A high-order discontinuous Galerkin method for compressible interfacial flows with consistent and conservative Phase Fields
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White, William J. (ORCID:0000000322164500)↗
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Results for “Phase field method”
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A Thermo‐Flow‐Mechanics‐Fracture Model Coupling a Phase‐Field Interface Approach and Thermo‐Fluid‐Structure Interaction
This work proposes a novel approach for coupling non-isothermal fluid dynamics with fracture mechanics to capture thermal effects within fluid-filled fractures accurately. This method addresses critical aspects of calculating fracture width in enhanced geothermal systems, where the temperature effects of fractures are crucial. The proposed algorithm features an iterative coupling between an interface-capturing phase-field fracture method and interface-tracking thermo-fluid-structure interaction using arbitrary Lagrangian–Eulerian coordinates. We use a phase-field approach to represent fractures and reconstruct the geometry to frame a thermo-fluid-structure interaction problem, resulting in pressure and temperature fields that drive fracture propagation. We developed a novel phase-field interface model accounting for thermal effects, enabling the coupling of quantities specific to the fluid-filled fracture with the phase-field model through the interface between the fracture and the intact solid domain. We provide several numerical examples to demonstrate the capabilities of the proposed algorithm. In particular, we analyze mesh convergence of our phase-field interface model, investigate the effects of temperature on crack width and volume in a static regime, and highlight the method's potential for modeling slowly propagating fractures.
fracture↗
Sprain energy consequences for damage localization and fracture mechanics
The 2023 smooth Lagrangian Crack-Band Model (slCBM), inspired by the 2020 invention of the gap test, prevented spurious damage localization during fracture growth by introducing the second gradient of the displacement field vector, named the “sprain,” as the localization limiter. The key idea was that, in the finite element implementation, the displacement vector and its gradient should be treated as independent fields with the lowest ( C 0 ) continuity, constrained by a second-order Lagrange multiplier tensor. Coupled with a realistic constitutive law for triaxial softening damage, such as microplane model M7, the known limitations of the classical Crack Band Model were eliminated. Here, we show that the slCBM closely reproduces the size effect revealed by the gap test at various crack-parallel stresses. To describe it, we present an approximate corrective formula, although a strong loading-path dependence limits its applicability. Except for the rare case of zero crack-parallel stresses, the fracture predictions of the line crack models (linear elastic fracture mechanics, phase-field, extended finite element method (XFEM), cohesive crack models) can be as much as 100% in error. We argue that the localization limiter concept must be extended by including the resistance to material rotation gradients. We also show that, without this resistance, the existing strain-gradient damage theories may predict a wrong fracture pattern and have, for Mode II and III fractures, a load capacity error as much as 55%. Finally, we argue that the crack-parallel stress effect must occur in all materials, ranging from concrete to atomistically sharp cracks in crystals.
Science & Technology - Other Topics↗
Southwest Regional Partnership on Carbon Sequestration: Phase III (Final Scientific/Technical Report)
The Southwest Regional Partnership on Carbon Sequestration (SWP) is one of 7 regional partnerships formed in 2003 under the U.S. Department of Energy’s (DOE) Regional Carbon Sequestration Partnerships (RCSPs) initiative. The overall purpose of the initiative was to help determine and implement the technology, infrastructure, and regulations most appropriate to promote carbon storage in different regions of the country. Covering Arizona, Colorado, New Mexico, Oklahoma, Utah, and parts of Texas, Wyoming, and Kansas, the SWP evaluated regional carbon storage and utilization potential and focused on technologies and sites that could complement the region’s strong position in energy production. The project progressed through three phases: • Phase I (2003–2005): Characterized regional geologic formations and CO 2 sources, assessed sequestration potential, and identified pilot test sites. • Phase II (2005–2013): Conducted small-scale field tests to validate sequestration methods, including geologic and terrestrial projects. • Phase III (2008–2022): Demonstrated large-scale CO 2 injection at a commercial oil field to test monitoring, verification, and long-term storage strategies. This report covers Phase III. The final project site, the Farnsworth Unit (FWU) in Texas, provided real-world testing of reservoir characterization, monitoring, and risk evaluation tools and processes that could be used in any commercial scale carbon capture, utilization, and storage (CCUS) project. Extensive data collection and analysis helped refine best practices for reservoir characterization, injection monitoring, and storage verification. The SWP contributed to national databases, DOE best practice manuals, and regional geological assessments to support future sequestration efforts. Key lessons learned include the importance of robust data management, strategic site selection, regulatory