Related papers: Phase Field Models versus Parametric Front Trackin…
The phase-field method is reviewed from the general perspective of converting a free boundary problem into a set of coupled partial differential equations. Its main advantage is that it avoids front tracking by using phase fields to locate…
We present a new phase-field model of solidification which allows efficient computations in the regime when interface kinetic effects dominate over capillary effects. The asymptotic analysis required to relate the parameters in the…
Phase field equations describe the novel approach to the Stefan problems. We calculate these equations numerically performed in two-dimensions. We take full advantage of the phase field parameter $\varphi$ to track the interface on which…
The description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach from the literature is shown to fail to produce the correct…
Three different topics in phase-field modelling of solidification are discussed, with particular emphasis on the limitations of the currently available modelling approaches. First, thin-interface limits of two-sided phase-field models are…
We compare time-dependent solutions of different phase-field models for dendritic solidification in two dimensions, including a thermodynamically consistent model and several ad hoc models. The results are identical when the phase-field…
We briefly review the state-of-the-art in phase-field modeling of microstructure evolution. The focus is placed on recent applications of phase-field simulations of solid-state microstructure evolution and solidification that have been…
The phase-field crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field crystal dynamics can be…
We optimize a numerical time-stabilization routine for the phase-field crystal (PFC) models of solidification. By numerical experiments, we showcase that our approach can improve the accuracy of underlying time integration schemes by a few…
We introduce unconditionally stable finite element approximations for a phase field model for solidification, which take highly anisotropic surface energy and kinetic effects into account. We hence approximate Stefan problems with…
In materials science the phase field crystal approach has become popular to model crystallization processes. Phase field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic…
A brief review of the Stefan problem of solidification from a mixture, and its main numerical solution methods is given. Simulation of this problem in 2D or 3D is most practically done on a regular grid, where a sharp solid-liquid interface…
A phase-field approach to the dynamics of liquid-solid interfaces that evolve due to precipitation and/or dissolution is presented. For the purpose of illustration and comparison with other methods, phase field simulations were carried out…
We extend the phase-field approach to model the solidification of faceted materials. Our approach consists of using an approximate gamma-plot with rounded cusps that can approach arbitrarily closely the true gamma-plot with sharp cusps that…
Directional solidification of water-based solutions has emerged as a versatile technique for templating hierarchical porous materials. However, the underlying mechanisms of pattern formation remain incompletely understood. In this work, we…
Phase field models are powerful tools to tackle free boundary problems. For phase transformations involving diffusion, the evolution of the non conserved phase field is coupled to the evolution of the conserved diffusion field. Introducing…
The phase-field method has become in recent years the method of choice for simulating microstructural pattern formation during solidification. One of its main advantages is that time-dependent three-dimensional simulations become feasible.…
A phase-field model that allows for quantitative simulations of low-speed eutectic and peritectic solidification under typical experimental conditions is developed. Its cornerstone is a smooth free-energy functional, designed so that the…
We present a phase-field crystal (PFC) model for solidification that accounts for thermal transport and a temperature-dependent lattice parameter. Elasticity effects are characterized through the continuous elastic field computed from the…
We present a phase field model of solidification which includes the effects of the crystalline orientation in the solid phase. This model describes grain boundaries as well as solid-liquid boundaries within a unified framework. With an…