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[Display omitted] Parallel computing with multiple graphics processing units (GPUs) for adaptive mesh refinement (AMR) is a powerful method that improves the computational efficiency of phase-field (PF) simulations of dendrite growth. Octree-type block-structured AMR is often used in parallel computation because of its good parallelism; however, the process of filling the buffer region with physical data from adjacent blocks constitutes a major overhead cost that reduces computational performance. In this study, the mother-leaf (ML) method, which can reduce this overhead, was applied to accelerate parallel-GPU AMR PF simulations of dendrite growth. To evaluate the computational performance of the ML method, single- and parallel-GPU AMR PF simulations of dendrite growth were performed. The results show that single- and parallel-GPU AMR computations with the ML method accelerate the PF simulations of dendrite growth approximately 1.2–1.6 times and 1.2–1.4 times, respectively, compared to the conventional method without the ML method. In large-scale dendrite-growth PF simulations, such accelerations are significant for investigating various dendrite growth phenomena. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • A multiphase-field-lattice Boltzmann model is developed. • The effects of natural convection on superalloy dendrite growth are studied. • The fluid flow velocity in the mushy zone is obtained and analyzed. Abstract The natural convection is able to change dendrite morphology and cause freckles formation in alloy solidification. Though great progress has been made in in - situ observation techniques and numerical models, the interaction between the melt flow and the growing dendrite in directionally solidified superalloy has not been well understood. In this study, the dendrite growth with natural convection in directional solidified nickel-based superalloy was investigated using a developed multiphase-field-lattice Boltzmann model. The PanNickel thermodynamic database was used to present realistic data for the multicomponent superalloy solidification simulation. A range of temperature gradients and pulling velocities were applied to investigate the effects of solidification conditions on dendrite growth and melt flow. First, the microsegregation pattern of each alloy component was obtained, and the simulation results were compared with the experimental results. Then, the dendrite morphology change and the variation of fluid velocity in the mushy zone under different solidification conditions were analyzed. The normalized average fluid velocity in the mushy zone was obtained and can be used to predict freckle formation. Finally, the effects of grain orientation on the dendrite morphology and melt convection were studied and the results were analyzed. [ABSTRACT FROM AUTHOR]

Graphical abstract Abstract A quantitative cellular automaton (CA) model for dendritic and anomalous eutectic growth has been developed. Solid/liquid(SL) interface curvature plays an important role on the dendritic and eutectic growth kinetics. In order to improve the accuracy of calculated interface curvature, a height function method was used in this research. Simulation results showed that the precision of the interface curvature has been significantly improved. And the quantitative ability of present CA model has also been improved through the simulations of equilibrium shapes. Using the quantitative CA model, directional solidification of dendritic and eutectic growth has been investigated, as well as the anomalous eutectic growth during laser remelting process. For anomalous eutectic, it is found that the very fine lamellar eutectic growing at much smaller cooling rate is the reason to observe the lamellar to anomalous transition. [ABSTRACT FROM AUTHOR]

The microstructure formation of a nickel-based superalloy during solidification in three dimensions was investigated using the phase-field method. To accelerate the large-scale phase-field simulation, a parallel computing approach was developed using the graphic processing unit (GPU), and the limitation of insufficient GPU memory was circumvented by employing an asynchronous concurrent algorithm. The performance of the GPU-based parallel computing method was tested and the results demonstrate that a maximum performance of 774.292 GFLOPS (giga floating-point operations per second) can be obtained using a single NVIDIA GTX1080 GPU. In simulations of isothermal solidification, the microstructure evolution of a single and multiple dendrites under different undercooling levels was shown in detail. During the solidification, the dendrite tip growth velocity and fraction solid were recorded and then analyzed. In simulations of directional solidification, the formation of primary dendrite arms under different temperature gradients was investigated, and the simulated microstructure was in good agreement with experimental observations. Additionally, the distribution of primary dendrite arm spacing was quantitatively analyzed by Voronoi tessellation. Finally, simulation of polycrystalline growth in directional solidification was conducted to study the dendrite competitive growth. The unusual overgrowth phenomenon was observed in the initial growth stage, while as the solidification process proceeded, the dendrites with small inclination angles were more likely to overgrow the dendrites with large inclination angles. [ABSTRACT FROM AUTHOR]

