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DOE OSTI2024

Parallel-in-Time Methods for Method-of-Lines Discretizations of Nonlinear Hyperbolic PDEs and Systems (Final Report)

The work for the subcontract is situated in the area of parallel-in-time integration for hyperbolic partial differential equations (PDEs). Parallel-in-time integration is an active area of research due to its ability to enable faster numerical simulations for applications throughout many areas of science. The work in this subcontract builds on a variety of results that were obtained, as part of the work performed for Subcontract No. B648355, for the Multigrid Reduction-in-Time (MGRIT) method from [1] applied to hyperbolic PDEs. This subcontract extends these results further to more efficient methods and to the case of method-of-lines discretizations for nonlinear hyperbolic PDES and systems of PDEs. The following is a summary of the research performed and results achieved during milestone periods 1, 2 and 3 by the PI (Hans De Sterck) and Postdoctoral Research Associate (Oliver Krzysik), for required tasks 1-4 (as listed in the Statement of Work): Research over the previous year has been split into three main projects: (i) solution of acoustic equation system; (ii) solution of nonlinear scalar hyperbolic PDEs; (iii) solution of nonlinear hyperbolic systems of PDEs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

High Power Targetry R&D and support for future generation accelerator

A high-power target system is a key beam element to complete future High Energy Physics (HEP) experiments. The target endures high power pulsed beam, leading to high cycle thermal stresses/pressures and thermal shocks. The increased beam power will also create significant challenges such as corrosion and radiation damage that can cause harmful effects on the material and degrade their mechanical and thermal properties during irradiation. This can eventually lead to the failure of the material and drastically reduce the lifetime of targets and beam intercepting devices. Designing a reliable target is already a challenge for MW class facilities today and has led several major accelerator facilities to operate at lower power due to target concerns. With present plans to increase beam power for next generation accelerator facilities in the next decade and the multi-year time-scale to acquire the knowledge on material behavior under such extreme environment, timely R&D of robust high-power targets is critical to fully secure the physics benefits of ambitious accelerator power upgrades. The next generation of high-power targets for future accelerators will use more complex geometries, novel materials, and new concepts allowing better high heat flux cooling methods. Advanced numerical simulations need to be developed to satisfy the physical design requirements of reliable beam-intercepting devices. In parallel, radiation hardened beam instrumentation irradiation methods for high-power targets must be further developed. Additional irradiation facilities are needed since only a few facilities worldwide offer beams for target testing, and the beam provided may not be appropriate for the specific facility or project. Thus, a comprehensive research and development program must be implemented to address the challenges that multi-MW targets face.

Pellemoine, F.↗

DOE OSTI2024

Topanga: A kinetic ion plasma code for large-scale ionospheric simulations on magnetohydrodynamic timescales

Topanga is a kinetic ion code developed for simulating large-scale plasma phenomena in the Earth's ionosphere on magnetohydrodynamic timescales. It is a domain-decomposed parallel code that runs on high-performance computing platforms. Features of Topanga include spherical geometry for simplified boundary conditions and computational efficiency; a hybrid plasma model with inertia-less fluid electrons, kinetic ions, and an electric field specified via an Ohm's law; a Maxwell-FDTD (finite difference time domain) plasma model which retains the displacement current in Maxwell's equations and models electron currents in the ionosphere with a tensor conductivity; sponge-layer boundary conditions for absorption of electromagnetic and plasma waves incident on the domain boundaries; and a novel mixed-implicit algorithm for evolving the EM fields inside the Maxwell-FDTD region that is stable over many orders of magnitude in the electron–ion collision frequency. We verify the numerical methods used in Topanga on a pair of test problems. The first test involves modeling a three-dimensional collisionless shock using the hybrid set of equations. The second test involves modeling a spherical TEM mode in vacuum using the Maxwell-FDTD set of equations. Finally, we demonstrate how using the combined set of hybrid and Maxwell-FDTD equations to model the Starfish Prime high-altitude nuclear test recovers a “missing” EM signal on the ground that is not present when using only the hybrid set of equations. The magnitude of this signal in the simulation containing the Maxwell-FDTD region agrees well with the E3a portion of the magnetohydrodynamic electromagnetic pulse from Starfish Prime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Investigating the Interaction Between Circulating Tumor Cells and Local Hydrodynamics via Experiment and Simulations