navigation, and effective industry collaboration. The project’s findings will inform ongoing and future carbon storage initiatives. Task 1 (Regional Characterization) • The SWP continued to participate in national outreach efforts and NATCARB. • The SWP evaluated multiple potential sites before selecting the FWU as the primary field test location. Task 2 (Public Outreach and Education) • The SWP contributed to national databases, DOE best practice manuals, and regional geological assessments to support future sequestration efforts. Task 3 (Permitting and Regulatory Compliance) • The SWP ensured compliance with federal and state regulations, including National Environmental Policy Act (NEPA) requirements. • The SWP obtained all necessary permits for drilling, injection, and monitoring activities. Task 4 (Site Characterization and Planning) • The SWP developed work plans for four key activities: characterization, simulation, monitoring and verification, and risk evaluation. • The SWP collected and synthesized legacy data from multiple sources to build initial static geological models and dynamic reservoir models demonstrating project feasibility. • The SWP conducted an initial risk evaluation and developed mitigation plans. Task 5 (Field Operations and Data Collection) • The SWP drilled, logged, and cored three characterization wells to gather critical subsurface data. • The SWP conducted multiple geophysical surveys, including 3D seismic, crosswell seismic, and vertical seismic profiling, to improve reservoir characterization. Task 6 (Monitoring and Verification) • The SWP performed extensive geological characterization using data from characterization wells and seismic surveys. • The SWP established a surface monitoring network to track CO 2 flux in soil gas, groundwater chemistry, and near-surface atmospheric CO 2 levels. • The SWP built and refined reservoir models to study the effects of relative permeability on simulation behavior and improve calibration with experimental data. Task 7 (Risk Assessment and Model Refinement) • The SWP conducted multiple studies to evaluate reservoir integrity, predict CO 2 plume behavior and improve predictive modeling capabilities. • The SWP refined geological models and used them to enhance the accuracy of simulation models. • The SWP continued quantitative risk assessment of top-ranked risks and strengthened the link between qualitative and quantitative risk methodologies.
02 PETROLEUM↗
High-speed quantitative X-ray multi-contrast imaging with deep learning based modulated pattern analysis
The advent of X-ray multi-contrast imaging methods, providing absorption, phase, and dark-field images, holds tremendous promise for complementary and non-destructive visualization of inner structures within materials and bio-samples. However, the low efficiency in measuring and analyzing X-ray modulated patterns has hindered their application in high-resolution in situ imaging. In this work, the Enhanced Scanning Pattern-based Imaging Neural Network (ESPINNet) is introduced as a powerful tool for achieving high-speed, high-resolution quantitative imaging. ESPINNet is faster than correlation-based speckle tracking methods such as XSVT and UMPA, and provides a balanced performance in terms of resolution and speed for data collection by using fewer scanning images. In comparison with our previously developed neural network, ESPINNet introduces the capability to generate dark-field images, further enhancing its versatility. By leveraging scanning patterns, ESPINNet significantly improves resolution and measurement precision. Furthermore, its adaptability to various modulation patterns, including those produced by sandpaper, coded masks, or gratings, ensures broad applicability. These features enable real-time 2D and 3D multi-contrast imaging, positioning ESPINNet as a transformative solution for applications in materials science and biomedical research, particularly for high-speed and in situ measurements.
X-ray at-wavelength metrology↗
Microstructure prediction for Ti-22Al-25Nb in laser powder bed fusion
This work presents a physics-informed framework for predicting solidification morphology and defect susceptibility in additively manufactured Ti–22Al–25Nb across a broad processing space. The framework integrates solidification microstructure selection (SMS) analysis with a single-track defect-based printability map to establish a unified methodology linking processing parameters to both interfacial morphology and manufacturability. Thermal gradients G and solidification rates R are first computed using the Thermo-Calc Additive Manufacturing (TC-AM) module, a finite-interface-dissipation (FID) phase-field (PF) model coupled with CALPHAD method is then employed to systematically distinguish planar and dendritic regimes as functions of $G$ and $R$. By superimposing the printability map onto the morphology projections, a comprehensive process–structure framework is obtained. Across most processing conditions, the predicted microstructure is predominantly dendritic, while planar growth emerges only under selected laser power $P$ and scan speed $v$ combinations. In addition to morphology classification, the framework quantifies the dendritic area fraction and introduces a width-based morphology descriptor to characterize the spatial extent of planar/dendritic regions within the melt pool. It provides mechanistic insight into the interplay between solidification physics and defect formation, offering practical guidance for parameter selection and microstructural control in Ti–22Al–25Nb additive manufacturing (AM).
