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At least 1,081 records · Page 60
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Assessment of diffuse-interface methods for compressible multiphase fluid flows and elastic-plastic deformation in solids

This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook, Subramaniam et al., and Adler and Lele, in which artificial diffusion terms are added to the individual phase mass fraction transport equations and are coupled with the other conservation equations. The second method is the gradient-form approach that is based on the quasi-conservative method of Shukla et al., in which the diffusion and sharpening terms (together called regularization terms) are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. The third approach is the divergence-form approach that is based on the fully conservative method of Jain et al., in which the regularization terms are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. In the present study, all three diffuse-interface methods are used in conjunction with a four-equation, multicomponent mixture model, in which pressure and temperature equilibria are assumed among the various phases. The primary objective of this work is to compare these three methods in terms of their ability to: maintain constant interface thickness throughout the simulation; conserve mass, momentum, and energy; and maintain accurate interface shape for long-time integration. The second objective of this work is to consistently extend these methods to model interfaces between solid materials with strength. To assess and compare the methods, they are used to simulate a wide variety of problems, including (1) advection of an air bubble in water, (2) shock interaction with a helium bubble in air, (3) shock interaction and the collapse of an air bubble in water, and (4) Richtmyer–Meshkov instability of a copper–aluminum interface. The current work focuses on comparing these methods in the limit of relatively coarse grid resolution, which illustrates the true performance of these methods. In conclusion, this is because it is rarely practical to use hundreds of grid points to resolve a single bubble or drop in large-scale simulations of engineering interest.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

gLaSDI: Parametric physics-informed greedy latent space dynamics identification

A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. Here, an interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residual-based error indicator and random-subset evaluation is introduced to search for the optimal training samples on the fly. Further, to exploit local latent-space dynamics captured by the local DI models for an improved modeling accuracy with a minimum number of local DI models in the parameter space, a -nearest neighbor convex interpolation scheme is employed. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including Burgers equations, nonlinear heat conduction, and radial advection. The proposed adaptive greedy sampling outperforms the conventional predefined uniform sampling in terms of accuracy. Compared with the high-fidelity models, gLaSDI achieves 17 to 2,658× speed-up with 1 to 5% relative errors.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Dyn$\mathrm{AMO}$: Multi-agent reinforcement learning for dynamic anticipatory mesh optimization with applications to hyperbolic conservation laws

Here we introduce DynAMO, a reinforcement learning paradigm for Dynamic Anticipatory Mesh Optimization. Adaptive mesh refinement is an effective tool for optimizing computational cost and solution accuracy in numerical methods for partial differential equations. However, traditional adaptive mesh refinement approaches for time-dependent problems typically rely only on instantaneous error indicators to guide adaptivity. As a result, standard strategies often require frequent remeshing to maintain accuracy. In the DynAMO approach, multi-agent reinforcement learning is used to discover new local refinement policies that can anticipate and respond to future solution states by producing meshes that deliver more accurate solutions for longer time intervals. By applying DynAMO to discontinuous Galerkin methods for the linear advection and compressible Euler equations in two dimensions, we demonstrate that this new mesh refinement paradigm can outperform conventional threshold-based strategies while also generalizing to different mesh sizes, remeshing and simulation times, and initial conditions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Anti-symmetric and positivity preserving formulation of a spectral method for Vlasov-Poisson equations

We analyze the anti-symmetric properties of a spectral discretization for the one-dimensional Vlasov-Poisson equations. The discretization is based on a spectral expansion in velocity with the symmetrically weighted Hermite basis functions, central finite differencing in space, and an implicit Runge Kutta integrator in time. The proposed discretization preserves the anti-symmetric structure of the advection operator in the Vlasov equation, resulting in a stable numerical method. We apply such discretization to two formulations: the canonical Vlasov-Poisson equations and their continuously transformed square-root representation. The latter preserves the positivity of the particle distribution function. We derive analytically the conservation properties of both formulations, including particle number, momentum, and energy, which are verified numerically on the following benchmark problems: manufactured solution, linear and nonlinear Landau damping, two-stream instability, bump-on-tail instability, and ion-acoustic wave.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Generative AI models for learning flow maps of stochastic dynamical systems in bounded domains

Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary interactions. Despite the success of machine learning-based methods in learning SDEs, existing learning methods are not applicable to SDEs in bounded domains because they cannot accurately capture the particle exit dynamics. We present a unified hybrid data-driven approach that combines a conditional diffusion model with an exit prediction neural network to capture both interior stochastic dynamics and boundary exit phenomena. Our ML model consists of two major components: a neural network that learns exit probabilities using binary cross-entropy loss with rigorous convergence guarantees, and a training-free diffusion model that generates state transitions for non-exiting particles using closed-form score functions. The two components are integrated through a probabilistic sampling algorithm that determines particle exit at each time step and generates appropriate state transitions. Here, the performance of the proposed approach is demonstrated via three test cases: a one-dimensional simplified problem for theoretical verification, a two-dimensional advection-diffusion problem in a bounded domain, and a three-dimensional problem of interest to magnetically confined fusion plasmas.

Bounded domains↗
DOE OSTI2026

ECLEIRS: Exact conservation law embedded identification of reduced states for parameterized nonlinear conservation laws from sparse and noisy data

Multi-query applications such as parameter estimation, uncertainty quantification and design optimization for parameterized partial differential equation (PDE) systems are expensive. While reduced/latent state dynamics approaches for parameterized PDEs offer a viable alternative, these approaches rely on high-quality data and struggle with highly sparse spatiotemporal noisy measurements typically obtained from experiments. Furthermore, there is no guarantee that these models satisfy governing physical conservation laws. In this article, we propose a reduced state dynamics approach, referred to as ECLEIRS, that embeds exact conservation in the solution and flux representation by utilizing a space-time divergence-free neural network formulation. We compare ECLEIRS with other reduced state dynamics approaches, those that do not enforce any physical constraints and those with physics-informed loss functions, for three shock-propagation problems: 1-D advection, 1-D Burgers and 2-D Euler equations. In conclusion, the numerical experiments conducted in this study demonstrate that ECLEIRS provides the most accurate prediction of dynamics for unseen parameters even in the presence of highly sparse and noisy data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A fourth order sharp immersed method for the incompressible Navier-Stokes equations with stationary and moving boundaries and interfaces

We propose a fourth order Navier-Stokes solver based on the immersed interface method (IIM), for flow problems with stationary and one-way coupled moving boundaries and interfaces. Our algorithm employs a Runge-Kutta-based projection method that maintains high-order temporal accuracy in both velocity and pressure for steady and unsteady velocity boundary conditions. Fourth order spatial accuracy is achieved through a novel fifth order IIM discretization scheme for the advection term, as well as existing high-order interface-corrected finite difference schemes for the other differential operators. Using a set of manufactured flow problems with stationary and moving boundaries, we demonstrate fourth order convergence of velocity and pressure in the infinity norm, both inside the domain and on the immersed boundaries. The solver’s performance is further validated through a range of practical flow simulations, highlighting its efficiency over a second order scheme. Finally, we showcase the ability of our immersed discretization scheme to handle interface-coupled multiphysics problems by solving a conjugate heat transfer problem with multiple immersed solids. Overall, the proposed approach robustly combines the efficiency of high order discretization schemes with the flexibility of immersed discretizations for flow problems with complex, moving boundaries and interfaces.

42 ENGINEERING↗
DOE OSTI2026

An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations

We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator as a weighted sum of Hamiltonian evolutions, thereby emulating a dissipative problem by mixing various time scales. We introduce an efficient encoding of the LCHS into a quantum circuit based on a simple coordinate transformation that turns the dependence on the summation index into a trigonometric function. Classically, this method is equivalent to the use of a highly accurate Fejér-Clenshaw-Curtis quadrature formula. Quantumly, this significantly simplifies block-encoding of a dissipative problem and allows one to perform an exponential number of Hamiltonian simulations by a single Quantum Signal Processing (QSP) circuit. The resulting LCHS circuit has high success probability and the selector scales logarithmically with the number of terms in the LCHS sum and linearly with time. Careful analysis of error convergence proves that this method is more efficient than other LCHS circuits that have recently appeared in the literature. We verify the quantum circuit and its scaling by simulating it on a digital emulator of fault-tolerant quantum computers and, as a test problem, solve the advection-diffusion equation. The proposed algorithm can be used for simulating a wide class of nonunitary initial-value problems including the Liouville equation with added dissipation and linear embeddings of nonlinear systems, such as the Koopman-von Neumann and Carleman embeddings.

