Concepts of modeling surface energy anisotropy in phase-field approaches

Oleg Tschukin,Michael Selzer,Alexander Silberzahn,Daniel Schneider,Britta Nestler,Prince G K Amos

doi:10.1186/s40517-017-0077-9

Abstract

To simulate the growth of geological veins, it is necessary to model the crystal shape anisotropy. Two different models, classical and natural models, which incorporate the surface energy anisotropy into the objective functional of Ginzburg–Landau type, are presented here. Phase-field evolution equations, considered in this work, are derived using the variational approach, and correspond to the conservative Allen–Cahn-type equation. For three characteristic anisotropy formulations, we show what kind of difficulties arise in the simulations for the presented models. Particularly, if the anisotropy becomes strong, the phase-field evolution equations become ill-posed. Thus, we present regularized phase-field models and discuss the corresponding simulation results. Furthermore, in the scope of the grain growth simulation, we extend the original two-phase models to multiphases.

Highlights

In the field of geothermal energy, new developing and integrating technologies are necessary for its establishment as a key element in the future global energy concept
For three characteristic anisotropy formulations, we show what kind of difficulties arise in the simulations for the presented models
The technical details of this construction are presented by Eggleston et al (2001) and applied, in particular, in the phasefield simulations by Fleck et al (2011). We disregard this approach of the regularization of the anisotropy formulation, but consider the regularization of the phase-field model, whereby an additional term is incorporated into the objective functionals [Eqs. (12) and (14)]

Summary

Background

In the field of geothermal energy, new developing and integrating technologies are necessary for its establishment as a key element in the future global energy concept. The technical details of this construction are presented by Eggleston et al (2001) and applied, in particular, in the phasefield simulations by Fleck et al (2011) We disregard this approach of the regularization of the anisotropy formulation, but consider the regularization of the phase-field model, whereby an additional term is incorporated into the objective functionals [Eqs. Numerical experiments Simulations rendered in the present work are performed using the solver PACE3D (Parallel Algorithms of Crystal Evolution in 3D), consisting of over 560,000 lines of C code In this multifunctional solver, the phase-field equations are basically solved in three dimensions in an efficient manner, coupled with physical processes like mass and heat diffusion, fluid flow, elastic and plastic effects, etc.

Discussion

Conclusions