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DOE OSTI2024

Proton radiography inversions with source extraction and comparison to mesh methods

In this article, proton radiography is a central diagnostic technique for measuring electromagnetic (EM) fields in high-energy-density, laser-produced plasmas. In this technique, protons traverse the plasma where they accumulate small EM deflections which lead to variations in the proton fluence pattern on a detector. Path-integrated EM fields can then be extracted from the fluence image through an inversion process. In this work, experiments of laser-driven foils were conducted on the OMEGA laser and magnetic field reconstructions were performed using both “fluence-based” techniques and high-fidelity “mesh-based” methods. We implement nonzero boundary conditions into the inversion and show their importance by comparing against mesh measurements. Good agreement between the methods is found only when nonzero boundary conditions are used. We also introduce an approach to determine the unperturbed proton source profile, which is a required input in fluence reconstruction algorithms. In this approach, a fluence inversion is embedded inside of a mesh region, which provides overconstrained magnetic boundary conditions. A source profile is then iteratively optimized to satisfy the boundary information. This method substantially enhances the accuracy in recovering EM fields. Lastly, we propose a scheme to quantify uncertainty in the final inversion that is introduced through errors in the source retrieval.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Physics‐Informed Machine Learning Method for Large‐Scale Data Assimilation Problems

Abstract We develop a physics‐informed machine learning approach for large‐scale data assimilation and parameter estimation and apply it for estimating transmissivity and hydraulic head in the two‐dimensional steady‐state subsurface flow model of the Hanford Site given synthetic measurements of said variables. In our approach, we extend the physics‐informed conditional Karhunen‐Loéve expansion (PICKLE) method to modeling subsurface flow with unknown flux (Neumann) and varying head (time‐dependent Dirichlet) boundary conditions. We demonstrate that the PICKLE method is comparable in accuracy with the standard maximum a posteriori (MAP) method, but is significantly faster than MAP for large‐scale problems. Both methods use a mesh to discretize the computational domain. In MAP, the parameters and states are discretized on the mesh; therefore, the size of the MAP parameter estimation problem directly depends on the mesh size. In PICKLE, the mesh is used to evaluate the residuals of the governing equation, while the parameters and states are approximated by the truncated conditional Karhunen‐Loéve expansions with the number of parameters controlled by the smoothness of the parameter and state fields, and not by the mesh size. For a considered example, we demonstrate that the computational cost of PICKLE increases near linearly (as N 1.15 ) with the number of grid nodes N , while that of MAP increases much faster (as N 3.28 ). We also show that once trained for one set of Dirichlet boundary conditions (i.e., one river stage), the PICKLE method provides accurate estimates of the hydraulic head for any value of the Dirichlet boundary conditions (i.e., for any river stage).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Magnetic potential based formulation for linear and non-linear 3D RF sheath simulation

Abstract This paper reports a new numerical scheme to simulate the radio-frequency (RF) induced RF sheath, which is suitable for a large 3D simulation. In the RF sheath boundary model, the tangential component of the electric field ( E t ) is given by the gradient of a scalar electric field potential. We introduce two additional scalar potentials for the tangential components of the magnetic field, which effectively impose the normal electric displacement ( D n ) on the plasma sheath boundary condition via in-homogeneous Neumann boundary condition and constrain the tangential electric field on the surface as curl-free ( ∇ × E t = 0 ). In our approach, the non-linear sheath impedance is formulated as a natural extension of the large thickness (or asymptotic) sheath limit ( D n = 0 ), allowing for handling both asymptotic and non-linear regimes seamlessly. The new scheme is implemented using the Petra-M finite element method analysis framework and is verified with simulations in the literature. The significance of non-linearity is discussed in various plasma conditions. An application of this scheme to asymptotic RF sheath simulation on the WEST ICRF antenna side limiters is also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Energizing charged particles by an orbit instability in a slowly rotating magnetic field

In this work, the stability of charged particle motion in a uniform magnetic field with an added spatially uniform transverse rotating magnetic field (RMF) is studied analytically. It is found that the stability diagram of a single particle's orbit depends critically on the chosen boundary conditions. We show that for many boundary conditions and wide regions in the parameter space, RMFs oscillating far below the cyclotron frequency can cause linear instabilities in the motion which break μ invariance and energize particles. Such energization may appear at odds with the adiabatic invariance of μ; however, adiabatic invariance is an asymptotic result and does not preclude such heating by magnetic fields oscillating at slow frequencies. This mechanism may contribute to heating in the edge plasma of field-reversed configurations (FRCs) in rotamak-FRC experiments. Furthermore, these RMF-driven instabilities may significantly enhance azimuthal current drive during the formation of FRCs in such devices.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Parametric Study to Assess Technical Prospect Feasibility for Offshore CO 2 Storage

