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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Leveraging MARVEL and SPHERE to Demonstrate NEAMS Thermal Hydraulics Codes

The Single Primary Heat Extraction and Removal Emulator (SPHERE) and Microreactor Applications Research Validation and Evaluation (MARVEL) were utilized to demonstrate thermal hydraulics codes of the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. A recent long-duration test of a sodium heat pipe conducted at the SPHERE facility was utilized for the validation of the heat pipe code Sockeye. The first 10 hours of operation featured a startup of the heat pipe from room temperature; this portion was modeled with Sockeye and compared to the experimental data. Measurements included several thermocouple measurements across the length of the heat pipe surface. Two of Sockeye’s heat pipe models were applied to experiment, as well as several models of the cooling at the condenser end of the heat pipe. Sockeye results gave a decent match to the experimental data, with notable discrepancy in the condenser section, where experimental data indicated a significant inactive length of the heat pipe. The MARVEL microreactor was modeled through a coupled simulation of System Analysis Module (SAM) and SubChannel Module (SCM). This multiscale coupled simulation was performed as an exercise to demonstrate the compatibility and applicability of these codes for thermal-hydraulic analysis of microreactors. The coupling between the SCM and SAM codes for multiscale modeling of MARVEL, was achieved through a domain overlapping approach. In this example a transient SAM simulation provided boundary conditions to SCM, and SCM provided pressure drop to SAM.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2026

FY26 Progress on Demonstration of a Multiphysics Steady State Capability for Modeling Core Radial Expansion in SFRs

Under the U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) Program, an integrated multiphysics approach is being developed to model the core bowing phenomena important to liquid metal-cooled fast reactors. Core bowing is an important passive safety mechanism in liquid metal-cooled fast reactors and involves multiphysics effects including radiation transport, fluid flow, heat transfer, and mechanical response to temperature and flux gradients. This report summarizes recent progress on developing a multiphysics, MOOSE-based workflow to predict core bowing and associated reactivity feedback. Significant new capabilities in the reactor physics code Griffin - sodium backfill and pin power reconstruction for deformed geometries - were applied in this effort. This year’s work included verification, code comparisons, sensitivity studies, and coupled demonstrations that advance the state of MOOSE-based core bowing workflow. Griffin’s sodium backfill capability was verified by demonstrating that its automated treatment of geometry expansion and material-density updates reproduces manual calculations exactly, confirming solid mass conservation and proper coolant backfilling in expanded geometries. Reconstructed pin powers were compared for Griffin’s ductheterogeneous and ring-heterogeneous treatments in single-, seven-, and nineteen-assembly cases, with best agreement observed in lower-leakage configurations and the duct-heterogeneous approach offering substantially lower computational cost. Thermal-hydraulic sensitivity sensitivities showed that MOOSE SCM, SAM, and CFD are expected to produce similar deformation predictions despite variances in their temperature predictions, and that explicit treatment of inter-assembly flow becomes increasingly important as gap flow rate increases. Finally, coupled demonstrations on small multi-assembly configurations using Griffin, MOOSE Solid Mechanics, MOOSE SCM, and Heat Conduction produced physically consistent reactivity feedback from thermal expansion and bowing. The coupled demonstrations simulated grid plate expansion as well as resultant core bowing at full power conditions. Simplifications were made in current workflow, namely the assumption of instantaneous full power conditions following hot zero power, and pre-expanding the Griffin geometry axially due to lack of an axial fuel pin expansion model and temperature feedback to Griffin.

Wozniak, Nicholas↗
DOE OSTI2025

Implementation of disruptive designs for gas turbine components using direct energy deposition additive manufacturing

