Results for “Refining” — Page 25

DOE OSTI2024

Thermal Integration of Advanced Nuclear Reactors with a Reference Refinery, Methanol Synthesis, and a Wood Pulp Plant (Rev.1)

The present report is intended to provide process flow diagrams (PFDs) and energy and mass balance data sheets for a U.S. industrial sector subset with which nuclear heat and power could be integrated—a subset that includes the oil refining, methanol and pulp and paper industries. Coupling options for integrating nuclear energy into these industries are quantitatively outlined for reference systems, and future work will extend this analysis in greater detail. Opportunities for integrating small modular nuclear reactors (SMNRs) were investigated for each of the industrial process configurations. Aspen HYSYS and Cycle-Tempo models for a high-temperature gas-cooled reactor were developed to evaluate the proposed integration. This introductory evaluation provides a general description and assessment of the operating principles, reactor coolant core outlet temperature, and reactor size to be integrated with industry. The industrial processes of oil refining and the production of methanol, pulp and paper were simulated by using Aspen HYSYS, Aspen Plus, and the PRELIM (Petroleum Refinery Life Cycle Inventory Model) tool to develop process details. Cycle-Tempo models then extend the process modeling results to obtain net energy demands (e.g., heat, steam, and electricity) when accounting for process steam and waste heat recovery. This information is intended to foster the analysis of integrating an SMNR to decarbonize industrial facilities. The SMNR would provide reliable, competitive, and sustainable clean energy while reducing carbon emissions and other environmental impacts, such as water withdrawals, consumption, and contamination. The refining industry, exhibited in Figure ES1, is a leading consumer of fossil -fuel-based heat, power, and hydrogen in the U.S. industrial sector, generating over 164 million metric tons (MMT) of CO 2 emissions in 2023. The overall mass and energy pertaining to a generalized complex refinery in the United States is reflected in Figure ES1, along with energy metrics regarding integration with a nuclear power plant (NPP). Data sheets were developed to indicate the energy requirements for the overall refinery and each refinery process. The data sheet for the overall refinery is shown in Table ES2.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

A Block-Structured Adaptive Mesh Framework to Solve Radiation Transfer Equation in Irregular Embedded Geometries

Radiation transport arises in various scientific, industrial, and medical fields, and understanding its effect in applications is needed to make accurate predictions, safety assessments and performance optimizations. Solving the Radiation Transport Equation (RTE) is challenging due to its integro-differential nature, which involves both differential and integral terms. The differential term describes the change in radiation intensity due to absorption and emission, while the integral term accounts for scattering. The accurate modeling of radiation is further complicated in many applications due to the complex, irregular geometries. Various methods exist for solving the RTE, including the zonal, Monte Carlo, spherical harmonics, discrete ordinates, and finite volume methods. Traditional mesh-based approaches, which rely on structured or unstructured meshes, struggle with irregular geometries due to: a) the difficulty of conforming structured grids to irregular domains, b) challenges in enforcing boundary conditions correctly, and c) the additional computational cost of unstructured mesh methods. This work presents a second-order accurate method for solving the RTE in irregular geometries. The radiation intensity is discretized using the finite-volume method in both spatial and angular directions on regular Cartesian grid blocks. Leveraging the block-structured adaptive mesh refinement (AMR) framework provided by AMReX, our method refines the grid locally to reduce spatial discretization error, ensuring a converged numerical solution while minimizing computational costs elsewhere. A two-stage deferred correction approach is employed: First, a first-order discretization on grid blocks is solved using an algebraic multigrid method in HYPRE. Second, a correction term is applied explicitly to achieve second-order accuracy. The correction term is calculated by approximating the radiation flux on cell faces using a Total Variation Diminishing (TVD) scheme. This approach ensures quick convergence of the multigrid method while preserving higher-order accuracy of the numerical solution. Irregular geometries are resolved as embedded boundaries (EB), resulting in both cut cells and regular cells. In cut cells, we modify the fluxes using face fractions and incorporate additional contributions from EB boundary conditions. To ensure higher-order convergence near the EB interface, the correction term is modified by interpolating the radiation intensity to fictitious ghost points. The implementation takes advantage of modern supercomputers by leveraging AMReX’sMPI/X parallelization strategy where X can be MPI or a GPU accelerator including CUDA, HIP and DPC++. We validate our solver using classical test cases, both with and without EB, demonstrating accuracy and efficiency. Additionally, we analyze the impact of adaptive mesh refinement on solution accuracy and computational cost, highlighting the advantages of our approach for high-resolution radiation transport simulations.