[Display omitted] • Data assimilation system for dendrite growth with liquid flow and solid motion. • Phase-field lattice Boltzmann method is used as a simulation model. • Twin experiments of an isolated equiaxed dendrite grows with sedimentation. • Validation of the developed data assimilation system via the twin experiments. • Kinematic viscosity is inferred in the twin experiments. Integrating phase-field simulations and in situ observation experiments is a promising approach to better understand dendrite growth during alloy solidification. To integrate simulations and experiments, we developed a data assimilation system using an ensemble Kalman filter for dendrite growth with liquid flow and solid motion. In this system, we used the phase-field lattice Boltzmann (PF–LB) model as the simulation model. Through twin experiments in which an isolated equiaxed dendrite grows with sedimentation owing to the density difference between the solid and liquid phases, we validated that the developed data assimilation system can effectively incorporate the observation data into the PF–LB simulation. In addition, we discuss the accuracy of data assimilation in different conditions by comparing the results of columnar dendrite growth with natural convection. [ABSTRACT FROM AUTHOR]

Based on DFT calculations, we have revealed some conditions for the Li dendrite-free, dendrite-formation, and dendrite-suppression processes. [Display omitted] • Three types of competitive intrinsic kinetics processes have been identified. • The dendrite-free, -forming, and -suppressing conditions are revealed. • Adjusting the intrinsic kinetics to suppress the dendrite growth was demonstrated. Although many works have been devoted to designing the dendrite-suppression lithium anodes through modifying the growth environments or electrode configurations, studies on their related intrinsic kinetics processes are still lacking. Using DFT calculations, the intrinsic kinetics processes to control the dendrite growth in different environments are investigated herein. Under different coverage concentrations and distributions of lithium, three types of competitive kinetics processes have been identified and defined as the two-dimensional (2D) accumulation, 2D dispersion, and 3D accumulation kinetics processes based on the near-neighboring interactions in the same layer. It was found that the dendrite-free condition can be realized under the natural growth processes based on the dominant 2D accumulation processes, but the dominant kinetics processes can be replaced by the 3D accumulation processes during the nonuniform deposition processes under the condition of moderate coverage concentration, leading to the formation of dendrites. Correspondingly, the suppression condition for the dendrite growth requires that the 2D dispersion kinetics processes can triumph over the 3D accumulation kinetics processes. Therefore, we employed the lithium-affinity molecules to illustrate how to adjust the 2D dispersion kinetics processes to suppress dendrite growth. These results provide microscopic guidance suppressing dendrite growth. [ABSTRACT FROM AUTHOR]

Due to the extensive applications in the automotive and aerospace industries of Al–7Si–Mg casting alloys, an understanding of their dendrite microstructural formation in three dimensions is of great importance in order to control the desirable microstructure, so as to modify the performance of castings. For this reason, a three-dimensional cellular automaton model (3-D CA) allowing for the prediction of dendrite growth of ternary alloys is presented. The growth kinetics of the solid/liquid (S/L) interface is calculated based on the solutal equilibrium approach. This proposed model introduces a modified decentered octahedron algorithm for neighborhood tracking, in order to eliminate the effects of mesh dependency on dendrite growth. The thermodynamic and kinetic data needed in the simulations are obtained through coupling with the Pandat software package in combination with thermodynamic/kinetic/equilibrium phase diagram calculation databases. The solute interactions between alloying elements are considered in the model. The model was first used to simulate the Al–7Si dendrite, followed by a validation using theoretical predictions. The influence of Mg content on the dendrite growth dynamics and dendrite morphologies was investigated. Also, the model was applied to Al–7Si–0.5Mg dendrite simulation both with and without a consideration of solute interactions between the Si and Mg alloying elements and the effects on dendrite growth process was analyzed using the simulation results. This model was finally used in order to simulate the dendrite growth in different crystallographic orientations in an Al–7Si–0.36Mg ternary alloy during polycrystalline solidification, resulting in a predicted secondary dendrite arm spacing (SDAS) and dendrite volume fraction data that show a reasonable agreement with experimental results. The single dendrite and polycrystalline growth simulations effectively demonstrate the capability of this model in predicting the three-dimensional dendrite microstructure of ternary alloys. [ABSTRACT FROM AUTHOR]