This research aims to develop a framework for establishing the correlation between in-situ monitoring data, process parameters, and microstructure evolution in blown-powder laser-directed energy deposition (DED) additive manufacturing (AM). To achieve this, a comprehensive manufacturing framework has been developed, spanning from in-situ data acquisition, melt-pool simulation, microstructure modeling, and statistical microstructure quantification. A machine learning-based surrogate model is constructed to predict melt pool geometry directly from in-situ coaxial camera data. The surrogate model is trained using outputs from a high-fidelity melt pool simulation, which provides accurate melt pool dimension data under varying process conditions. The predicted melt pool geometry is then used as input to a microstructure model to predict microstructural features. To rigorously compare and analyze microstructures, the project introduces statistical metrics that quantify differences based on key features such as morphology and texture. Microstructures are represented using advanced statistical descriptors including angular chord length distribution, two-point spatial statistics, orientation distribution function, and global spherical harmonic. These representations are used to compute four distinct “dissimilarity scores” that quantitatively capture differences in texture and morphology. This framework is demonstrated to enable automated calibration of simulation parameters by minimizing discrepancies between simulated and target microstructures. The technology developed in this project enables direct correlation between in-situ monitoring data and resulting microstructure, paving the way for adaptive microstructure control in metal AM. This capability strengthens the connection between process parameters and final material properties, facilitating more precise and reliable material design.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Performance evaluation of CMIP6 models on the Arctic-Siberian Plain teleconnection affecting the East Asian heat waves

The frequency and intensity of summer heat waves in East Asia have increased sharply in recent decades, significantly impacting public health and the economy. The Arctic-Siberian Plain (ASP) teleconnection pattern has been identified as a key driver, with ASP warming amplifying atmospheric circulation patterns conducive to extreme temperatures. This study evaluates the ability of Coupled Model Inter-comparison Project phase 6 models to simulate the ASP pattern across interannual variability (IAV) and intra-seasonal variability (ISV) timescales using the Common Basis Function method. The multi-model mean shows statistically significant pattern correlations with ERA5 reanalysis, with correlation coefficients of 0.90 and 0.99 for IAV and ISV, respectively. While the ASP pattern is generally well captured, models exhibit substantial inter-model diversity in the intensity and position of anticyclonic anomalies over the ASP and East Asia. Models with ASP pattern variability similar to reanalysis better reproduce extreme East Asian temperatures, whereas those over- or underestimating ASP variability exhibit lower skill. These performance differences are related to differences in simulating key variables associated with the development of the ASP pattern. Our findings highlight the role of the ASP pattern in modulating extreme heat events, as models with improved ASP simulations align more closely with observed temperature extremes. Refining ASP representations in models could enhance seasonal heat wave predictions, improving climate adaptation strategies.

Arctic-Siberian Plain (ASP)↗
DOE OSTI2026

Simulation of Divertor Performance in ST40 Under Dynamic Double-Null Plasmas

A power fraction model was implemented for the simultaneous prediction of 3-D surface temperature evolution at all four divertor targets in near-double-null (DN) tokamak configurations, which is especially important for compact high-field devices that may not have the ability to dissipate large amounts of power on the high-field side. Evaluating the power-sharing between the four divertor strike points in a disconnected DN configuration is important for understanding the overall power balance, as well as for optimizing the power exhaust performance and prolonging the survivability of the plasma facing components (PFCs). This power-sharing is typically evaluated in terms of the separation between the primary and secondary separatrices at the outboard midplane, $\textit {dR}_{\text {sep}}$. The Heat flux Engineering Analysis Toolkit (HEAT) is coupled with Brunner’s power fraction model to simulate the deposited heat flux and resultant temperature change on 3-D divertor targets in a dynamic DN (DDN) pulse operation in ST40, a high-field spherical tokamak. The simulation results showed that with DDN operation, the operation time has significantly increased compared with single-null geometry configurations.

ST40↗
DOE OSTI2025

Market Driven Residential Energy Codes: Comparing Performance in a Changing Technological Environment