computational fluid dynamics (CFD)↗

DOE OSTI2025

Detection and Association of Operational Events using DAS and Seismometers (FY 2025 Mid-Year Report)

This mid-year report summarizes ongoing work to identify anomalous vibration signals indicative of potential containment breaches. This work includes compiling continuous seismic datasets and testing and refining underground detection and geolocation techniques. In the first two quarters of FY25, we have completed two project work plan tasks: (1) creating a database of continuous waveforms and ground truth event data from multiple modalities and (2) refining and implementing a detection and association algorithm to create a catalog of anomalous underground activities. This report contains a summary of the seismic database including the continuous seismic data collected by a dense array of surface seismic stations above Pleasant Gap Mine, and continuous seismic data collected using subsurface distributed acoustic sensing (DAS) in the subsurface at Sanford Underground Research Facility (SURF) and the ground truth information gathered from both sites. This report also includes results from refining and applying a dynamic power spectral density detector to both continuous seismic datasets. Finally, the report provides an initial catalog of subsurface operational events from both sensing modalities.

58 GEOSCIENCES↗

DOE OSTI2026

Long-Duration High-Resolution Large-Eddy Simulations of Hurricane Laura (2020) for Infrastructure Design

This dataset provides long-duration large-eddy simulations (LES) of Hurricane Laura (2020), capturing the turbulent boundary-layer wind field during the storm's passage at horizontal grid spacings of 55.55 m and 10 m. Hurricane Laura made landfall as a Category 4 storm in southwestern Louisiana at 06:00 UTC on 27 August 2020, producing widespread damage to coastal infrastructure. The simulations characterize the spatial and temporal variability of the turbulent wind at heights spanning the lowest 300 m of the boundary layer, throughout the approach and passage of the storm's eyewall over a fixed location. To resolve the spatial heterogeneity of wind and turbulence conditions across the storm, seven independent refined LES runs are performed at radial locations spanning the storm relative to its direction of motion. The refinement positions are defined on a normalized radial coordinate r ̂=r/R, where R≈21 km is Laura's radius of maximum wind, and lie between r ̂=-1.5 and r ̂=+1.5 in ∆r ̂=0.5 increments along a line perpendicular to the storm's track at the midpoint of the simulation. Negative r ̂ corresponds to locations south-southwest of the storm center and positive r ̂ to locations north-northeast. The dataset is segmented into seven radial refinement groups.

17 WIND ENERGY↗

DOE OSTI2023

Controlling the Plastic Anisotropy of Magnesium Alloy by Tailoring the Grain Size and Yttrium Content

Hexagonal close-packed (HCP) magnesium alloys are widely used in automotive and aerospace industries due to their low density and high specific-strength. Their applicability is mainly restricted due to poor formability and pronounced plastic anisotropy. The formability is usually improved by altering the chemistry (adding rare-earth elements like Y) or modulating the microstructure (e.g., grain refinement). However, grain refinement alone cannot yield the desired ductility, and the scarcity of rare-earth elements also limits the extent to which the alloying strategy can be used. To overcome these issues, in this work, it is proposed that the formability of Mg alloys can be improved by combining the grain refinement and alloying approaches. To quantitively explore this possibility, a crystal-plasticity-based constitutive model, which is sensitive to both alloying concentration and grain sizes, is developed. To demonstrate, the model is applied to study the combined effect of Y content and grain size on the mechanical responses of Mg alloy. The calculations are used to build maps of plastic anisotropy measures, such as tension–compression asymmetry ratio and Lankford coefficients, for a wide range of Y content and grain sizes. From these maps, the grain size that would yield the desired performance of Mg alloy for a fixed Y content can be identified. This work provides an accelerated pathway to optimize both the microstructure and chemistry simultaneously to achieve formability and to reduce the dependence on alloying.