Introduction: The biological and mechanical properties of circulating tumor cells (CTCs) in combination with the hemodynamics affect the preference of metastatic sites in the vasculature. Despite the extensive literature on the effects of biological properties on cell adhesion, the effects of hydrodynamic forces on primary attachment remains an active area of research. Here, using simulations in conjunction with experimentation, we provide new insight into the interplay of CTCs dynamics and local hydrodynamics. Methods: A flow experiment of CTC attachment was performed within a bioprinted, double branching endothelialized vessel. Simulations of fluid flow and CTC transport in the reconstructed and idealized bifurcated vessel were respectively performed by HARVEY, our in-house massively parallel computational fluid dynamics solver. HARVEY is based on the lattice Boltzmann and finite element methods to model the fluid and cells dynamics. The immersed boundary method is employed for resolving the fluid–structure interaction. Results: CTC attachment was quantified experimentally at all regions of the complex vessel. The results demonstrate a clear preference for CTCs to attach at the branch points. To elucidate the effect of the vessel topology on the location of attachment, a fluid-only simulation was performed assessing the differences in the hydrodynamics along the vessel. CTC transport in idealized bifurcated vessels was subsequently studied to examine the effects of cell deformability on the local hydrodynamics patterns and, thus, the preference of attachment sites. Conclusions: The current work provides evidence on the correlation of the hydrodynamics forces arising from the vessel topology and CTC properties on the attachment regions.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2026

Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method

While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to improve the accuracy of deep learning-based solutions for time-dependent PDEs is to use the learned model as the coarse propagator in the Parareal method and a traditional numerical method as the fine solver. However, successful integration of deep learning into the Parareal method requires consistency between the coarse and fine solvers, particularly for PDEs exhibiting rapid changes such as sharp transitions. Here, to ensure this consistency, we propose using convolutional neural networks (CNNs) to learn the fully discrete time-stepping operator defined by the same numerical scheme employed as the fine solver. We demonstrate the effectiveness of the proposed method in solving the classical and mass-conservative Allen–Cahn (AC) equations. Through iterative updates in the Parareal algorithm, our approach achieves a significant computational speedup compared to traditional fine solvers while converging to high-accuracy solutions. Our results highlight that the proposed hybrid Parareal algorithm effectively accelerates simulations, particularly when implemented on multiple GPUs, and converges to the desired accuracy in only a few iterations. Another advantage of our method is that the CNN model is trained on trajectory-based data generated from random initial conditions, such that the trained model can be used to solve the AC equations with various initial conditions without retraining. This work demonstrates the potential of integrating neural network methods into parallel-in-time frameworks for efficient and accurate simulations of time-dependent PDEs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Coarse-grained simulation of colloidal self-assembly, cation exchange, and rheology in Na/Ca smectite clay gels

Knowledge Gap: The aggregation of clay minerals—layered silicate nanoparticles—strongly impacts fluid flow, solute migration, and solid mechanics in soils, sediments, and sedimentary rocks. Experimental and computational characterization of clay aggregation is inhibited by the delicate water-mediated nature of clay colloidal interactions and by the range of spatial scales involved, from 1 nm thick platelets to flocs with dimensions up to micrometers or more. Simulations: Using a new coarse-grained molecular dynamics (CGMD) approach, we predicted the microstructure, dynamics, and rheology of hydrated smectite (more precisely, montmorillonite) clay gels containing up to 2,000 clay platelets on length scales up to 0.1 μm. Further, simulations investigated the impact of simulation time, platelet diameters (6 to 25nm), and the ratio of Na to Ca exchangeable cations on the assembly of tactoids (i.e., stacks of parallel clay platelets) and larger aggregates (i.e., assemblages of tactoids). We analyzed structural features including tactoid size and size distribution, basal spacing, counterion distribution in the electrical double layer, clay association modes, and the rheological properties of smectite gels. Findings: Our results demonstrate new potential to characterize and understand clay aggregation in dilute suspensions and gels on a scale of thousands of particles with explicit representation of counterion clouds and with accuracy approaching that of all-atom molecular dynamics (MD) simulations. For example, our simulations predict the strong impact of Na/Ca ratio on clay tactoid formation and the shear-thinning rheology of clay gels.