This report is a white paper on the parametric study to assess technical prospect feasibility for CO 2 storage with and without CO 2 -EOR. The SECARB Offshore GOM team reviewed key parameters that previous modeling experience suggests have the largest impact on CO 2 plume size and CO 2 -EOR performance (SSEB, 2019) These parameters include tectonic impacts (reservoir dip and fault block size), reservoir properties (permeability) and development strategies (well field payout, waterflood, and CO 2 flooding strategies). These parameters are further evaluated in this study in order to identify upper and lower boundary conditions for the parametric values. The boundary conditions are needed to set constraints for key parameters when performing modeling assessments. Understanding the key parametric values for the GOM will facilitate locating successful offshore carbon capture utilization and storage (CCUS) projects in terms of plume size, CO 2 stored and, in the case of EOR, oil recovery. Importantly, this white paper focuses on both technical factors (geologic and engineering), but does not address economic, commercial, or stakeholder considerations. The report is organized into four sections and includes a review of the datasets used to define the parameter ranges, the results of a full-physics reservoir simulation, a summary of a reduced order modeling approach to evaluate the impact of the study parameters, and, finally, a discussion of the work that will occur during the next phase of the project.

02 PETROLEUM↗

DOE OSTI2023

Multiphysics Simulations of MSRE with NEAMS Thermal Hydraulics Tools

This report documents the benchmarks being developed and simulations performed using tools and codes developed under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, utilizing MSRE experimental data. In FY23, three main work scopes were investigated under the NEAMS MSR work package at ANL. The first scope investigated the Griffin-SAM coupling model for simulating the pump startup transient experiment of MSRE. The analyses start with a simple model (single-channel, single-lattice), gradually adding more details (multi-channel, full-core) into the model. The results show that the reactivity loss curve is very sensitive to the axial boundary conditions and the radial core discretization. The simple model can predict a similar reactivity trend as that of the more sophisticated model, which is likely due to error cancellation. Accurately modeling the axial boundary condition may further improve the reactivity trend but would require significant efforts to generate the mesh of the MSRE inlet and upper plenum. The core channel radial discretization for the Griffin-SAM coupled model also depends on the flow distribution. Given the complex geometry in the inlet plenum, the flow distribution needed to be calculated from CFD analysis, which was performed using the NekRS code. This analysis employed a MSRE CAD model developed by Copenhagen Atomics. The CAD model was disassembled to keep the inlet plenum region only, which was subsequently cleaned and modified so that the mesh generated is under the memory limit. The results are merged to a few radial regions to show that the flow rate is highest in the central region. This would be useful for future improvement of the Griffin-SAM coupling model of the MSRE core. The last task investigated is tritium transport modeling using the standalone SAM code. This task aimed to initiate the effort to demonstrate and validate the tritium transport model implemented in SAM. The preliminary investigation employed an MSRE model consisting of the primary loop. Three tritium transport pathways were examined including the retention in the graphite, the permeation through the HX tube wall, and the removal from the off-gas system. The results compare well with the MSRE data, but improvements are still needed on the initial conditions (i.e., the present state may not have reached equilibrium), the boundary conditions, the off-gas system modeling, and a better numerical strategy to reach the equilibrium state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Helical spin structure in iron chains with hybridized boundaries

In this paper, we have compared the magnetic properties of well-controlled ultra-short (≤50 nm) atomic iron (Fe) chains embedded in Fe-phthalocyanine films with those in Fe–hydrogen (H2) phthalocyanine superlattices. Surprisingly, we found that the coercivity of the atomic chains with free boundary conditions is independent of the chain length, whereas the one subject to hybridization of the chain ends exhibits an unexpected length dependence. These findings suggest that ferromagnetism in the free-boundary condition system is caused by an intrinsic indirect exchange. On the other hand, controlled boundary conditions produce a helical spin structure due to an extrinsic indirect exchange, which arises from the interaction between iron atoms at the ends of the chain and the hydrogen in the H 2 phthalocyanine spacer. As a consequence, during magnetic reversal, ultra-short iron chains subject to boundary clamping develop a helical spin structure, leading to increased coercivity. These findings suggest unique insights and ideas for the design of atomic-scale ultra-dense magnetic storage nanodevices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Sensitivity of Grass Fires Burning in Marginal Conditions to Atmospheric Turbulence