The research project is undertaken to better understand the changing relationship between the two basic methods of building energy code compliance – prescriptive and performance – and how those methods relate to each other with respect to advancements in building energy computer simulation standards and capabilities. The International Energy Efficiency Code (IECC) is a model code adopted by many jurisdictions across the United States. Historically, the prescriptive compliance methodology has been preferred in most jurisdictions. The prescriptive methodology requires meeting or exceeding specific efficiency minimums for each envelope component. This tends to be a simple method to teach and verify. A more involved prescriptive alternative called the Total UA alternative is sometimes used. This method requires some multiplication, summing, and comparison to compute, so it is done with a fairly simple computer program. However, advances in computer and building energy simulation technology have resulted in increased use of more detailed performance compliance methods. The performance compliance method establishes the annual energy cost threshold via hourly simulation models. The compliance threshold is determined with a comparison building model simulation with geometry similar to the proposed home and with energy feature parameters and efficiencies as specified in the IECC. This project examines relationships between the two methods of building energy code compliance, including: • Overall annual energy use based on utility bill analysis by compliance method • Code official work processes with respect to compliance methods • Gaps and issues associated with building code compliance methods • Simulated energy use difference between compliance methods • Code compliance cost as a function of compliance method • Code compliance labeling effectiveness for high performance residences • Getting to net zero energy use and net zero greenhouse gas emissions through high performance code alternatives • Electronic code permitting and compliance alternatives

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

A Digital Twin of Scalable Quantum Clouds

Quantum computing has emerged as a transformative technology capable of solving complex problems beyond the limit of classical systems. The rapid development of quantum processors has led to the proliferation of cloud-based quantum computing services offered by platforms such as IBM, Google, and Amazon. These platforms introduce unique challenges in resource allocation, job scheduling, and multi-device orchestration as quantum workloads become increasingly complex. In this work, we present a digital twin of quantum cloud infrastructures: a framework designed to model and simulate the behavior of real quantum cloud systems. Developed in Python using the SimPy discrete-event simulation library, the framework replicates key aspects of quantum cloud environments, including detailed quantum device modeling, job lifecycle management, and job fidelity. It incorporates noise-aware fidelity estimation, making it the first of its kind to simulate superconducting gate-based quantum cloud systems at an administrative level with job fidelity. We present use cases as proof of concept, demonstrating that our quantum cloud simulation framework can act as a digital twin of a quantum cloud and support the modeling and implementation of practical systems.

Luo, Waylon [Kent State University]↗
DOE OSTI2026

Convective Biases in the US DOE Global Storm‐Resolving Model: Insights From Regionally Refined Simulations During the CACTI Campaign

Accurately simulating convective processes in complex terrain remains a critical challenge for global storm-resolving models (GSRMs). This study systematically evaluates moist convective biases in the Regionally Refined Mesh configuration of the U.S. Department of Energy Simple Cloud-Resolving E3SM Atmosphere Model (RRM-SCREAM) using comprehensive observations and large-eddy simulations from the Cloud, Aerosol, and Complex Terrain Interactions (CACTI) campaign in the mountainous area of central Argentina. Comparisons of simulations with high-resolution observations and reanalysis data indicate that RRM-SCREAM effectively captures large-scale meteorological patterns, including regional atmospheric gradients and diurnal variability. However, RRM-SCREAM disproportionately produces smaller precipitation clusters referred to as “popcorn convection,” and exaggerated rainfall intensities compared to observations and reference models. Detailed examination of a representative orographic shallow-to-deep convective transition case shows that RRM-SCREAM delays initial shallow convection growth due to lower-tropospheric dryness and sustained convective inhibition, but once triggered, deep convection becomes overly vigorous with excessively strong vertical velocities and elevated cloud ice content, linked to a thermodynamic structure characterized by suppressed low-level moistening and excessive upper-level moisture retention. Our results highlight specific deficiencies in the model representation of convective vertical velocity, cloud microphysical processes, and convective precipitation organization within RRM-SCREAM. Addressing these biases is essential for improving the predictions of convective clouds and precipitation in the global high-resolution atmospheric models.

Su, Tianning [Lawrence Livermore National Laborato↗
DOE OSTI2024

Equivalent-Circuit Models of Grid-Forming IBRs for Electromagnetic-Transient Simulations

We derive equivalent-circuit models of control- and physical-layer subsystems of grid-forming (GFM) inverter-based resources (IBRs) for electromagnetic-transient (EMT) simulations. Three different primary controllers are considered: Droop, Virtual Synchronous Machine (VSM), and dispatchable Virtual Oscillator Control (dVOC). In addition, the models include cascaded voltage- and current-control loops, and LCL output filters. Simulations for a single-inverter setup and for a network of five inverters in a modified IEEE 14-bus topology are presented. The equivalent-circuit models simulated with analog electronic circuit-simulator software (in our case, LTspice) offer the same accuracy, and with no explicit tuning of the solver, lower computational burden compared to block-diagram-based implementations in commercial off-the-shelf EMT software (in our case, MATLAB-Simulink).

