Phase Field Method

A. Karma, W.-J. Rappel. Phase field method for computationally efficient modeling of solidification with arbitrary interface kinetics. Phys Rev E 55 R3017, 1996 A. Karma, W.-J. Rappel. Quantitative phase field modeling of dendritic growth in two and three dimensions. Phys Rev E 57 4111, 1998. 

H.-J. Diepers, C. Beckermann, I. Steinbach. Modeling of convection-influenced coarsening of a binary alloy mush using the phase-field method. In ... 

Numerical models of conserved order-parameter evolution and of nonconserved order-parameter evolution produce simulations that capture many aspects of observed microstructural evolution. These equations, as derived from variational principles, constitute the phase-field method [9]. The phase-field method depends on models for the homogeneous free-energy density for one or more order parameters, kinetic assumptions for each order-parameter field (i.e., conserved order parameters leading to a Cahn-Hilliard kinetic equation), model parameters for the gradient-energy coefficients, subsidiary equations for any other fields such as heat flow, and trustworthy numerical implementation. 

J.A. Warren and W.J. Boettinger. Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field method. Acta Metall, 43(2) 689-703, 1995. 

Chen L-Q (2008) Phase-field method of phase transitions/domain structures in ferroelectric thin films a review. J Am Ceram Soc 91 1835... 

We now briefly consider another important aspect of nonequilibrium thermodynamics, namely phase transformations and how they are modelled. Galenko and Jou198 develop a thermodynamic formalism for rapid phase transformations within a diffuse interface of a binary system in which the system is in a state of local nonequilibrium. The phase-field method, in which the phase- field variable O varies smoothly and continuously between one pure phase (in which O = +1) and another (in which -1), is used to derive... 

Gao, L.T., Feng, X.Q., and Gao, H.J. (2009) A phase field method for simulating morphological evolution of vesicles in electric fields. Journal of Computational Physics, 228 (11),... 

We note that the area of modehng the self-assembly of quantum dots is very active. Various numerical methods have been developed for the solution of the evolution equation for the film surface shape that include non-local elastic effects and anisotropy, such as phase-field methods, finite element methods and others [31]. Also, numerous investigations are devoted to atomistic modeling of self-assembly of quantum dots, as well as to the combination of modeling at small and large scales. These investigations are reviewed in [32]. 

Diffuse interface model Free-surface flow Front capmring Front tracking Interface tracking Interfacial flow Level set method Phase-field method Volume-of-fluid (VOF) method... 

Vedantam and Panchagunula suggested to use a semi-empirical phase field method, which had been used successfiiUy to study various wetting transitions. In this method, the order-parameter T] x,y) is selected in such a manner that = 0 for the nonwetted regions of the surface and = 1 for wetted regions, whereas 0 < < 1... 

The phase field method also accounts in a natural way for the contact line tension term and leads to the Boruvka and Neumann equation ... 

Ordering Process analyzed by Phase Field Method, CVM and PPM... 

HYBRIDIZED CALCULATION OF PHASE FIELD METHOD AND CLUSTER... 

T. Miyazaki, T. Koyama and T. Kozakai, Computer simulations of die phase transformation in real alloy systems based on the phase field method. Mater. Set. >tg., A t2,38-49(2()01). 

M. Ohno and T Mohri, Disorder-LIo transition investigated by phase field method with CVM local free... 

There are three main assumptions used in the conventional versions of the phase-field method (PFM) [7-9] ... 

P. Bellon, Phase field methods, in R.J.M. Konings (Ed.), Comprehensive Nuclear Materials, Elsevier, Oxford, 2012. 

The purpose of this section is to give an overview of the pertinent high resolution methods often referred in the literature on multiphase reactor modeling. These are The Maker and Cell (MAC) method [102], the Simplified MAC method [6], the volume of fluid (VOF) method[114], the level set (LS) front capturing method [22, 199, 228], the front tracking method [235, 241] and Anally a brief description of the phase-field method [8]. 

The gradient energy coefficient used in the phase field method An empirical parameter in F-OPT theory (—)... 

The dynamical behavior of fluid vesicles in simple shear flow has been stodied experimentally [190-193], theoretically [194-201], numerically with the boundary-integral technique [202,203] or the phase-field method [203,204], and with meso-scale solvents [37,180,205]. The vesicle shape is now determined by the competition of the curvature elasticity of the membrane, the constraints of constant volume V and constant surface area S, and the external hydrodynamic forces. 

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