36 MATERIALS SCIENCE↗
Automated and Accelerated Continuum Model Development for Electrochemical Systems (Abbreviated Report)
Despite the availability of computational resources and advancements in numerical computing capabilities, the multiscale models core to understanding, predicting the behaviors of, and designing energy and environmental systems involving porous media are still 1.) developed through by-hand derivations and 2.) limited by many methodological assumptions employed during model derivation. As a result, the advancement of effective media models for engineering DOE mission-critical systems (e.g., batteries, flow batteries, electrolyzers, geothermal systems, subsurface chemical storage systems, etc.) is slow (i.e., it takes years for models to traverse from stages of “development” to “practical utilization”), hindering our ability to effectively optimize such systems and stay at the cutting-edge of the energy frontier. In this work, we aimed to address these limitations by 1.) automating and accelerating multiscale model derivation via symbolic computing and 2.) develop a novel multiscale modeling methodology for flow and transport through porous media that avoids the typical assumptions hindering previous models. As a result of our efforts, we 1.) developed a hybrid symbolic-numeric code called Fouriera for fully-automating the implementation of multiphysical and phase-field models via the Fourier spectral method for materials science research, and 2.) advanced a multiscale modeling methodology called The Method of Finite Averages that rigorously predicts the behaviors of flow and transport through heterogeneous porous media under the influence of non-local effects and strong advection. Ultimately, these deliverables provide strong foundations from which further efforts can advance multiscale modeling tools and capabilities that do not intrinsically rely on 1.) the speed and mathematical capabilities of humans, nor 2.) the methodological assumptions limiting current models.
36 MATERIALS SCIENCE↗
Error field identification through torque balance on a saturated island in DIII-D
Measurement of the electromagnetic torque on a magnetic island could be an attractive method for error field identification in the early phase of ITER operation. Previous DIII-D experiments (Strait 2014 Nucl. Fusion 54 073004; Shiraki et al 2015 Plasma Phys. Control. Fusion 57 025016) have demonstrated the principle of this approach using a stationary or slowly rotating island, while recent developments in magnetic data analysis (Sweeney and Strait 2019 Phys. Plasmas 26 012509) allow the field of a rapidly rotating island to be readily distinguished from that of the wall currents induced by its rotation. In a recent experiment, a rotating n = 1 magnetic perturbation forced a saturated magnetic island to rotate, thus sampling all toroidal phases periodically in a single discharge. The phase and amplitude of the error field are inferred from analysis of the time-dependent torque balance on the island, including torques from the error field, the applied magnetic perturbation, and the wall currents induced by rotation of the applied perturbation and the island. Furthermore, results agree well with those from more conventional methods.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Second Harmonic Generation Electric Field Triplet Interferometry for Absolute Phasing
We report second harmonic generation (SHG) electric field triplet interferometry performed using three mutually coherent ultrafast pulses in a common path with controllable relative phases, namely, the light fields of a sample signal (SI), a reference oscillator (RO), and a local oscillator (LO). The ROLO phase determined from the interference of the light fields produced by two quartz wafers is subtracted from the phase determined from the SIROLO interferogram to yield the signal phase, ϕ SI . The new method also calibrates the measured SHG intensity from a given sample internally by sending the fundamental light field reflected from the sample into one of the quartz wafers in the ROLO element. The approach avoids having to exchange the sample against a reference material with a known χ(2) value or known phase and accounts on-the-fly for situations where the reflected fundamental light field intensity changes with experimental conditions. The new method is successfully benchmarked against z-cut α-quartz, fused silica held at its point of zero charge, and hematite nanolayers in air, across three different interferometers. Furthermore, the approach should be applicable for other second-order nonlinear spectroscopies, such as vibrational or electronic sum-frequency generation.
Interfaces↗
Phase-field modeling of orientation-dependent crack growth in ductile single crystals with anisotropic elasticity
Crack growth in ductile single crystals (DuSCs) is orientation dependent due to the anisotropies of crystal plasticity and elastic tensor. This study develops a phase-field model incorporating both crystal plasticity and crack growth and proposes a general method to decompose the elastic energy into compressive and tensile parts to prevent crack growth under compression in the phase-field description. The phase-field model, in combination with three Euler angles, is employed to simulate orientation-dependent crack growth in DuSCs. The contributions from crystal plasticity and anisotropic elasticity are compared, and the former is found to dominate in the anisotropy of crack growth in copper single crystals. Furthermore, the simulation results demonstrate that crystal orientation strongly affects the heterogeneous distribution of plastic strain and the interaction between plastic strain and crack growth. High-throughput phase-field simulations are performed with exhaustive crystal orientations, and the results are explained based on the anisotropy of the Taylor factor.