Novikau, I [Lawrence Livermore National Laboratory↗
DOE OSTI2020

Using a coupled dispersion model to estimate depletion of a tritium oxide plume by a forest

Tritium processing facilities may release tritium oxide (HTO) to the atmosphere which poses potential health risks to exposed co-located workers and to offsite individuals. Most radiological consequence analyses determine HTO dose by applying Gaussian plume models to simulate the transport of HTO. Within these models, deposition velocity is used to assess the sum of all deposition processes acting on the plume. While this may account for vegetative and soil uptake or respiration processes, it may currently lack inclusion of the complex interactions within heterogeneous forested environments. In this complex morphology, dispersion patterns are significantly altered by changing flow regimes above and below the forest canopy and by the transfer of plume material across the canopy boundary. To determine the effects of a heterogeneous forest canopy on an airborne HTO plume, a Gaussian plume model coupled with an advection-diffusion plume model was applied to estimate transport in the free atmosphere above the forest and within the forest canopy and understory. During 2012, wind speed and wind direction measurements taken at 5 heights, ranging from 2-m to 28-m, on an instrumented meteorological tower located in a loblolly pine forest at the Department of Energy (DOE) Savannah River Site (SRS), near Aiken, SC. From these measurements, model predictions were made over a full spectrum of meteorological conditions. Deposition and resuspension velocities were calculated based on the model-predicted flux of plume material across the top of the forest canopy. Additionally, net deposition velocity of the plume material was calculated as the difference between the deposition and resuspension velocities. The 1st and 5th percentile net deposition velocities were estimated to be 0.7 cm s-1 and 1.2 cm s-1, respectively.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗
DOE OSTI2024

Hydrologic connectivity and dynamics of solute transport in a mountain stream: Insights from a long-term tracer test and multiscale transport modeling informed by machine learning

The movement of solutes in a watershed is a complex process with multiple interactions and feedbacks across spatial and temporal scales. Modeling the dynamics of solute transport along diverse hydrologic pathways within watersheds – from hillslopes to stream channels and in and out of the hyporheic zones – is challenging but critically important, as these processes integrate and contribute to the biogeochemical functioning of the river corridor up to the river network scale. Here we use results from a long-term network-scale tracer test at the H.J. Andrews experimental forest in western Cascade Mountains, Oregon, USA to inform a multiscale framework for transport in stream corridors. The framework uses a Lagrangian-based subgrid model to represent the effects of hyporheic exchange flow and advective transport at stream network scales. The spatially and temporally resolved stream discharge needed for the transport model is imputed across the river system by an entity-aware long short-term memory network. Modeled concentrations show good agreements with the observations and exhibit power scaling laws indicative of a very wide range of timescales over which hyporheic exchange flow occurs. Our results demonstrate a data-informed modeling framework that links dynamical processes occurring at small scales to a network context to help understand how changes at reach scale cascade into network-scale effects, providing a useful tool for sustainable river basin management.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Characterizing the impact of finite matrix block size on conservative particle transport through three-dimensional fracture networks