electromagnetic transient simulation↗
DOE OSTI2024

Leveraging Optimal Sparse Sensor Placement to Aggregate a Network of Digital Twins for Nuclear Subsystems

Nuclear power plants (NPPs) require continuous monitoring of various systems, structures, and components to ensure safe and efficient operations. The critical safety testing of new fuel compositions and the analysis of the effects of power transients on core temperatures can be achieved through modeling and simulations. They capture the dynamics of the physical phenomenon associated with failure modes and facilitate the creation of digital twins (DTs). Accurate reconstruction of fields of interest (e.g., temperature, pressure, velocity) from sensor measurements is crucial to establish a two-way communication between physical experiments and models. Sensor placement is highly constrained in most nuclear subsystems due to challenging operating conditions and inherent spatial limitations. This study develops optimized data-driven sensor placements for full-field reconstruction within reactor and steam generator subsystems of NPPs. Optimized constrained sensors reconstruct field of interest within a tri-structural isotropic (TRISO) fuel irradiation experiment, a lumped parameter model of a nuclear fuel test rod and a steam generator. The optimization procedure leverages reduced-order models of flow physics to provide a highly accurate full-field reconstruction of responses of interest, noise-induced uncertainty quantification and physically feasible sensor locations. Accurate sensor-based reconstructions establish a foundation for the digital twinning of subsystems, culminating in a comprehensive DT aggregate of an NPP.

42 ENGINEERING↗
DOE OSTI2026

Trigonometric continuous-variable gates and hybrid quantum simulations of the sine-Gordon model

Hybrid qubit-qumode quantum computing platforms provide a natural setting for simulating interacting bosonic quantum field theories. However, existing continuous-variable gate constructions rely predominantly on polynomial functions of canonical quadratures. In this work, we introduce a complementary universality paradigm based on trigonometric continuous-variable gates, which enable a Fourier-like representation of bosonic operators and are particularly well suited for periodic and non-perturbative interactions. We present an ancilla-based framework for implementing trigonometric gates with arguments given by arbitrary Hermitian functions of qumode quadratures. The protocol yields unitary gates deterministically, and non-unitary gates through probabilistic post-selection. As a concrete application, we develop a hybrid qubit-qumode quantum simulation of the lattice sine-Gordon model. Using these gates, we prepare ground states via quantum imaginary-time evolution, simulate real-time dynamics, compute time-dependent vertex two-point correlation functions, and extract quantum kink profiles under topological boundary conditions. Our results demonstrate that trigonometric continuous-variable gates provide a physically natural framework for simulating interacting field theories on near-term hybrid quantum hardware, while establishing a parallel route to universality beyond polynomial gate constructions. We expect that the trigonometric gates introduced here to find broader applications, including quantum simulations of condensed matter systems, quantum chemistry, and biological models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Machine learning force field model for kinetic Monte Carlo simulations of itinerant Ising magnets

Here, we present a scalable machine learning (ML) framework for large-scale kinetic Monte Carlo (kMC) simulations of itinerant electron Ising systems. As the effective interactions between Ising spins in such itinerant magnets are mediated by conducting electrons, the calculation of energy change due to a local spin update requires solving an electronic structure problem. Such repeated electronic structure calculations could be overwhelmingly prohibitive for large systems. Assuming the locality principle, a convolutional neural network (CNN) model is developed to directly predict the effective local field and the corresponding energy change associated with a given spin update based on Ising configuration in a finite neighborhood. As the kernel size of the CNN is fixed at a constant, the model can be directly scalable to kMC simulations of large lattices. Our approach is reminiscent of the ML force field models widely used in first-principles molecular dynamics simulations. Applying our ML framework to a square-lattice double-exchange Ising model, we uncover unusual coarsening of ferromagnetic domains at low temperatures. Our work highlights the potential of ML methods for large-scale modeling of similar itinerant systems with discrete dynamical variables.

machine learning↗
DOE OSTI2024

Extended dynamic mode decomposition for model reduction in fluid dynamics simulations

