The Finite Phase-Field Method - A Numerical Diffuse Interface Approach for Microstructure Simulation with Minimized Discretization Error

2011 ◽  
Vol 1369 ◽  
Author(s):  
Janin Eiken
Keyword(s):  
Phase Field ◽  
Finite Size ◽  
Numerical Differentiation ◽  
Field Method ◽  
Discretization Error ◽  
Sharp Interface ◽  
Diffuse Interface ◽  
Phase Field Method ◽  
Interface Width ◽  
Microstructure Simulation

ABSTRACTThe Phase-field method is recognized as the method of choice for space-resolved microstructure simulation. In theoretic phase-field approaches, the underlying diffuse interface representation is discussed in the sharp interface limit. Applied phase-field models, however, have to cope with interfaces of finite size. Numerical solution based on finite differences naturally implies a discretization error. This error may result in significant deviations from the analytical sharp-interface solution, especially in cases of interface-controlled growth. Benchmark simula-tions revealed a direct correlation between the accuracy of the finite-difference solution and the number of numerical cells used to resolve the finite-sized interface width. This poses a problem, because high numbers of interface cells are unfavorable for numerical performance. To enable efficient high-accuracy computations, a new Finite Phase-Field approach is proposed, which closely links phase-field modeling and numerical discretization. The approach is based on a parabolic potential function, corresponding to phase-field solutions with a sinusoidal interface pro-file. Consideration of this profile during numerical differentiation allows an exact quantification of the bias evoked by grid spacing and interface width, which then a priori can be compensated.

Application of Interface-Tracking Method Based on Phase-Field Model to Numerical Analysis of Isothermal and Thermal Two-Phase Flows

2007 ◽  
Author(s):  
Naoki Takada
Keyword(s):  
Phase Field ◽  
Density Ratio ◽  
Phase Field Model ◽  
Field Method ◽  
Diffuse Interface ◽  
Phase Field Method ◽  
Navier Stokes ◽  
Interface Tracking ◽  
Two Phase Flows ◽  
Two Phase

For interface-tracking simulation of two-phase flows in various micro-fluidics devices, the applicability of two versions of Navier-Stokes phase-field method (NS-PFM) was examined, combining NS equations for a continuous fluid with a diffuse-interface model based on the van der Waals-Cahn-Hilliard free-energy theory. Through the numerical simulations, the following major findings were obtained: (1) The first version of NS-PFM gives good predictions of interfacial shapes and motions in an incompressible, isothermal two-phase fluid with high density ratio on solid surface with heterogeneous wettability. (2) The second version successfully captures liquid-vapor motions with heat and mass transfer across interfaces in phase change of a non-ideal fluid around the critical point.

Thermodynamic Calculation of Al-Cu Eutectic Alloy with Microstructure Simulation Using Phase Field Method

2011 ◽  
Vol 295-297 ◽  
pp. 468-472 ◽  
Author(s):  
Jin Jun Tang ◽  
Jian Zhong Jiang ◽  
Chun Hua Tang ◽  
Da Hui Chen ◽  
Li Qun Hou
Keyword(s):  
Free Energy ◽  
Eutectic Alloy ◽  
Phase Field ◽  
Regular Solution Model ◽  
Field Method ◽  
Phase Field Method ◽  
Multiple Point ◽  
Microstructure Simulation ◽  
Thermo Calc Software ◽  
New Phase

Phase-field method can be used to describe the complicated morphologies of crystal growth without explicitly tracking the complex phase boundaries. The conformation of volume free energy is very important for microstructure simulation with phase-field method. However, the conformation of volume free energy is still correspondingly simple and ideal at present. In this paper, a new conformation method of free energy is mentioned. Free energy of each phase at appointed states is calculated by Thermo-Calc software. In order to avoided calculation, free energy of each phase is fitted by multiple-point function according to sub- regular solution model. It is obtained that the free energy data and phase graph data of α phase, θ phase and L phase in the extension, temperature (791-841) K and component (0-35)Cu(at.%) with Al-Cu eutectic alloy. The new phase model is also founded, and used to calculate microstructure evolution of Al-Cu eutectic alloy.