Abstract Atmospheric forcing and interactions between the fire and atmosphere are primary drivers of wildland fire behavior. The atmosphere is known to be a chaotic system that, although deterministic, is very sensitive to small perturbations to initial conditions. We assume that as a result of the tight coupling between fire and atmosphere; wildland fire behavior, in turn, should also be sensitive to perturbations in atmospheric initial conditions. Observations suggest that low intensity prescribed fire, in particular, is susceptible to small perturbations in the wind field, which can significantly alter fire spread. Here, we employ a computational fluid dynamics model of coupled fire‐atmosphere interactions to answer the question: How sensitive is fire behavior to small variations in atmospheric turbulence? We perform ensemble simulations of fires in homogenous grass fuels. The only difference between ensemble members is the state of the turbulent atmosphere provided to the model throughout the simulation. The atmospheric state is a function of the initial conditions applied at the start of the simulation and boundary conditions applied throughout the simulation. We find a wide range of outcomes, with area burned ranging from 2,212 to 11,236 m 2 (>400% change), driven primarily by sensitivity to initial conditions, with nonnegligible contributions from boundary condition variability during the initial 30 s of simulation. Our results highlight the need for ensemble simulations, especially when considering fire behavior in marginal burning conditions.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

One-shot omnidirectional pressure integration through matrix inversion

In this work, we present a method to perform 2D and 3D omnidirectional pressure integration from velocity measurements with a single-iteration matrix inversion approach. This work builds upon our previous work, where the rotating parallel ray approach was extended to the limit of infinite rays by taking continuous projection integrals of the ray paths and recasting the problem as an iterative matrix inversion problem. This iterative matrix equation is now 'fast-forwarded' to the 'infinity' iteration, leading to a different matrix equation that can be solved in a single step, thereby presenting the same computational complexity as the Poisson equation. We observe computational speedups of ~10 6 when compared to brute-force omnidirectional integration methods, enabling the treatment of grids of ~10 9 points and potentially even larger in a desktop setup at the time of publication. Further examination of the boundary conditions of our one-shot method shows that omnidirectional pressure integration implements a boundary condition where the boundary points are treated as interior points to the extent that information is available. Finally, we show how the method can be extended from the regular grids typical of particle image velocimetry to the unstructured meshes characteristic of particle tracking velocimetry data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Mesoscale to Microscale Simulations over Complex Terrain with the Immersed Boundary Method in the Weather Research and Forecasting Model

Improvements to the Weather Research and Forecasting (WRF) Model are made to enable multiscale simulations over highly complex terrain with dynamically downscaled boundary conditions from the mesoscale to the microscale. Over steep terrain, the WRF Model develops numerical errors that are due to grid deformation of the terrain-following coordinates. An alternative coordinate system, the immersed boundary method (IBM), has been implemented into WRF, allowing for simulations over highly complex terrain; however, the new coordinate system precluded nesting within mesoscale simulations using WRF’s native terrain-following coordinates. Here, the immersed boundary method and WRF’s grid-nesting framework are modified to seamlessly work together. This improved framework for the first time allows for large-eddy simulation over complex (urban) terrain with IBM to be nested within a typical mesoscale WRF simulation. Simulations of the Joint Urban 2003 field campaign in Oklahoma City, Oklahoma, are performed using a multiscale five-domain nested configuration, spanning horizontal grid resolutions from 6 km to 2 m. These are compared with microscale-only simulations with idealized lateral boundary conditions and with observations of wind speed/direction and SF 6 concentrations from a controlled release from intensive observation period 3. The multiscale simulation, which is configured independent of local observations, shows similar model skill predicting wind speed/direction and improved skill predicting SF 6 concentrations when compared with the idealized simulations, which require use of observations to set mean flow conditions. Use of this improved multiscale framework shows promise for enabling large-eddy simulation over highly complex terrain with dynamically downscaled boundary conditions from mesoscale models.