High computational cost and storage/memory requirements of fluid dynamics simulations constrain their usefulness as a predictive tool. Reduced-order models (ROMs) provide a viable solution to this challenge by extracting the key underlying dynamics of a complex system directly from data. We investigate the efficacy and robustness of an extended dynamic mode decomposition (xDMD) algorithm in constructing ROMs of three-dimensional cardiovascular computations. Focusing on the ROMs' accuracy in representation and interpolation, we relate these metrics to the truncation rank of singular value decomposition, which underpins xDMD and other approaches to ROM construction. Our key innovation is to relate the truncation rank to the singular values of the original flow problem. This result establishes a priori guidelines for the xDMD deployment and its likely success as a means of data compression and reconstruction of the system's dynamics from dominant spatiotemporal structures present in the data.

Mechanics↗
DOE OSTI2024

NSTX-U research advancing the physics of spherical tokamaks

Abstract The objectives of NSTX-U research are to reinforce the advantages of STs while addressing the challenges. To extend confinement physics of low- A , high beta plasmas to lower collisionality levels, understanding of the transport mechanisms that set confinement performance and pedestal profiles is being advanced through gyrokinetic simulations, reduced model development, and comparison to NSTX experiment, as well as improved simulation of RF heating. To develop stable non-inductive scenarios needed for steady-state operation, various performance-limiting modes of instability were studied, including MHD, tearing modes, and energetic particle instabilities. Predictive tools were developed, covering disruptions, runaway electrons, equilibrium reconstruction, and control tools. To develop power and particle handling techniques to optimize plasma exhaust in high performance scenarios, innovative lithium-based solutions are being developed to handle the very high heat flux levels that the increased heating power and compact geometry of NSTX-U will produce, and will be seen in future STs. Predictive capabilities accounting for plasma phenomena, like edge harmonic oscillations, ELMs, and blobs, are being tested and improved. In these ways, NSTX-U researchers are advancing the physics understanding of ST plasmas to maximize the benefit that will be gained from further NSTX-U experiments and to increase confidence in projections to future devices.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Interactions between land use, fires, and dust as drivers of global climate change (Final Technical Report)

This award to UC Irvine and Cornell University led to the publication of 18 papers, three of which are highly cited. According to ISI Web of Science, the body of work from this grant has been cited over 476 times by May 2025. Several additional publications remain in review. This grant contributed to several significant science advances, including an improved understanding of the influence of fire aerosols on global photosynthesis (Xu et al., 2021), dust-driven teleconnections between Africa and South America (Li et al., 2021), the role of fire aerosols in triggering phytoplankton blooms in the Arctic (Ardyna et al., 2022), and wildfire responses to heat waves (Li et al., in review). Several other studies are being written up for publication, and will acknowledge funding support. These efforts include an analysis in which the magnitude of tropical fire emissions from land use change is constrained by comparing E3SMv3 simulations with atmospheric observations. This work has revealed that carbon cycle model estimates of land use change may considerably overestimate the global tropical deforestation flux. The project also contributed to several technical advances, including a new process-based and scale-aware desert dust emission scheme for global climate models (Leung et al., 2023), an improved representation of dust and its influence on radiation in E3SM (Feng et al., 2022), an improved representation of the dust parameterization in the Community Earth System Model (Li et al., 2022), and an improved coupling of wildfires with atmospheric chemistry in E3SM v3.

58 GEOSCIENCES↗
DOE OSTI2026

Interpretable Deep Learning for Advancing Field-Enhanced Catalysis

This DOE Early Career project developed a physics-informed, interpretable AI-and-modeling framework to understand and exploit electric-field effects in heterogeneous catalysis, with ammonia cracking and synthesis as a representative pathway. The team built and validated methods to map local electric fields on metal surfaces and nanoparticles, showing that low-coordination features (tips/edges/corners) can concentrate fields by several-fold relative to flat facets. Using DFT-generated datasets, the project created physics-guided machine learning models that rapidly predict local electric fields and field-dependent adsorption energetics with near-DFT accuracy while reducing computational cost by orders of magnitude. These predictions were integrated with microkinetic modeling to quantify how field-dipole interactions reshape reaction energetics and mechanisms, enabling large increases in predicted catalytic rates and substantial reductions in operating temperature under favorable field conditions. To accelerate discovery of earth-abundant catalysts, the project combined interpretable ML screening (with electronic-structure descriptors identified as key drivers) with a generative inverse-design workflow based on diffusion models and physics constraints. The resulting closed-loop approach, linking simulation, mechanistic modeling, and AI, provides reusable tools and datasets for designing catalysts and operating conditions in field-enhanced catalysis, with broad relevance to electrostatic catalysis, plasma catalysis, electrocatalysis, and other energy-related chemical transformations.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2024