36 MATERIALS SCIENCE↗

DOE OSTI2022

MAUD Interface Tool Kit (MILK)

Materials Analysis Using Diffraction (MAUD) is an open source Rietveld refinement program which fits diffraction models to diffraction spectra allowing quantitative diffraction analysis. The scripting interface developed here using python facilitates the choice of parameters to refine during the Rietveld fitting process and provides a simple MPI framework for running MAUD instances in parallel. The scripting language facilitates batch, custom, and reproducible Rietveld refinements of large datasets.

Savage, Daniel↗

DOE OSTI2020

The Port Hope Areas Initiative's Port Granby Project: The Decontamination of Site Equipment from a Low Level Waste Facility - 20330

The Port Hope Area Initiative (PHAI) is the Government of Canada's response to the community recommended solutions for the remediation and safe, long-term management of historic low-level radioactive waste (LLRW) that was the result of uranium and radium processing operations in the Municipality of Port Hope, Ontario from the 1930's to the 1980's. The Eldorado refinery, on the shores of Lake Ontario, began refining radium-226 from pitchblende ore, later transitioning to the refining of uranium ore. Process residues were deposited at the Welcome Waste Management Facility in Port Hope until the mid-1950's switching to the Port Granby Waste Management Facility (PGWMF), which continued to accept waste until the late 1980's. The Port Granby Project involves the construction of a new, secure long-term waste management facility (LTWMF) and supporting infrastructure, and the excavation and relocation of approximately 1,200,000 m{sup 3} of historic low-level radioactive waste and marginally contaminated soil from the PGWMF to the newly constructed LTWMF. Since the project's inception in 2016, the bulk of the material has since been moved to the final long term storage cell. This has taken over 500,000 person-hours and a large amount of one site heavy equipment to accomplish including excavators, bulldozers, rock trucks, baker tanks and vacuum trucks. While many of the pieces of heavy equipment and water management equipment has further work to do on site, several of the sites larger items have already undergone the decontamination process prior to release from the site. This process has posed a serious challenge as the waste has a caustic nature to it and over the last few years it has had time to work its way into the metallic structures and framework of the equipment. Coupled with the tight work spaces and in some cases confined work areas there have been many issues that needed to be addressed to successfully reach a state where items can be free released to the unrestricted limits of the sites license. This ongoing process has led to a more refined decontamination program at the Port Granby Facility and has had a rather high success rate considering the length of time the equipment has been exposed to the waste materials on site. This paper discusses the varied challenges of decontamination faced at a low-level radioactive waste facility with a focus on the following aspects: - Challenges faced regarding different equipment types and the solutions implemented by Wood to address these challenges; - An examination of various decontamination methods employed throughout the project; and - Lessons learned over three years of remediation work and how they impact the decontamination process. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2026

Hydrogeological assessment of CO2 containment assurance and wellbore integrity at a Gulf Coast storage site

