation employing finite-rate chemical kinetics. Three databases are generated focussing on the inclusion of the Soret effect, the recirculation of exhaust gas, and blending with methane. A simple rescaling of a classic thermal diffusion model is presented and shown to mimic multicomponent diffusion with very low computational cost and little-to-no loss in accuracy. It is also shown that a previously developed model for mean local flame speeds in lean premixed hydrogen flames can still be used provided Soret effects are taken into account in one-dimensional calculations. The addition of exhaust gas to the unburned mixture is found to enhance thermodiffusive instability; the primary mechanism for this was shown to be the highly-efficient third-body nature of water, with the reduction of adiabatic flame temperature a second-order effect. Again, the existing mean local flame speed model proved sufficient. Finally, blending with methane was found to reduce the thermodiffusive response of the flame, more so than the existing model suggests, despite adjustment of the fuel Lewis number; an adapted model is presented to account for this.

08 HYDROGEN↗

DOE OSTI2020

Lyapunov and Clearing Timescales in Planetary Chaotic Zones

Debris disks in planetary systems are known to possess gaps “opened” by planets in their close-to-coorbital neighborhoods; the gaps are free from low-mass material such as planetesimals. We consider the escape process of the initially zero-eccentric particles from the gap zone in a scenario consisting of two basic consequent stages: (1) the particle orbit's eccentricity is inflated, while its specific energy is relatively constant, and (2) the particle orbit's semimajor axis is inflated, while its specific angular momentum is relatively constant. During the first stage, the chaotic transport (diffusion) proceeds along the “staircase” of (p + 1):p (with integer p ≫ 1) overlapping particle–planet resonances, and during the second stage, it proceeds along the p:1 particle–planet resonance staircase. A specialized two-dimensional area-preserving map (a “tokamap” version) is derived to describe the first stage, while a multiharmonic Kepler map theory is used to describe the second stage. We derive the μ (mass parameter) scaling for the clearing timescale in the planetary chaotic zone. At small μ, it turns out to be inverse-quadratic in μ. The μ scaling for the Lyapunov timescale inside the gap is also derived. The derived scalings are in qualitative agreement with available numerical-experimental data.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

A score-based diffusion model approach for adaptive learning of stochastic partial differential equation solutions

In this paper, we propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Generative design of de novo proteins based on secondary-structure constraints using an attention-based diffusion model

We report two generative deep-learning models that predict amino acid sequences and 3D protein structures on the basis of secondary-structure design objectives via either the overall content or the per-residue structure. Both models are robust regarding imperfect inputs and offer de novo design capacity because they can discover new protein sequences not yet discovered from natural mechanisms or systems. The residue-level secondary-structure design model generally yields higher accuracy and more diverse sequences. These findings suggest unexplored opportunities for protein designs and functional outcomes within the vast amino acid sequences beyond known proteins. Our models, based on an attention-based diffusion model and trained on a dataset extracted from experimentally known 3D protein structures, offer numerous downstream applications in the conditional generative design of various biological or engineering systems. Future work could include additional conditioning and an exploration of other functional properties of the generated proteins for various properties beyond structural objectives.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

A Phase-Field Model for In-Space Manufacturing of Binary Alloys

The integrity of the final printed components is mostly dictated by the adhesion between the particles and phases that form upon solidification, which is a major problem in printing metallic parts using available In-Space Manufacturing (ISM) technologies based on the Fused Deposition Modeling (FDM) methodology. Understanding the melting/solidification process helps increase particle adherence and allows to produce components with greater mechanical integrity. We developed a phase-field model of solidification for binary alloys. The phase-field approach is unique in capturing the microstructure with computationally tractable costs. The developed phase-field model of solidification of binary alloys satisfies the stability conditions at all temperatures. The suggested model is tuned for Ni-Cu alloy feedstocks. We derived the Ginzburg-Landau equations governing the phase transformation kinetics and solved them analytically for the dilute solution. We calculated the concentration profile as a function of interface velocity for a one-dimensional steady-state diffuse interface neglecting elasticity and obtained the partition coefficient, k, as a function of interface velocity. Numerical simulations for the diluted solution are used to study the interface velocity as a function of undercooling for the classic sharp interface model, partitionless solidification, and thin interface.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Learning subgrid-scale models with neural ordinary differential equations

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary differential equations (NODEs). Solving systems with fine temporal and spatial grid scales is an ongoing computational challenge, and closure models are generally difficult to tune. Machine learning approaches have increased the accuracy and efficiency of computational fluid dynamics solvers. In this approach neural networks are used to learn the coarse- to fine-grid map, which can be viewed as subgrid-scale parameterization. We propose a strategy that uses the NODE and partial knowledge to learn the source dynamics at a continuous level. Our method inherits the advantages of NODEs and can be used to parameterize subgrid scales, approximate coupling operators, and improve the efficiency of low-order solvers. Numerical results with the two-scale Lorenz 96 ODE, the convection-diffusion PDE, and the viscous Burgers' PDE are used to illustrate this approach.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Asymptotic-preserving semi-implicit finite volume scheme for extended magnetohydrodynamics

A Finite Volume (FV) scheme is developed for solving the extended magnetohydrodynamic (XMHD) equations, yielding accurate results in the ideal, resistive, and Hall MHD limits. This is accomplished by first re-writing the XMHD equations such that it allows the algorithm to retain the use of ideal MHD Riemann solvers and the constrained transport method to preserve divergence-free magnetic fields. Incorporation of electron inertia and displacement current introduces additional numerical stiffness which motivates a semi-implicit FV scheme that re-formulates the XMHD model as a relaxation system. The equations are then advanced in time using an explicit 2nd-order Runge–Kutta scheme with operator splitting applied to the implicit source term updates at each sub-stage. For additional numerical stability, a density-dependent slope limiter is implemented to increase flux diffusivity at low density regions where non-ideal effects become significant. The algorithm is subsequently implemented in a scalable adaptive mesh refinement (AMR) framework. As the new algorithm retains many aspects of the ideal MHD formulations, it asymptotes naturally to the ideal MHD limit. Moreover, it shows promising results at the resistive and Hall MHD limits. This is verified against reference test problems for ideal, resistive and Hall MHD.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