Anisotropy in wavelet-based phase field models

Journal article

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.

Authors: Korzec, M; Muench, A; Suli, E; Wagner, B

• Publication status: Accepted
• Peer review status: Peer reviewed
• Publisher: American Institute of Mathematical Sciences
• Journal: Discrete and Continuous Dynamical Systems Series B: a journal bridging mathematics and sciences
• Publication date: 2016-01-01
• EISSN: 1553-524X
• ISSN: 1531-3492
• Keywords: sharp interface model; wavelets; phase-field model; free boundaries