Abstract
The construction of relevant initial conditions in the phase-field models for interfacial problems is discussed. If the model is supposed to have a local equilibrium at the interface, it must be based on a local distance function. However, since for the Cartesian coordinates non-uniform boundaries occur, the initial conditions have to be corrected in order to match the actual phenomena. We discuss the volume correction method, image initialisation, non-overlapping multi component concentration, etc. The methods presented can be used in the initial guess constructions for various phase-field models.
Original language | English |
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Pages (from-to) | 618-646 |
Number of pages | 29 |
Journal | East Asian Journal on Applied Mathematics |
Volume | 11 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2021 Aug |
Bibliographical note
Funding Information:H. Kim and C. Lee were supported by the Basic Science Research Program of the National Research Foundation of Korea (NRF) funded by the Ministry of Education under Grants NRF-2020R1A6A3A13077105 and NRF-2019R1A6A3A13094308, respectively. The corresponding author (J. Kim) expresses thanks for the support from Korea University.
Publisher Copyright:
© 2021 Global-Science Press.
Keywords
- Allen-Cahn equation
- Cahn-Hilliard equation
- Level set function
- Phase-field model
ASJC Scopus subject areas
- Applied Mathematics