Abstract A large-scale carbon capture and storage (CCS) initiative on the Texas Gulf Coast serves as a premier demonstration of the U.S. Department of Energy’s CarbonSAFE program. Targeting deep saline formations, specifically Oligo-Miocene deltaic sequences, the project aims to establish technical and commercial viability for geologic CO2 storage within a major industrial corridor. This study provides a rigorous hydrogeological assessment to support Class VI permitting by quantifying the high degree of containment security. Utilizing a compositional reservoir simulator, we developed a suite of 27 distinct simulation cases to evaluate vertical plume dynamics near both planned injection wells and proximal legacy infrastructure. To ensure numerical accuracy near wellbores, we implemented a refined mesh strategy, determining that a 5.6 ft × 5.6 ft grid refinement offered the optimal balance between computational efficiency and descriptive precision. The modeling framework utilized a systematic sensitivity-based approach to evaluate the mechanical redundancy of the subsurface system by performing a bounding analysis of wellbore interfaces against hypothetical high-permeability microannuli. By systematically isolating competing physical drivers, including permeability, porosity, gas hysteresis, thermal gradients, salinity, and solubility trapping (quantified via Henry’s law with dynamically adjusted coefficients), this work moves beyond binary assessments to establish a nuanced hierarchy of containment factors. The results confirm that primary trapping mechanisms (e.g., gas hysteresis and solubility), combined with the site's unique geomechanical stratigraphy, significantly restrict vertical mobility and reinforce the robust containment security of the reservoir. Baseline results demonstrate substantial vertical separation between the CO2 plume and the upper confining system, ensuring robust containment. Sensitivity analysis reveals that even under highly conservative bounding scenarios—assuming theoretical 10-Darcy pathways at specific wellbore locations—the 2,900-ft thick multi-layered confining zone remains a reliable barrier. In these hypothetical upper-bound cases, peak upward fluxes of CO2 and saltwater after 15 years of injection remain localized and dissipate rapidly within the lower sections of the confining interval, leaving the integrity of the seal uncompromised. Furthermore, the study identifies that while localized wellbore pathways define theoretical upper bounds of vertical migration, the Area of Review (AoR) is primarily sensitive to regional thermal gradients and hysteresis, which can influence the AoR by over 3,000 acres in pessimistic configurations. Also, primary trapping mechanisms, specifically gas hysteresis and solubility, work in tandem with the Gulf Coast’s unique geomechanical stratigraphy to significantly restrict vertical mobility. Ductile, smectite-rich mudstones facilitate natural borehole convergence and the self-healing of potential conduits, creating a natural geomechanical bridge that effectively mitigates migration potential at both current injection points and legacy-well locations. This comprehensive modeling effort demonstrates that the integration of high-resolution wellbore simulations and regional geomechanical observations confirms the long-term storage security of the studied site, providing a physics-based foundation for industrial-scale CCS deployments. This modeling framework establishes a baseline for future research into coupled geomechanical effects, such as time-dependent borehole convergence, to further refine long-term containment projections. Acknowledgements We thank the Gulf Coast Carbon Center (GCCC) at the Bureau of Economic Geology for foundational research support. We appreciate Alex Bump for technical guidance and David Hoffman for model mesh generation. This work used TACC’s Frontera cluster for simulations and CMG Ltd. software licenses provided to UT-Austin. This material is based upon work supported by the Department of Energy under Award Number DE-FE0032338. Disclaimer This material is based upon work supported by the U.S. Department of Energy’s Fossil Energy and Carbon Management Office under the CarbonSAFE program, award Number DE-FE0032338. The views expressed herein do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

58 GEOSCIENCES↗

DOE OSTI2026

Hydrogeological assessment of CO2 containment assurance and wellbore integrity at a Gulf Coast storage site