42 ENGINEERING↗

DOE OSTI2026

Elevating SolTrace's Capabilities for the Next Generation of Concentrating Solar Analysis

SolTrace is an open-source Monte Carlo ray tracing software developed at NREL. SolTrace can characterize concentrating solar thermal (CST) collector optical performance and is CST technology agnostic. Shown in Fig. 1, SolTrace is a foundational tool in NREL's CST system and component modeling suite. SolTrace's generic surface elements can flexibly model novel collector and receiver designs to predict spatial and temporal flux distributions - critical to understand for CST component design, performance prediction, and system integration. Since its initial development, SolTrace has over 1,650 references on Google Scholar, over 9,800 downloads since 2017, and has served the CST research and development community as a benchmark of 3rd party verification. SolTrace provides users with many options for defining surface shape and boundaries. However, SolTrace provides limited documentation which can result in a steep learning curve for new users. Additionally, SolTrace lacks the computational performance required to evaluate optical performance of a CST system over the course of a year and/or iteratively over design parameters in a timely manner. To address this, we are working towards a new release of SolTrace that enables increased computational throughput by implementing ray tracing acceleration structures and enabling GPU parallelization. Additionally, we are working to improve SolTrace's usability, accessibility, and maintainability by (1) automating solar position time-dependent simulation processes, (2) creating general CST collector templates of grouped elements, (3) updating the user interface to better visualize model inputs and outputs, and (4) creating a user support network through forums, "how to" videos, and documentation.

14 SOLAR ENERGY↗

DOE OSTI2020

Large-Eddy Simulations of Idealized Atmospheric Boundary Layers Using Nalu-Wind

Accurate prediction of wind-plant performance relies, in part, on properly characterizing the turbulent atmospheric boundary layer (ABL) flow in which wind turbines operate. Large-eddy simulation (LES) is a powerful tool for simulating ABLs because it resolves the largest, most energetic scales of three-dimensional turbulent motions. Yet LES predictions are well known to depend on modeling choices such as grid resolution, numerical discretization schemes, and closures for unresolved scales of turbulence. Here, we evaluate how these choices influence predictions of ABL winds using Nalu-Wind, a wind-specific fork of the open-source, generalized, unstructured, massively parallel flow solver NaluCFD/Nalu.

17 WIND ENERGY↗

DOE OSTI2020

Cross-field electron diffusion due to the coupling of drift-driven microinstabilities

In this paper, the nonlinear interaction between kinetic instabilities driven by multiple ion beams and magnetized electrons is investigated. Electron diffusion across magnetic field lines is enhanced by the coupling of plasma instabilities. Here, a two-dimensional collisionless particle-in-cell simulation is performed accounting for singly and doubly charged ions in a cross-field configuration. Consistent with prior linear kinetic theory analysis and observations from coherent Thomson scattering experiments, the present simulations identify an ion-ion two-stream instability due to multiply charged ions (flowing in the direction parallel to the applied electric field) which coexists with the electron cyclotron drift instability (propagating perpendicular to the applied electric field and parallel to the ExB drift). Small-scale fluctuations due to the coupling of these naturally driven kinetic modes are found to be a mechanism that can enhance cross-field electron transport and contribute to the broadening of the ion velocity distribution functions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Toward a 2D Local Implementation of Quantum Low-Density Parity-Check Codes

Geometric locality is an important theoretical and practical factor for quantum low-density parity-check (qLDPC) codes that affects code performance and ease of physical realization. For device architectures restricted to two-dimensional (2D) local gates, naively implementing the high-rate codes suitable for low-overhead fault-tolerant quantum computing incurs prohibitive overhead. In this work, we present an error-correction protocol built on a bilayer architecture that aims to reduce operational overheads when restricted to 2D local gates by measuring some generators less frequently than others. We investigate the family of bivariate-bicycle qLDPC codes and show that they are well suited for a parallel syndrome-measurement scheme using fast routing with local operations and classical communication (LOCC). Through circuit-level simulations, we find that in some parameter regimes, bivariate-bicycle codes implemented with this protocol have logical error rates comparable to the surface code while using fewer physical qubits. Published by the American Physical Society 2025

Berthusen, Noah (ORCID:0000000275862786)↗

DOE OSTI2021

Artificial Intelligence for Multiphysics Nuclear Design Optimization with Additive Manufacturing