Computational Solid Mechanics↗
Inference of phase field fracture models
The phase field approach to modeling fracture uses a diffuse damage field to represent cracks. This representation mollifies singularities that arise in computations with sharp interface models and some of the resultant difficulties in the mathematical and numerical treatment of fracture. Phase field fracture models have proven effective at representing crack propagation, branching, and merging. Specific formulations, beginning with brittle fracture, have also been shown to converge to classical solutions. Extensions to cover the range of material failure, including ductile and cohesive fracture, lead to an array of possible models. There exists a large body of literature focusing on this class of models and on the impact of model form on the predicted crack evolution. However, there have not been systematic studies into how optimal models may be chosen. Here, we take a first step in this direction by developing formal methods for identification of the best parsimonious model of phase field fracture given full-field data on the damage and deformation fields. We consider some of the main models that have been used for the degradation of elastic response due to damage and its propagation. Our approach builds upon Variational System Identification (VSI), a weak form variant of the Sparse Identification of Nonlinear Dynamics (SINDy). Furthermore, in this first communication we focus on synthetically generated data but we also consider central issues associated with the use of experimental full-field data, such as data sparsity and noise.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Data for Propagation Method and Planting Density Influence Canopy Developmental Transition and Biomass Productivity in Miscanthus × giganteus
Understanding how establishment practices influence the mechanisms underlying Miscanthus × giganteus (miscanthus) productivity and canopy development is critical for optimizing management. Data was collected during the juvenile (2011–2013) and mature (2024) phases of a long-term field experiment established in Urbana, Illinois, to evaluate the effects of propagation method (plug propagation [PP] and rhizome propagation [RP]), planting density (1.0, 0.75, and 0.25 plants m⁻²), and nitrogen application (0 and 67 kg N ha⁻¹) on end-of-season biomass yield, tiller mass, tiller density, and tiller height. Linear regression models identified the dominant predictors of yield across stand ages and management regimes. Planting density, nitrogen (N) application, and propagation method significantly influenced early yield and canopy development. During the juvenile phase, biomass yield was driven by tiller density due to canopy expansion; in the mature phase, yield became driven by tiller mass. The PP plots produced higher tiller density than the RP plots, resulting in faster canopy closure and higher juvenile-phase yields. Rhizome-propagated (RP) plots produced lower tiller density, but individual tillers were 3.3–6.4 g tiller−1 heavier than PP tillers. After the canopy reached equilibrium, the PP and RP yields were similar because greater RP tiller mass compensated for its lower tiller density. Higher planting density resulted in greater yield and tiller density during the second year (2012), but this effect was absent from the third year (2013) onward. In the juvenile phase, N fertilization enhanced yield by 1.6–3.4 Mg ha−1. Initiating fertilization in 2013 on unfertilized plots produced biomass similar to that in fertilized plots, suggesting yield recovery in the mature phase. These findings revealed that establishment strategies, including propagation method and planting density, influence juvenile miscanthus canopy development and productivity, transitioning from tiller-density- to mass-dominated yields, but not mature phase productivity.
Miscanthus↗
Identifying Topological Defects in Lamellar Phases through Contour Analysis of Complex Wave Fields
Lamellar phases frequently contain structural imperfections that significantly affect their behaviors and properties. Our previous research successfully reconstructed real-space configurations of defective lamellar phases from diffuse scattering patterns, indicating the presence of phase vortices as a potential method for identifying topological defects disrupting the smectic ordering. Here, this report presents a mathematical framework using regularized wave fields to represent defective lamellar structures in real space. Phase singularities, resulting from the interference of random waves and indicating lamellar order disruption, are identified through a contour integral. These wave fields, derived from coherent scattering in reciprocal space, were validated via computational benchmarks analyzing small-angle neutron scattering data from AOT surfactant solutions, facilitating further statistical analysis of the defects. Our study highlights the potential to extract meaningful information about topological defects in lyotropic phases by inversely analyzing experimentally measured two-point static correlations. Our method allows for detailed structural analysis of various lyotropic phases, both particulate and nonparticulate, in their quiescent states and facilitates quantitative investigation of defects’ role in phase transitions. By integrating small-angle scattering, deep learning, and vortex tangle analysis, our comprehensive approach shows promise in addressing complex challenges in the structural analysis of soft matter systems.