Abstract A large-scale carbon capture and storage (CCS) initiative on the Texas Gulf Coast serves as a premier demonstration of the U.S. Department of Energy’s CarbonSAFE program. Targeting deep saline formations, specifically Oligo-Miocene deltaic sequences, the project aims to establish technical and commercial viability for geologic CO2 storage within a major industrial corridor. This study provides a rigorous hydrogeological assessment to support Class VI permitting by quantifying the high degree of containment security. Utilizing a compositional reservoir simulator, we developed a suite of 27 distinct simulation cases to evaluate vertical plume dynamics near both planned injection wells and proximal legacy infrastructure. To ensure numerical accuracy near wellbores, we implemented a refined mesh strategy, determining that a 5.6 ft × 5.6 ft grid refinement offered the optimal balance between computational efficiency and descriptive precision. The modeling framework utilized a systematic sensitivity-based approach to evaluate the mechanical redundancy of the subsurface system by performing a bounding analysis of wellbore interfaces against hypothetical high-permeability microannuli. By systematically isolating competing physical drivers, including permeability, porosity, gas hysteresis, thermal gradients, salinity, and solubility trapping (quantified via Henry’s law with dynamically adjusted coefficients), this work moves beyond binary assessments to establish a nuanced hierarchy of containment factors. The results confirm that primary trapping mechanisms (e.g., gas hysteresis and solubility), combined with the site's unique geomechanical stratigraphy, significantly restrict vertical mobility and reinforce the robust containment security of the reservoir. Baseline results demonstrate substantial vertical separation between the CO2 plume and the upper confining system, ensuring robust containment. Sensitivity analysis reveals that even under highly conservative bounding scenarios—assuming theoretical 10-Darcy pathways at specific wellbore locations—the 2,900-ft thick multi-layered confining zone remains a reliable barrier. In these hypothetical upper-bound cases, peak upward fluxes of CO2 and saltwater after 15 years of injection remain localized and dissipate rapidly within the lower sections of the confining interval, leaving the integrity of the seal uncompromised. Furthermore, the study identifies that while localized wellbore pathways define theoretical upper bounds of vertical migration, the Area of Review (AoR) is primarily sensitive to regional thermal gradients and hysteresis, which can influence the AoR by over 3,000 acres in pessimistic configurations. Also, primary trapping mechanisms, specifically gas hysteresis and solubility, work in tandem with the Gulf Coast’s unique geomechanical stratigraphy to significantly restrict vertical mobility. Ductile, smectite-rich mudstones facilitate natural borehole convergence and the self-healing of potential conduits, creating a natural geomechanical bridge that effectively mitigates migration potential at both current injection points and legacy-well locations. This comprehensive modeling effort demonstrates that the integration of high-resolution wellbore simulations and regional geomechanical observations confirms the long-term storage security of the studied site, providing a physics-based foundation for industrial-scale CCS deployments. This modeling framework establishes a baseline for future research into coupled geomechanical effects, such as time-dependent borehole convergence, to further refine long-term containment projections. Acknowledgements We thank the Gulf Coast Carbon Center (GCCC) at the Bureau of Economic Geology for foundational research support. We appreciate Alex Bump for technical guidance and David Hoffman for model mesh generation. This work used TACC’s Frontera cluster for simulations and CMG Ltd. software licenses provided to UT-Austin. This material is based upon work supported by the Department of Energy under Award Number DE-FE0032338. Disclaimer This material is based upon work supported by the U.S. Department of Energy’s Fossil Energy and Carbon Management Office under the CarbonSAFE program, award Number DE-FE0032338. The views expressed herein do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

58 GEOSCIENCES↗

DOE OSTI2020

An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS

Here, we present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff–Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell’s mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith’s theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires C 1 -continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-α method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton–Raphson scheme. Finally, the interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.

42 ENGINEERING↗

DOE OSTI2022

GW-PINN: A deep learning algorithm for solving groundwater flow equations

Machine learning methods provide new perspective for more convenient and efficient prediction of groundwater flow. In this study, a deep learning method “GW-PINN” without labeled data for solving groundwater flow equations with wells was proposed. GW-PINN takes the physics inform neural network (PINN) as the backbone and uses either the hard or soft constraint in the loss function for training. A locally refined sampling strategy (LRS) is adopted to generate the consistent spatial sampling points for problems with strong hydraulic head change, and then combined with an appropriate temporal sampling scheme to obtain the final spatial-temporal sampling points. A snowball-style two-stage training strategy by dividing the temporal domain into two subdomains is designed to decrease the sampling points. Five cases were designed to test the training performance of GW-PINN under different sampling strategies and two constraints. The predicted results of GW-PINN were compared with MODFLOW and the analytical solution. The results demonstrate that GW-PINN possesses strong ability in capturing the hydraulic head change for both confined and un-confined aquifers. The hard constraint owns more robust learning ability than the soft constraint. The LRS strategy can generate more accurate results with much fewer sampling points than traditional sampling strategies, and the snowball-style two-stage training strategy is significantly efficient for problems with the drastic change of hydraulic head. Additionally, the application of GW-PINN as a surrogate model for parameterized groundwater flow equations is illustrated. This study provides an option tool for efficient groundwater flow simulation, especially for those with local refinements are needed.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

hp -VPINNs: Variational physics-informed neural networks with domain decomposition

We formulate a general framework for hp-variational physics-informed neural networks (hp-VPINNs) based on the nonlinear approximation of shallow and deep neural networks and hp-refinement via domain decomposition and projection onto the space of high-order polynomials. The trial space is the space of neural network, which is defined globally over the entire computational domain, while the test space contains piecewise polynomials. Specifically in this study, the hp-refinement corresponds to a global approximation with a local learning algorithm that can efficiently localize the network parameter optimization. Here, we demonstrate the advantages of hp-VPINNs in both accuracy and training cost for several numerical examples of function approximation and in solving differential equations.