The geometric flexibility of additively manufactured metals and ceramics generates a very large and open design space that requires advanced modeling and simulation tools for physics simulations and the rigorous definition of design problems. This effort deploys artificial intelligence (AI) and machine learning (ML) algorithms to understand the design space, evaluate potential designs, and more efficiently generate optimized results. The Transformational Challenge Reactor (TCR) program is leveraging advances in several scientific areas—including materials, manufacturing, sensors and control systems, data analytics, and high-fidelity modeling and simulation—to accelerate the design, manufacturing, qualification, and deployment of advanced nuclear energy systems. Through a manufacturing-informed design approach, the TCR program seeks to integrate digital data for rapid nuclear innovation; accelerate the adoption of advances in manufacturing, materials, and computational sciences for nuclear applications; and dramatically reduce deployment costs and timelines for new nuclear reactor technologies. This report documents efforts under the TCR program to leverage advanced modeling and simulation techniques driven by AI/ML algorithms on high-performance computing (HPC) systems to yield more optimized TCR core designs. A multiphysics ML surrogate model was developed to run on the HPC architectures. The surrogate model is trained on high-fidelity simulation data of coupled neutronics and thermofluidics and is used to quickly evaluate thousands of candidate core designs in parallel, which drives the evolution of the cooling channel shapes to minimize temperature peaking and material stress. Outcomes from these activities provide design information and feedback into the core design efforts.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Climate Model Output Rewriter

The Climate Model Output Rewriter (CMOR) software was first developed by LLNL’s PCMDI program in early 2000s and was formally released with v1.0 (July 2006), v2.0 (January 2011), and v3.1(June 2016). CMOR is used to produce Climate and Forecast Convention (http://cfconventions.org/) CF-compliant netCDF files, in the standard format required to satisfy the World Climate Research Program (WCRP) Coupled Model Intercomparison Project (CMIP). The software has been used across multiple phases of the Earth System Modeling (ESM) project CMIP (CMIP3, CMIP5, CMIP6, and planned use in CMIP7) along with numerous parallel projects focused on preparation observations for use in model evaluation (obs4MIPs) and forcing datasets (input4MIPs) to guide ESM simulations to meet strict experimental protocols. More information can be obtained from the CMOR website and code repositories: https://cmor.llnl.gov/; https://github.com/pcmdi/cmor; https://github.com/PCMDI/cmor3_documentation The ESM variable definitions used as input for CMOR can also be viewed in code repositories: https://github.com/PCMDI/cmip3-cmor-tables/; https://github.com/PCMDI/cmip5-cmor-tables/; https://github.com/PCMDI/cmip6-cmor-tables/

Mauzey, ChristopherF↗

DOE OSTI2024

Experimental Investigation of Low-Frequency Distributed Acoustic Sensor Responses to Two Parallel Propagating Fractures

Low-frequency distributed acoustic sensing (LF-DAS) is a diagnostic tool for hydraulic fracture propagation with far-field monitoring using fiber optic sensors. LF-DAS senses strain rate variation caused by stress field change due to fracture propagation. Fiber optic sensors are installed in the monitoring wells in the vicinity of a fractured well. From the strain responses, fracture propagation can be evaluated. To understand subsurface conditions with multiple propagating fractures, a laboratory-scale hydraulic fracture experiment was performed simulating the LF-DAS response to fracture propagation with embedded distributed optical fiber strain sensors under these conditions. The experiment was performed using a transparent cube of epoxy with two parallel radial initial flaws centered in the cube. Fluid was injected into the sample to generate fractures along the initial flaws. The experiment used distributed high-definition fiber optic strain sensors with tight spatial resolutions. The sensors were embedded at two different locations on opposite sides of the initial flaws, serving as observation/monitoring locations. We also employed finite element modeling to numerically solve the linear elastic equations of equilibrium continuity and stress–strain relationships. The measured strains from the experiment were compared to simulation results from the finite element model. The experimentally derived strain and strain-rate waterfall plots from this study show the responses to both fractures propagating, while the fracture at the lower position took most of the fluid during the experiment. Interestingly, a fracture first began propagating from the upper flaw of the two flaws, but once the lower fracture was initiated, it grew much faster than the upper fracture. Both fibers were intercepted by the lower fracture, further verifying the strain signature as a fracture is approaching and intersecting an offset fiber.