Highlights: [•] The relationships between the critical parameters and the macro variables are built. [•] The transient welding conditions are applied to the dendrite growth simulation. [•] We obtain the evolutions of concentration and morphology. [•] The evolution of the tip velocity is obtained in the solidification of welding pool. [•] Primary arm spacing in simulation result agrees well with that in experiment result. [ABSTRACT FROM AUTHOR]

A lattice Boltzmann-phase field coupled model is developed and utilized to investigate dendrite growth with melt convection in magnetic field. In this model, the two-relaxation-time scheme with D2Q9 vectors is extended to simulate the magnetofluid flow, the anisotropic scheme is developed to model dendrite growth of binary alloys, and the finite volume method is utilized to simulate the solute transport with anti-trapping current. After model validation, the growth of single dendrite and multi-dendrites of a binary alloy with magnetic field and melt flow are numerically investigated. The results show that the magnetic flow on dendrite growth cannot be ignored, the magnetic field can greatly change dendrite growth by affecting the flow field and then affecting solute transport. This work provides a numerical solution to reveal the internal mechanism of dendritic growth under external magnetic fields. [Display omitted] • A phase field-lattice Boltzmann model to simulate dendrite growth in a magnetic field. • Magnetic field, melt flow, Solute transport and phase transition are coupled. • The magnetic field can significantly influence evolution of dendrite morphology. [ABSTRACT FROM AUTHOR]

[Display omitted] • Multi-phase-field lattice Boltzmann (MPF-LB) model with a double-obstacle potential. • The MPF-LB model can express from growth of multiple mobile dendrites to grain growth. • The MPF-LB model was verified against a model with the double-well potential. • The MPF-LB model was applied to showering and semi-solid deformation processes. The formation process of equiaxed structures during alloy solidification is a complicated multiphysics problem as it includes solid–liquid phase transformations, transport of solute and heat, liquid flow, solid motion, solid–solid interactions, and grain growth after solidification completion. In this study, a multi-phase-field (MPF) model with the double-obstacle (DO) potential is introduced to our previous model [T. Takaki et al., Comput. Mater. Sci., 147 (2018) 124–131] to express the formation process of equiaxed structures accurately and efficiently, from the growth of multiple mobile dendrites to the grain growth with grain boundary anisotropy after solidification. The accuracy of the resulting MPF-lattice Boltzmann (MPF-LB) model with the DO potential is evaluated by comparison with the results obtained using a model with the double-well potential through simulations of purely diffusive dendrite growth, the growth of an immobile dendrite with forced convection, and the growth of a mobile dendrite under shear flow. Finally, the model is applied to both large-scale polycrystalline solidification and semi-solid deformation processes. [ABSTRACT FROM AUTHOR]

• Enthalpy based model for binary alloy microstructure evolution. • Nucleation and growth of multiple equiaxed and columnar dendrites. • Solidification based on specified cooling rate and undercooling. • Captures heat transfer, species transfer, shrinkage and convection. • Predicts 3d dendritic solidification with secondary and tertiary arms. An enthalpy based solidification model is presented to simulate the evolution of binary alloy microstructure. The model is capable of simulating the nucleation and growth of multiple equiaxed and columnar grains subjected to a given undercooling or cooling rate. Thermal and species transport, forced convection, buoyancy driven convection, shrinkage driven flow and formation of secondary arms are incorporated in the model. The developed model uses a volume averaged enthalpy based solidification solver which is coupled with a pressure based flow solver and a probabilistic nucleation model. Simulations are performed to show the ability of the model in predicting microstructure evolution, flow pattern and microsegregation. Subsequently, the model is used to study the effect of cooling rate on grain size and solute segregation during microstructure evolution, formation of secondary arms and the effect of undercooling on primary arm spacing in columnar grain growth. The effect of natural convection on columnar dendrite growth is also studied. It is found that grain size and solute segregation decreases with increase in cooling rate. Also, it is observed that for columnar growth the primary arm spacing decreases with increase in initial undercooling but remains almost unaffected with change in specified number of nuclei. The developed model is extended to capture three-dimensional dendrite growth with secondary arms. [ABSTRACT FROM AUTHOR]