42 ENGINEERING↗

DOE OSTI2022

Smoothed boundary method for simulating incompressible flow in complex geometries

Simulating flow through porous media with explicit considerations of complex microstructures is very challenging using conventional sharp-interface methods because of the difficulties in generating meshes conformal to complex geometries. In this work, a diffuse interface embedded boundary method known as the Smoothed Boundary Method (SBM) is utilized to facilitate simulations of fluid dynamics involving complex geometries. In diffuse-interface methods, the geometry is described by a domain parameter. The SBM allows the straightforward reformulation of the time-dependent Navier-Stokes equations in terms of this domain parameter, using only algebraic identities. Thus, enforcing the appropriate boundary conditions at the irregular embedded boundary is greatly simplified. Adaptive mesh refinement is used to increase the accuracy of the diffuse interface method by allowing thinner interfacial thickness to be used in the domain parameter. Here, the SBM-formulated Navier-Stokes equations are solved with the Finite Difference Method on refined mesh systems. Sharp-interface Finite Element Method simulations using the commercial software COMSOL on body-conforming meshes are also provided for comparison. Favorable agreement between the two methods is observed. Since it is no longer necessary for the mesh to conform to the complex geometry, the grid system for the SBM simulations can be generated rapidly and without additional manual interventions, making the entire simulation process more expedient.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Towards improved speed and accuracy of laser powder bed fusion simulations via multiscale spatial representations

Due to the growing popularity of laser powder bed fusion (LPBF) as a metal additive manufacturing technique, there is a strong need to be able to accurately predict build outcomes. Full fidelity simulations of this process are not feasible due to the vast range of length and time scales inherent to it. While part-scale codes for simulating residual stress and distortion have shown reasonable predictive capability, they often neglect many aspects of the process occurring over smaller length/time scales, and thus are unable to capture effects of process parameter adjustments or the behavior of fine features. One way of capturing aspects at more refined length scales is through the use of adaptive mesh refinement (AMR). AMR allows for the process to be simulated at scales approaching the physical spatial dimensions without drastically increasing the total degrees of freedom in the simulation. This manuscript describes the implementation of an AMR algorithm within a multiphysics, parallelized finite element code, and its application to the LPBF problem. In this work, part-scale examples are provided where the use of AMR has allowed for higher fidelity thermal and thermomechanical simulations, as compared to experimental measurements. Results from these higher resolution simulations show that while AMR is a necessary component for increased accuracy in a computationally efficient manner, other improvements are also necessary, including handling of the multiple time scales inherent to the problem and the need for improved AM-specific material models.

42 ENGINEERING↗

DOE OSTI2022

Effect of loading path on grain misorientation and geometrically necessary dislocation density in polycrystalline aluminum under reciprocating shear

Solid phase processing (SPP) is a promising alloy fabrication technique to produce fine and homogeneous grain structures for high-performance alloys. However, there is very limited modeling capability to understand and predict the grain refinement during SPP. In this work, the crystal plasticity theory was used to study elastic-plastic deformation in polycrystalline aluminums under large shear deformation. Two approaches, kernel averaged misorientation (KAM) and grain reference orientation deviation (GROD), were used to assess the grain misorientations. The geometrically necessary dislocation (GND) density was computed with the plastic strain rate. The deformation simulations were carried out under two loading conditions to investigate the effect of loading paths on the evolutions of grain misorientation and GND density. The results show that the regions with high misorientation and GND density first appear near grain boundaries. These regions then extend toward interior grains. The loading path affects dislocation system activation and dislocation recovery, hence dislocation evolution and misorientation. In conclusion, both two- and three-dimensional simulations showed that the spatial and temporal evolutions of GROD, KAM, and GND density in are closely correlated, which indicates they all can be used as criteria of grain refinement or recrystallization.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad–Shafranov equation by extension from polygonal subdomains