Chemistry↗

DOE OSTI2022

N and P constrain C in ecosystems under climate change: Role of nutrient redistribution, accumulation, and stoichiometry

Abstract We use the Multiple Element Limitation (MEL) model to examine responses of 12 ecosystems to elevated carbon dioxide (CO 2 ), warming, and 20% decreases or increases in precipitation. Ecosystems respond synergistically to elevated CO 2 , warming, and decreased precipitation combined because higher water‐use efficiency with elevated CO 2 and higher fertility with warming compensate for responses to drought. Response to elevated CO 2 , warming, and increased precipitation combined is additive. We analyze changes in ecosystem carbon (C) based on four nitrogen (N) and four phosphorus (P) attribution factors: (1) changes in total ecosystem N and P, (2) changes in N and P distribution between vegetation and soil, (3) changes in vegetation C:N and C:P ratios, and (4) changes in soil C:N and C:P ratios. In the combined CO 2 and climate change simulations, all ecosystems gain C. The contributions of these four attribution factors to changes in ecosystem C storage varies among ecosystems because of differences in the initial distributions of N and P between vegetation and soil and the openness of the ecosystem N and P cycles. The net transfer of N and P from soil to vegetation dominates the C response of forests. For tundra and grasslands, the C gain is also associated with increased soil C:N and C:P. In ecosystems with symbiotic N fixation, C gains resulted from N accumulation. Because of differences in N versus P cycle openness and the distribution of organic matter between vegetation and soil, changes in the N and P attribution factors do not always parallel one another. Differences among ecosystems in C‐nutrient interactions and the amount of woody biomass interact to shape ecosystem C sequestration under simulated global change. We suggest that future studies quantify the openness of the N and P cycles and changes in the distribution of C, N, and P among ecosystem components, which currently limit understanding of nutrient effects on C sequestration and responses to elevated CO 2 and climate change.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Oblique instability of quasi-parallel whistler waves in the presence of cold and warm electron populations

Whistler waves propagating nearly parallel to the ambient magnetic field experience a nonlinear instability due to transverse currents when the background plasma has a population of sufficiently low energy electrons. Intriguingly, this nonlinear process may generate oblique electrostatic waves, including whistlers near the resonance cone with properties resembling oblique chorus waves in the Earth’s magnetosphere. Focusing on the generation of oblique whistlers, earlier analysis of the instability is extended here to the case where low-energy background plasma consists of both a “cold” population with energy of a few eV and a “warm” electron component with energy of the order of 100 eV. This is motivated by spacecraft observations in the Earth’s magnetosphere where oblique chorus waves were shown to interact resonantly with the warm electrons. The main new results are: 1) the instability producing oblique electrostatic waves is sensitive to the shape of the electron distribution at low energies. In the whistler range of frequencies, two distinct peaks in the growth rate are typically present for the model considered: a peak associated with the warm electron population at relatively low wavenumbers and a peak associated with the cold electron population at relatively high wavenumbers; 2) overall, the instability producing oblique whistler waves near the resonance cone persists (with a reduced growth rate) even in the cases where the temperature of the cold population is relatively high, including cases where cold population is absent and only the warm population is included; 3) particle-in-cell simulations show that the instability leads to heating of the background plasma and formation of characteristic plateau and beam features in the parallel electron distribution function in the range of energies resonant with the instability. The plateau/beam features have been previously detected in spacecraft observations of oblique chorus waves. However, they have been attributed to external sources and have been proposed to be the mechanism generating oblique chorus. In the present scenario, the causality link is reversed and the instability generating oblique whistler waves is shown to be a possible mechanism for formation of the plateau and beam features.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Comparison of water nanodroplet properties on different graphite-based substrates

The molecular structure and dynamics of water differ considerably at various interfaces. We compare the interfacial water structure–property relationship on three different carbon substrates, namely, amorphous carbon, compressed expanded natural graphite, and pure graphite by utilizing atomistic molecular dynamics simulations. The effect of different substrates on the structural and dynamical properties of water can readily be observed. Here, the density distributions parallel and normal to the substrates show oblate droplet structures. The normal to the substrate water distribution shows a strong hydration layer at the interface that does not vary with substrates. However, the disparity in the structure and dynamics on three different substrates shows that the surface morphologies of the substrates are critical for determining nanoscale water properties. Furthermore, it is observed that the formation of an interfacial water layer or the hydration layer is a direct consequence of both water “confinement” at the nanoscale and “attraction” between water molecules and the carbon substrates.

42 ENGINEERING↗

DOE OSTI2021

Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis (V.6.14) (Theory Manual)

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Theory Manual (V.6.15)

97 MATHEMATICS AND COMPUTING↗