36 MATERIALS SCIENCE↗
Gradient flow based phase-field modeling using separable neural networks
Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.
42 ENGINEERING↗
Referenceless, grating-based, single shot X-ray phase contrast imaging with optimized laser-driven K-α sources
With its ability to efficiently probe low-Z materials, X-ray phase imaging methods have recently raised high interest in multiple fields from biology and medical applications to high energy density (HED) physics. Initially developed with synchrotron light and X-ray tubes, we present a novel grating based Talbot X-ray deflectometer (TXD) diagnostic that was coupled with laser-generated K-α X-ray sources. The multi-terawatt laser (I > 1 × 10 14 W cm -2 ) was used as a testbed for diagnostic development. It was found that X-ray source chromaticity plays an important role in TXD. Indeed, the broadband spectrum of laser-generated X-ray sources may strongly impact image quality and thus diagnostic performance. We qualified X-ray emission from different laser-produced sources and determined laser, target, and deflectometer parameters that optimize TXD performance. We present the first results of referenceless grating-based X-ray imaging at high-power laser facilities and discuss the implications of this new development in HED research.
47 OTHER INSTRUMENTATION↗
A magnon band analysis of GdRu 2 Si 2 in the field-polarized state
Understanding the formation of skyrmions in centrosymmetric materials is a problem of fundamental and technological interest. GdRu 2 Si 2 is a candidate material that hosts a variety of multi-Q magnetic phases, including in zero-field. Here, inelastic neutron scattering is used to measure the spin excitations in the field-polarized phase of GdRu 2 Si 2 . Linear spin wave theory and a method of interaction invariant path analysis are used to derive a Hamiltonian accounting for the spectra. The Hamiltonian, dominated by bilinear (Ruderman-Kittel-Kasuya-Yosida) Heisenberg exchange, compares favorably to ab initio calculations. Dipolar interactions are a secondary energy scale to consider, with J D.D ~ 0.05 J RKKY . However, it is shown that in the field-polarized phase the dipolar interactions ‘self screen’ so that their effect is largely suppressed. No specific evidence for higher-order exchange is found. These aspects are discussed in the context of the lower field multi-Q states and the anisotropy of the system.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Calibrating a finite-strain phase-field model of fracture for bonded granular materials with uncertainty quantification
To study the mechanical behavior of mock high explosives, an experimental and simulation program was developed to calibrate, with quantified uncertainty, a material model of the bonded granular material Idoxuridine and nitroplasticized Estane-5703. This paper reports on the efficacy of such a framework as a generalizable methodology for calibrating material models against experimental data with uncertainty quantification. Additionally, this paper studies the effect of two manufacturing temperatures and three initial granular configurations on the unconfined compressive behavior of the resulting bonded granular materials. In each of these cases, the same calibration framework was used; in that, hundreds of high-fidelity direct numerical simulations using a new, graphics processing unit-enabled, high-performance finite element method software, Ratel, were run to calibrate a finite-strain phase-field fracture model against experimental data. It was found that manufacturing temperature influenced the elastic response of the mock high explosives, with higher temperatures yielding a stiffer response. By contrast, it was found that the initial configuration of the grains had a negligible impact on the overall behavior of the mock high explosives though it remains possible that local damage accumulation within the specimens could be altered by the initial configurations. Overall, the calibration framework was successful at creating well-calibrated models, showing its usefulness as an engineering and scientific tool.
36 MATERIALS SCIENCE↗
Evaluation and Development of Phase Array Ultrasonic Testing (PAUT) System for Additively Manufactured Parts
This research focuses on the application of advanced ultrasonic testing techniques developed by The Phased Array Company (TPAC) for inspecting defects in additive manufacturing (AM) parts. Traditionally, X-ray computed tomography is the standard for inspecting AM components. Although, the long inspection and analysis time, along with relatively high cost make implementation difficult. Thus, an alternative nondestructive evaluation (NDE) approach is necessary to support quality assurance efforts within the field of AM. TPAC is recognized as a leader in ultrasonic testing innovation, deploying sophisticated algorithms such as Total Focusing Method (TFM) and Phased Wave Imaging (PWI) for ultrasonic data processing and interpretation. This work will explore how the TFM and PWI algorithms can assist defect detection within polymer AM parts. The AM field is seeking novel NDE methods to provide support within quality control and assurance efforts. Advanced ultrasonics inspection have the potential to fulfill this need.
99 GENERAL AND MISCELLANEOUS↗