Phase-field model: Boundary layer, velocity of propagation, and the stability spectrum

1992 ◽  
Vol 46 (24) ◽  
pp. 16045-16057 ◽  
Author(s):  
Raz Kupferman ◽  
Ofer Shochet ◽  
Eshel Ben-Jacob ◽  
Zeev Schuss
Keyword(s):  
Boundary Layer ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Stability Spectrum ◽  
Layer Velocity ◽  
Velocity Of Propagation ◽  
The Stability

scholarly journals Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method

2017 ◽  
Vol 27 (11) ◽  
pp. 1993-2030 ◽  
Author(s):  
Xiaofeng Yang ◽  
Jia Zhao ◽  
Qi Wang ◽  
Jie Shen
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Approximation Schemes ◽  
Numerical Schemes ◽  
Time Step ◽  
Invariant Energy Quadratization ◽  
The Stability ◽  
2D And 3D ◽  
Well Posed

How to develop efficient numerical schemes while preserving energy stability at the discrete level is challenging for the three-component Cahn–Hilliard phase-field model. In this paper, we develop a set of first- and second-order temporal approximation schemes based on a novel “Invariant Energy Quadratization” approach, where all nonlinear terms are treated semi-explicitly. Consequently, the resulting numerical schemes lead to well-posed linear systems with a linear symmetric, positive definite at each time step. We prove that the developed schemes are unconditionally energy stable and present various 2D and 3D numerical simulations to demonstrate the stability and the accuracy of the schemes.

Numerical Simulation of Homogeneous Polycrystalline Grain Formation Using Multi-Phase-Field Model

2012 ◽  
Vol 197 ◽  
pp. 628-632 ◽  
Author(s):  
Takuya Uehara ◽  
Hideyuki Suzuki
Keyword(s):  
Grain Size ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Homogeneous Microstructure ◽  
Grain Formation ◽  
Polycrystalline Microstructure ◽  
The Stability ◽  
Multi Phase ◽  
Original Formula

A modified multi-phase-field model for regenerating a homogeneous polycrystalline microstructure was presented. An extra term was introduced to the original formula by Steinbach et al. by assuming that the stability of every grain constituting the microstructure depends on the grain size distribution. The effect of the term on the obtained microstructure was then verified by numerical simulations, and it was found that a homogeneous microstructure having nearly the same shape and size was generated. The influence of the parameter was also investigated, and it revealed that the parameter was dominative on the grain size at the steady state.

MARMOT Phase-Field Model for the U-Si System

2016 ◽  
Author(s):  
Larry Kenneth Aagesen ◽  
Daniel Schwen
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model

scholarly journals Phase-field modeling of grain evolutions in additive manufacturing from nucleation, growth, to coarsening

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Min Yang ◽  
Lu Wang ◽  
Wentao Yan
Keyword(s):  
Additive Manufacturing ◽  
Phase Field ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Nucleation Theory ◽  
Experimental Result ◽  
Classical Nucleation Theory ◽  
Validation Experiment ◽  
Powder Particles

AbstractA three-dimensional phase-field model is developed to simulate grain evolutions during powder-bed-fusion (PBF) additive manufacturing, while the physically-informed temperature profile is implemented from a thermal-fluid flow model. The phase-field model incorporates a nucleation model based on classical nucleation theory, as well as the initial grain structures of powder particles and substrate. The grain evolutions during the three-layer three-track PBF process are comprehensively reproduced, including grain nucleation and growth in molten pools, epitaxial growth from powder particles, substrate and previous tracks, grain re-melting and re-growth in overlapping zones, and grain coarsening in heat-affected zones. A validation experiment has been carried out, showing that the simulation results are consistent with the experimental results in the molten pool and grain morphologies. Furthermore, the grain refinement by adding nanoparticles is preliminarily reproduced and compared against the experimental result in literature.

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