Mass transfer of solutes between fractures and the surrounding rock matrix exerts a noticeable signature on the tail of travel time distributions. When the width of the matrix is assumed to be infinite and advective transport through the fracture is sufficiently fast, the tails of the travel time distributions exhibit a classically expected slope of ψ(t) ∝ t -3/2 . However, studies have yet to characterize how solute transfer between fractures via diffusion through finite matrix blocks influences the tail’s slope in three-dimensional fractured media. Here, in this study, we assess the impact of finite matrix block size on breakthrough curve shape at different spatio-temporal scales by con ducting particle tracking simulations in three-dimensional discrete fracture networks. We consider a variety of hydrodynamic and geostructural proper ties to determine their relative impact on the resulting travel time distributions. We observe that the impact of matrix diffusion through a finite block on travel time distributions is similar to that of an infinite matrix block when the fracture spacing is sufficiently large, matrix diffusion is relatively weak, or transport is considered at an early control plane distance. We observe that the converse of these conditions, results in deviations from the classical ψ(t) ∝ t -3/2 scaling. These results provide a first step toward developing a metric to assess when finite block size effects are expected to significantly influence transport.

58 GEOSCIENCES↗
DOE OSTI2019

A Method for Including Diffusive Effects in Texture Evolution

This work describes a model for representing grain misorientation in continuum models for texture evolution. The model relies on a connection, derived here, between the fluctuation of the reorientation velocity in discrete models of texture evolution and an isotropic diffusion operator that can be used to represent misorientation effects in continuum models for texture evolution. Previous work has developed a method for computing the fluctuation of the reorientation velocity in discrete models. These values, along with the average reorientation velocity, are used to set up inhomogeneous continuum advection and diffusion operators. Here, the complete homogenized continuum model uses the discrete harmonics to represent and evolve the orientation distribution function, now including a diffusion operator representing the effects of intragranular misorientation. Results from the new model are compared to fully-resolved crystal plasticity finite element simulations and experimental data to demonstrate the accuracy of the proposed diffusion operator and the overall method for simulating texture evolution.

(B) crystal plasticity↗
DOE OSTI2015

A case study of CUDA FORTRAN and OpenACC for an atmospheric climate kernel

The porting of a key kernel in the tracer advection routines of the Community Atmosphere Model – Spectral Element (CAM-SE) to use Graphics Processing Units (GPUs) using OpenACC is considered in comparison to an existing CUDA FORTRAN port. The development of the OpenACC kernel for GPUs was substantially simpler than that of the CUDA port. Also, OpenACC performance was about 1.5× slower than the optimized CUDA version. Particular focus is given to compiler maturity regarding OpenACC implementation for modern FORTRAN, and it is found that the Cray implementation is currently more mature than the PGI implementation. Still, for the case that ran successfully on PGI, the PGI OpenACC runtime was slightly faster than Cray. The results show encouraging performance for OpenACC implementation compared to CUDA while also exposing some issues that may be necessary before the implementations are suitable for porting all of CAM-SE. Furthermore, most notable are that GPU shared memory should be used by future OpenACC implementations and that derived type support should be expanded.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Large magnon-induced anomalous Nernst conductivity in single-crystal MnBi

Thermoelectric modules are a promising approach to energy harvesting and efficient cooling. In addition to the longitudinal Seebeck effect, transverse devices utilizing the anomalous Nernst effect (ANE) have recently attracted interest. For high conversion efficiency, it is required that the material have a large ANE thermoelectric power and low electrical resistance, which lead to the conductivity of the ANE. ANE is usually explained in terms of intrinsic contributions from Berry curvature. Our observations suggest that extrinsic contributions also matter. Studying single-crystal manganese-bismuth (MnBi), we find a high ANE thermopower (~10 μV/K) under 0.6 T at 80 K, and a transverse thermoelectric conductivity of over 40 A/Km. With insight from theoretical calculations, we attribute this large ANE predominantly to a new advective magnon contribution arising from magnon-electron spin-angular momentum transfer. We propose that introducing a large spin-orbit coupling into ferromagnetic materials may enhance the ANE through the extrinsic contribution of magnons.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Analytical modeling for redox flow battery design

Deeper market penetration of redox flow batteries requires optimization of the cell performance. Though important for optimization, detailed analytical solutions have not been developed for electrolyte flow, mass and charge transport, and reaction kinetics within redox flow batteries. To this end, here we present analytical solutions to active species concentration and over-potential based on advection-diffusion transport for ions and Bulter-Volmer model for interface reaction kinetics. The solutions were validated with results from a finite element model. These solutions were then applied to investigate the relationship between over-potential and state of charge, current density, reaction rate constant, flow velocity, diffusivity, total active species concentration, and electrode structure. Explicit formulas were identified for minimum activation over-potential and limiting current density as well as their dependence on electrolyte properties, operation conditions, and electrode structure. With our new mathematical formulas, this work provides a theoretical framework for flow battery design.

