WIAS Preprint No. 2050, (2014)

Anisotropy in wavelet based phase field models


Authors

  • Korzec, Maciek
  • Münch, Andreas
  • Süli, Endre
  • Wagner, Barbara

2010 Mathematics Subject Classification

  • 34E13 74N20 74E10

Keywords

  • Phase-field model, wavelets, sharp interface model, free boundaries

DOI

10.20347/WIAS.PREPRINT.2050

Abstract

Anisotropy is an essential feature of phase-field models, in particular when describing the evolution of microstructures in solids. The symmetries of the crystalline phases are reflected in the interfacial energy by introducing corresponding directional dependencies in the gradient energy coefficients, which multiply the highest order derivative in the phase-field model. This paper instead considers an alternative approach, where the anisotropic gradient energy terms are replaced by a wavelet analogue that is intrinsically anisotropic and linear. In our studies we focus on the classical coupled temperature - Ginzburg-Landau type phase-field model for dendritic growth. For the resulting derivative-free wavelet analogue existence, uniqueness and continuous dependence on initial data for weak solutions is proved. The ability to capture dendritic growth similar to the results obtained from classical models is investigated numerically.

Appeared in

  • Discrete Contin. Dyn. Syst. Ser. B, 21 (2016) pp. 1167--1187.

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