THERMAL MODELING OF HANFORD CESIUM AND STRONTIUM CANISTERS DURING SIMULATED LOADING

A computational fluid dynamics (CFD) model was built to simulate planned testing of heater assemblies within a canister and overpack for the Hanford Lead Canister (HLC) project. The HLC is a canister storage system that will contain heaters to simulate the decay heat of nuclear material and provide the canister storage system with environmental conditions equivalent to the operating conditions on a dry storage pad. The HLC will be equipped with long-term data collection and monitoring systems to provide an early warning of corrosion, pitting, cracking, or other signs of canister degradation that might threaten the integrity of the containment boundary over the potentially long term of dry storage. An important part of the HLC development is to make pretest numerical predictions for the behavior of the heated canister during the simulated radiolytic decay heat testing, which simulates the dry storage system during loading operations. The simulated radiolytic decay heat test is planned for mid-2024 in a configuration that includes the heater assembly, overpack, and canister, but with the lids removed to allow loading cesium and strontium capsules into the canister. One of the goals of the test is to evaluate the thermal behavior of the canister and overpack assembly in the ambient air of the test facility, which will provide data critical to validating the thermal models and understanding how the HLC will perform as a system once deployed. To best approximate real-world conditions, the CFD model includes the full air volume of the mock-up truck bay the heated canister test will be performed in, enabling detailed investigation of how the heated canister affects airflow around it. Rigorous pre-deployment testing of the complete HLC cask and canister system is intended to be completed before the HLC is deployed in the 2028 timeframe. This study presents the pre-test temperature predictions of the simulated radiolytic decay heat test. A description of the heater assembly, canister, and overpack system is presented. The model was developed with the commercial CFD software STAR-CCM+. An uncertainty analysis was run with the CFD model to determine the uncertainty in the temperature predictions and provide a range over which the predicted temperatures are expected to vary. The uncertainty analysis was preformed by coupling STAR-CCM+ with the software Dakota, which provides advanced parametric analyses, including quantification of margins and uncertainty with computational models. This work is expected to provide insight into SNF canister behavior.

Carpenter-Graffy, Dina E.↗
DOE OSTI2024

Comparison of excess free energy at an interface according to the applied interpolation scheme for elasticity: A phase-field method

Phase-field modeling is an effective simulation technique for modeling microstructure evolution of elastically anisotropic systems. To introduce the elastic energy contribution in a phase field model, an interpolation scheme is used to define the mechanical properties within the phases and across the continuous interface. Several existing interpolation schemes introduce a potential excess elastic energy at the interface, which undesirable effect on microstructure evolution needs to be evaluated. In this study, we focused on three interpolation schemes including Khachaturyan’ scheme (KHS), Voigt–Taylor’s scheme (VTS), and Steinbach–Apel’s scheme (SAS). Comparisons of these schemes’ performances were performed in three configuration types using the MOOSE (Multiphysics Object-Oriented Simulation Environment) framework: bi-crystal, isotropic particle-matrix and anisotropic particle-matrix. The contribution of excess elastic energy on the interface energy as a function of interface width and the computational time to steady-state were evaluated in these three configurations. SAS introduces the lowest excess elastic energy contribution and the VTS has the biggest contribution amongst the considered schemes. Moreover, when modeling precipitation in an anisotropic elastic material, the SAS approach seems to predict more physical convex shapes during growth, making it preferable to KHS and VTS. Finally, as currently implemented, SAS requires the largest computational time and KHS requires the smallest time to reach steady-state amongst the considered schemes.

36 MATERIALS SCIENCE↗