42 ENGINEERING↗

DOE OSTI2024

Eco-driving Profile Optimization by Dynamic Programming for Battery Electric Vehicles

Although full automation has not yet been achieved, automated vehicles are a valid research area. Not only would automated vehicles provide ultimate driver convenience, but they would maximize energy efficiency by eliminating undesired human driving behaviors and optimally controlling the powertrain. From the perspective of control related to energy saving, speed profile optimization is important for improving system efficiency and satisfying passenger demands. This study employs Dynamic Programming (DP) to solve the constrained optimal problem for travel time, distance, and speed limit by exploring all possible control options. The solutions obtained by DP demonstrate consistent control patterns combining four control modes-acceleration, cruising, coasting, and braking, with cruising or coasting being selective depending on the boundary conditions. Further, this study introduces DP-based simulation results and attempts to provide comprehensive interpretations of the optimal policy by analyzing the essential factors that affect the control problem, including boundary conditions, road load, and powertrain characteristics. Based on these interpretations, the control concepts can be explained as the optimal policy selecting the best control option based on system efficiency and boundary conditions. The results of DP are compared with a human-like driver model to show that the optimal speed profiles can effectively reduce energy consumption.

Autonomous vehicles↗

DOE OSTI2024

Perfectly Matched Layers and Characteristic Boundaries in Lattice Boltzmann: Accuracy vs Cost

Artificial boundary conditions (BCs) play a ubiquitous role in numerical simulations of transport phenomena in several diverse fields, such as fluid dynamics, electromagnetism, acoustics, geophysics, and many more. They are essential for accurately capturing the behavior of physical systems whenever the simulation domain is truncated for computational efficiency purposes. Ideally, an artificial BC would allow relevant information to enter or leave the computational domain without introducing artifacts or unphysical effects. Boundary conditions designed to control spurious wave reflections are referred to as nonreflective boundary conditions (NRBCs). Another approach is given by the perfectly matched layers (PMLs), in which the computational domain is extended with multiple dampening layers, where outgoing waves are absorbed exponentially in time. Here, in this work, the definition of PML is revised in the context of the lattice Boltzmann method. The impact of adopting different types of BCs at the edge of the dampening zone is evaluated and compared, in terms of both accuracy and computational costs. It is shown that for sufficiently large buffer zones, PMLs allow stable and accurate simulations even when using a simple zeroth-order extrapolation BC. Moreover, employing PMLs in combination with NRBCs potentially offers significant gains in accuracy at a modest computational overhead, provided the parameters of the BC are properly tuned to match the properties of the underlying fluid flow.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Gaussian process regression constrained by boundary value problems

We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and boundary conditions, but for which only scattered observations of the source term are available. Scattered observations of the solution may also be used in the regression. The framework combines co-kriging with the linear transformation of a Gaussian process together with the use of kernels given by spectral expansions in eigenfunctions of the boundary value problem. Furthermore, it benefits from a reduced-rank property of covariance matrices. We demonstrate that the resulting framework yields more accurate and stable solution inference as compared to physics-informed Gaussian process regression without boundary condition constraints.

42 ENGINEERING↗

DOE OSTI2022

Bulk and boundary quantum phase transitions in a square Rydberg atom array

Motivated by recent experimental realizations of exotic phases of matter on programmable quantum simulators, we carry out a comprehensive theoretical study of quantum phase transitions in a Rydberg atom array on a square lattice, with both open and periodic boundary conditions. In the bulk, we identify several first-order and continuous phase transitions by performing large-scale quantum Monte Carlo simulations and develop an analytical understanding of the nature of these transitions using the framework of Landau-Ginzburg-Wilson theory. Remarkably, we find that under open boundary conditions, the boundary itself undergoes a second-order quantum phase transition, independent of the bulk. These results explain recent experimental observations and provide important insights into both the adiabatic state preparation of novel quantum phases and quantum optimization using Rydberg atom array platforms.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Bounce-averaged theory in arbitrary multi-well plasmas: solution domains and the graph structure of their connections

Bounce-averaged theories provide a framework for simulating relatively slow processes, such as collisional transport and quasilinear diffusion, by averaging these processes over the fast periodic motions of a particle on a closed orbit. This procedure dramatically increases the characteristic time scale and reduces the dimensionality of the modelled system. The natural coordinates for such calculations are the constants of motion (COM) of the fast particle motion, which by definition do not change during an orbit. However, for sufficiently complicated fields – particularly in the presence of local maxima of the electric potential and magnetic field – the COM are not sufficient to specify the particle trajectory. In such cases, multiple domains in COM space must be used to solve the problem, with boundary conditions enforced between the domains to ensure continuity and particle conservation. Previously, these domains have been imposed by hand, or by recognising local maxima in the fields, limiting the flexibility of bounce-averaged simulations. Here, we present a general set of conditions for identifying consistent domains and the boundary condition connections between the domains, allowing the application of bounce-averaged theories in arbitrarily complicated and dynamically evolving electromagnetic field geometries. We also show how the connections between the domains can be represented by a directed graph, which can help to succinctly represent the trajectory bifurcation structure.