• The manuscript provides a numerical study of dendritic growth. • Different phase field models with different potentials and anisotropy functions are analysed. • The effect of interface width and grid spacing on the tip velocity is investigated. Phase-field model formulations with double well and double obstacle potentials, and different anisotropy models are investigated with respect to their potential to simulate (i) tip growth on a quantitative level, (ii) well resolved side-branching. The dilute binary alloy Al-4 at%Cu is used as a model alloy. The effects of the numerical resolution (the ratio of the capillary length to the grid spacing) on the growth velocity are studied by means of convergence tests for isothermal and directional solidification in comparison to the theoretical values calculated by the Green-function method (A. Karma, W.J. Rappel, Phys. Rev. E 57 (1998) 4323). An interface stability parameter is introduced as a measure for the estimation of the maximum value of the grid spacing for effective simulations. We show that predominantly the side-branching occurs at numerical resolution lower than the limit value needed to produce correct results in accordance to the convergence analysis. The best results for dendrite growth at a relevant numerical resolution are obtained for the double well potential. [ABSTRACT FROM AUTHOR]

• We developed the macroscopic model for considering S/L interface deflection, which could reflect the solidification parameters at any location of molten pool in the whole solidification process. • Under the given welding condition, the solidification parameters, G and R, were calculated out through the two models, and compared with each other. • The phase-field simulations of dendrite growth in the molten pool were carried out, including single crystal and bi-crystals, with the diverging and converging directions, respectively. The solidification process in the molten pool significantly determines the microstructures of weld metal. The motion of heat source makes the solidification parameters, temperature gradient G and growth rate R, changing continuously across the pool, as well as the solidification modes. It is meaningful to investigate the solidification evolution in the molten pool, with dynamic solidification parameters. The previous researches ignored the deflection of solid/liquid (S/L) interface with time, regarding the normal direction of interface being constant all the time. In this paper, we modified the macroscopic model for G and R without S/L interface deflection to the model with the interface deflection. The solidification parameters were calculated out through the two models and compared with each other. Then the phase-field simulations of dendrite growth in the molten pool were carried out, including single crystal and bi-crystals. The dendrite growth of single crystal and bi-crystals, with the diverging and converging directions, were compared and discussed. The simulations demonstrate that the model considering the interface deflection could represent the dendrite growth during welding more realistically. The investigations lay the foundation for revealing solidification behavior in the molten pool more precisely. [ABSTRACT FROM AUTHOR]

• The sharp front and capillary effects are modelled using a level set method. • A robust ghost-fluid technique is used to apply boundary conditions on the front. • Speed-curvature relation is quantified in terms of a probability distribution. • The proposed strategy captures coarsening phenomenon and dendritic structures. A high order level set model is developed for deterministic simulation of dendritic growth in unstable solidifying systems. The model captures motion of the front implicitly on a structured finite difference grid, enables calculation of its geometric properties and also applies boundary conditions on the immersed interface. Interfacial capillary effect is incorporated in the model through the Gibbs-Thomson condition. Canonical problems for evaluating grid convergence of the numerical method and validation tests for stability of a growing nucleus in the presence of isotropic surface tension are presented. The growth morphology of solidifying nuclei in undercooled metallic melts is quantitatively analyzed. Effects of crystal anisotropy and melt undercooling on the front geometry, propagation speed and formation of branched dendritic structures are examined. The complex morphological changes, such as remelting of secondary perturbations under specific conditions of undercooling, are also captured during the quantitative analysis. [ABSTRACT FROM AUTHOR]