In this work, we propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modeling magnetic plasma equilibrium in axisymmetric confinement devices. In the fixed boundary case, the equation is posed on curved domains with piecewise smooth curved boundaries that may present corners. The solution method we present is based on the hybridizable discontinuous Galerkin method and sidesteps the need for geometry-conforming triangulations thanks to a transfer technique that allows to approximate the solution using only a polygonal subset as computational domain. Moreover, the solver features automatic mesh refinement driven by a residual-based a posteriori error estimator. As the mesh is locally refined, the computational domain is automatically updated in order to always maintain the distance between the actual boundary and the computational boundary of the order of the local mesh diameter. Numerical evidence is presented of the suitability of the estimator as an approximate error measure for physically relevant equilibria with pressure pedestals, internal transport barriers, and current holes on realistic geometries.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

An adaptive scalable fully implicit algorithm based on stabilized finite element for reduced visco-resistive MHD

The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution methods for MHD are extremely challenging due to disparate time and length scales, strong hyperbolic phenomena, and nonlinearity. Additionally, therefore the development of scalable, implicit MHD algorithms and high-resolution adaptive mesh refinement strategies is of considerable importance. In this work, we develop a high-order stabilized finite-element algorithm for the reduced visco-resistive MHD equations based on the MFEM finite element library (mfem.org). The scheme is fully implicit, solved with the Jacobian-free Newton-Krylov (JFNK) method with a physics-based preconditioning strategy. Our preconditioning strategy is a generalization of the physics-based preconditioning methods in Chacón et al. (2002) to adaptive, stabilized finite elements. Algebraic multigrid methods are used to invert sub-block operators to achieve scalability. A parallel adaptive mesh refinement scheme with dynamic load-balancing is implemented to efficiently resolve the multi-scale spatial features of the system. Our implementation uses the MFEM framework, which provides arbitrary-order polynomials and flexible adaptive conforming and non-conforming meshes capabilities. Results demonstrate the accuracy, efficiency, and scalability of the implicit scheme in the presence of large scale disparity. The potential of the AMR approach is demonstrated on an island coalescence problem in the high Lundquist-number regime (≥ 10 7 ) with the successful resolution of plasmoid instabilities and thin current sheets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

A cell-centered AMR-ALE framework for 3D multi-material hydrodynamics. Part I: Lagrangian and indirect Euler AMR algorithms

Many applications of physics and engineering involve wide ranges of time and spatial scales. The numerical simulation of localized small scales such as shock waves and material interfaces requires a large number of computational cells in these regions. For these applications, Lagrangian and Arbitrary-Lagrangian-Eulerian (ALE) related methods are engaging since the moving mesh feature naturally brings mesh cells on shock discontinuities and material interfaces are carefully captured. In addition, Adaptive-Mesh-Refinement (AMR) strategies aim to optimize computational resources by concentrating finer mesh cells only in areas of interest while using coarser cells elsewhere. A key but challenging AMR requirement consists in efficiently distributing the computational effort to achieve high accuracy without the prohibitive computational costs associated with uniformly fine grids. Here, in this document, the coupling of the p4est AMR library with a cell-centered Lagrangian scheme is presented with the goal to perform reliable 3D Lagrangian-AMR and indirect Euler-AMR multi-material simulations. In particular, it is shown that starting from a 3D indirect ALE code, the memory management and load balancing requirements can be delegated to an external library (here the p4est library) to unlock ALE-AMR capabilities. First, we present a strategy to transcribe the octant-based connectivity of the 3D AMR framework with that of an unstructured mesh of polygonal cells used in Lagrangian hydrodynamics. Then, we show how refinement and coarsening operations must be adapted to the particular Lagrangian framework to ensure the conservation of volume during those steps. Finally, several numerical test cases are presented that demonstrate the capabilities of the Lagrangian-AMR and indirect Euler-AMR algorithms.

3D cell-centered Lagrangian numerical scheme↗