25 ENERGY STORAGE↗
DOE OSTI2016

Wellbore and groundwater temperature distribution eastern Snake River Plain, Idaho: Implications for groundwater flow and geothermal potential

A map of groundwater temperatures from the Eastern Snake River Plain (ESRP) regional aquifer can be used to identify and interpret important features of the aquifer, including aquifer flow direction, aquifer thickness, and potential geothermal anomalies. The ESRP is an area of high heat flow, yet most of this thermal energy fails to reach the surface, due to the heat being swept downgradient by the aquifer to the major spring complexes near Thousand Springs, ID, a distance of 300 km. Nine deep boreholes that fully penetrate the regional aquifer display three common features: (1) high thermal gradients beneath the aquifer, corresponding to high conductive heat flow in low-permeability hydrothermally-altered rocks; (2) isothermal temperature profiles within the aquifer, characteristic of an actively flowing groundwater; and (3) moderate thermal gradients in the vadose zone with values that indicate that over half of the geothermal heat flow is removed by advective transport in the regional aquifer system. This study utilized temperature data from 250 ESRP aquifer wells to evaluate regional aquifer flow direction, aquifer thickness, and potential geothermal anomalies. Because the thermal gradients are typically low in the aquifer, any measurement of groundwater temperature is a reasonable estimate of temperature throughout the aquifer thickness, allowing the construction of a regional aquifer temperature map for the ESRP. Mapped temperatures are used to identify cold thermal plumes associated with recharge from tributary valleys and adjacent uplands, and warm zones associated with geothermal input to the aquifer. Warm zones in the aquifer can have various causes, including local circulation of groundwater through the deep conductively dominated region, slow groundwater movement in low-permeability regions, or localized heat flow from deeper thermal features.

15 GEOTHERMAL ENERGY↗
DOE OSTI2018

Pyroclast cooling and saturation in water

In the submarine setting pyroclast cooling and saturation, by controlling the buoyancy of individual clasts and surrounding fluid, exert fundamental controls on the dispersal and fate of volcanic material. Here, we use laboratory experiments to understand and quantify how hot and air-filled pyroclasts cool and saturate in liquid water. By measuring internal temperature and clast submerged weight in over thirty experiments, we find that pumice cools and saturates in two stages. We observe that the first stage is marked by much higher rates of cooling and saturation than the second stage and that the transition between stages is sharp. We propose conceptual and quantitative models for each stage of pyroclast cooling and saturation. Specifically we argue that the first stage is defined by the presence of internal steam. That is, hot pyroclasts ingest liquid water and generate steam. Once a clast's internal pore space is filled with steam, heat loss to the surroundings causes condensation of internal vapor and clast saturation. Stage 1 ends when all internal steam has condensed. We test this idea with a Stefan Model with advection and conclude that heat loss, rather than permeability, controls the saturation of pyroclasts above the boiling temperature. We find that permeability matters for air-filled clasts with initial temperatures below the boiling point. Stage 2 begins after all internal vapor has condensed and we propose that stage 2 cooling and saturation are controlled by heat conduction and thermal contraction of trapped gas, respectively. From our understanding of the processes that govern the stage 1 to 2 transition, we derive an empirical average pyroclast cooling rate of q = 7.5 ± 0.5 W cm -2 . Finally, we develop quantitative models for cooling-controlled porous clast saturation and for buoyant clast rise to the ocean surface. We find that meter size clasts stay buoyant for more than 10 min - long enough to reach the surface from a depth of 1000 m. Lastly, the models developed here test our understanding of clast-scale processes and demonstrate that - in hot and porous clasts - the details of internal texture do not matter because clast saturation, and thus buoyancy and fate in the water column, are governed by heat transfer.

58 GEOSCIENCES↗