fusion plasma↗

DOE OSTI2021

Upscaling Reactive Transport and Clogging in Shale Microcracks by Deep Learning

Fracture networks in shales exhibit multiscale features. A rock system may contain a few main fractures and thousands of microcracks, whose length and aperture are orders of magnitude smaller than the former. It is computationally prohibitive to resolve all the fractures explicitly for such multiscale fracture networks. One traditional approach is to model the small-scale features (e.g., microcracks in shales) as an effective medium. Although this fracture-matrix conceptualization significantly reduces the problem complexity, there are classes of physical processes that cannot be accurately upscaled by effective medium approximations, e.g., microcrack clogging during mineral reactions. Here, we employ deep learning in place of effective medium theory to upscale physical processes in small-scale features. Specifically, we consider reactive transport in a fracture-microcrack network where microcracks can be clogged by precipitation. A deep learning multiscale algorithm is developed, in which the microcracks are upscaled as a wall boundary condition of the main fractures. The wall boundary condition is constructed by recurrent neural networks, which take concentration histories as input and predict the solute transport from main fractures to microcracks. The deep learning multiscale algorithm is firstly employed in specific scenarios, then a general model is developed which can work under various conditions. The new approach is validated against fully resolved simulations and an analytical solution, providing a reliable and efficient solution for problems that cannot be upscaled by effective medium models.

58 GEOSCIENCES↗

DOE OSTI2023

1-D coupled surface flow and transport equations revisited via the physics-informed neural network approach

The de Saint-Venant equation (SVE) and advection–diffusion equation (ADE) are commonly employed to solve solute transport problems in surface water. In this work, we propose a mesh-free method based on the physics-informed neural network (PINN) to solve the one dimensional (1-D) SVE, ADE, and the coupled SVE and ADE (SVE-ADE) under various initial and boundary conditions. The PINN model extends the architecture of deep neural networks (DNNs) with implementation of loss function, which are additionally subject to constraints imposed by the physical laws of SVE and ADE, along with their initial and boundary conditions. In such a manner, PINNs can be quickly steered to the true solution while obeying the physical laws. The results of PINN model are compared with the analytical and/or numerical solutions under various conditions to investigate its accuracy and efficiency in solving the SVE, ADE, and SVE-ADE. Our results indicate PINN can accurately simulate the shock wave morphology and avoid numerical dissipation in unsteady flow condition. The PINN method outweighed traditional numerical methods in several aspects, including its ability to function with small amounts of data, no grid discretization, and random selection of sampling points, etc. Additionally, the PINN method is also suitable for solving inverse problems with sparse and noisy data. With 1% noise and 2000 initial and boundary condition points (N u ), the errors of the estimated flow rate (v) and diffusion coefficient (D) are 0.003% and 0.105%, respectively, which indicate the accuracy and robustness of the proposed method. Finally, our results indicate the capability and robustness of the proposed PINN methodology for solving multi-physics problems, irrespective of the presence of sparse and noisy data in the training dataset.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

CFD Simulations of Molten Salts Within Plasma-Facing Components with Twisted Tape Inserts Under One-Sided–Heated Conditions

For liquid immersion blankets (LIBs), the heat removal within different plasma-facing components (PFCs) requires substantial heat removal capabilities that could benefit from the usage of heat transfer enhancements. Of consideration are twisted tape insert heat transfer enhancements that are ribbon-like metal pieces inserted within cooling channels that increase fluid mixing, resulting in higher heat transfer and pressure drop. Unlike traditional applications, PFCs such as divertor coolant tubes experience a significantly higher heat flux on one side versus the other or entirely one-sided heating. These conditions are not well studied for molten salts where the higher Prandtl numbers characteristic of the fluids are significantly higher than water, gases, and liquid metals. As an effort to study this knowledge gap, large eddy simulations were done with Prandtl numbers representative of FLiBe at proposed operating conditions. In this study, the effects of applying a surface heat flux to one side of a tube versus the entire tube with a twisted tape insert were investigated for the heat transfer coefficient and effects on the temperature profile. The findings of the study suggest that for Prandtl number fluids above unity, the Nusselt number was largely unaffected by the change in boundary condition. Both boundary conditions showed good agreement with the Manglik and Bergles Nusselt number correlation for tight-fitting twisted tapes. Finally, the outcomes of this study will be useful for future design studies of LIBs to provide fundamental guidance implementing twisted tape inserts and their performance in one-sided–heated conditions.

molten salts↗