Anisotropy in wavelet-based phase field models

Maciek Korzec, Andreas Münch, Endre Süli, Barbara Wagner

Research output: Contribution to journalArticlepeer-review

Abstract

When describing the anisotropic evolution of microstructures in solids using phase-field models, the anisotropy of the crystalline phases is usually introduced into the interfacial energy by directional dependencies of the gradient energy coefficients. We consider an alternative approach based on a wavelet analogue of the Laplace operator that is intrinsically anisotropic and linear. The paper focuses on the classical coupled temperature/Ginzburg--Landau type phase-field model for dendritic growth. For the model based on the wavelet analogue, existence, uniqueness and continuous dependence on initial data are proved for weak solutions. Numerical studies of the wavelet based phase-field model show dendritic growth similar to the results obtained for classical phase-field models.
Original languageEnglish (US)
Pages (from-to)1167-1187
Number of pages21
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume21
Issue number4
DOIs
StatePublished - Apr 1 2016
Externally publishedYes

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