Upgrading CALPHAD to microstructure simulation: the phase-field method

2009 ◽  
Vol 100 (2) ◽  
pp. 128-134 ◽  
Author(s):  
Suzana G. Fries ◽  
Bernd Boettger ◽  
Janin Eiken ◽  
Ingo Steinbach
Keyword(s):  
Phase Field ◽  
Field Method ◽  
Phase Field Method ◽  
Microstructure Simulation

scholarly journals Quasi-Brittle Fracture Modeling of Preflawed Bitumen Using a Diffuse Interface Model

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Yue Hou ◽  
Fengyan Sun ◽  
Wenjuan Sun ◽  
Meng Guo ◽  
Chao Xing ◽  
...  
Keyword(s):  
Brittle Fracture ◽  
Phase Field ◽  
Field Method ◽  
Field Variable ◽  
Diffuse Interface ◽  
Phase Field Method ◽  
Interface Model ◽  
Diffuse Interface Model ◽  
Bituminous Materials ◽  
Fracture Modeling

Fundamental understandings on the bitumen fracture mechanism are vital to improve the mixture design of asphalt concrete. In this paper, a diffuse interface model, namely, phase-field method is used for modeling the quasi-brittle fracture in bitumen. This method describes the microstructure using a phase-field variable which assumes one in the intact solid and negative one in the crack region. Only the elastic energy will directly contribute to cracking. To account for the growth of cracks, a nonconserved Allen-Cahn equation is adopted to evolve the phase-field variable. Numerical simulations of fracture are performed in bituminous materials with the consideration of quasi-brittle properties. It is found that the simulation results agree well with classic fracture mechanics.

scholarly journals Pore scale modelling of moisture transfer in building materials with the phase field method

2020 ◽  
Vol 172 ◽  
pp. 04004
Author(s):  
Michele Bianchi Janetti ◽  
Hans Janssen
Keyword(s):  
Phase Field ◽  
Building Materials ◽  
Moisture Transfer ◽  
Porous Matrix ◽  
Field Method ◽  
Diffuse Interface ◽  
Phase Field Method ◽  
Parallel Plates ◽  
Scale Modelling ◽  
Cahn Hilliard Equation

This study explores the applicability of the phase field method for modelling moisture storage and transport in porous materials. Accordingly, the system is treated as a continuum where the phases (liquid and humid air) are separated through a diffuse interface, which evolves in the pores until the equilibrium state is reached. The interface thickness is related to the surface tension, while the contact angle is defined as a boundary condition. The mass transfer in the porous matrix is driven by the Cahn-Hilliard equation and the phase transition is controlled by an equation of state. The above method is tested for a simple geometry (infinitely extended parallel plates), by comparing the numerical outcomes against available measured data and analytical solutions. The challenges arising for a further application to complex pore structures and real building materials are discussed.

scholarly journals Microstructure Simulation for Solidification of Magnesium–Zinc–Yttrium Alloy by Multi-phase-field Method Coupled with CALPHAD Database

2010 ◽  
Vol 50 (12) ◽  
pp. 1914-1919 ◽  
Author(s):  
Satoshi Minamoto ◽  
Sukeharu Nomoto ◽  
Atsushi Hamaya ◽  
Toshiaki Horiuchi ◽  
Seiji Miura
Keyword(s):  
Phase Field ◽  
Field Method ◽  
Phase Field Method ◽  
Microstructure Simulation ◽  
Multi Phase

scholarly journals A practical phase field method for an elliptic surface PDE

2020 ◽  
Author(s):  
John W Barrett ◽  
Klaus Deckelnick ◽  
Vanessa Styles
Keyword(s):  
Phase Field ◽  
Numerical Test ◽  
Quadrature Rule ◽  
Field Method ◽  
Grid Size ◽  
Diffuse Interface ◽  
Phase Field Method ◽  
Finite Element Scheme ◽  
Field Function ◽  
Spatial Grid

Abstract We consider a diffuse interface approach for solving an elliptic PDE on a given closed hypersurface. The method is based on a (bulk) finite element scheme employing numerical quadrature for the phase field function and hence is very easy to implement compared to other approaches. We estimate the error in natural norms in terms of the spatial grid size, the interface width and the order of the underlying quadrature rule. Numerical test calculations are presented, which confirm the form of the error bounds.

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