This short tutorial is used at the ChiMaD Phase Field Workshop XVI, March 19-21, 2024. The goal is to provide an introduction to the driving force extension method in our recent paper:
Jin Zhang, Alexander F. Chadwick, David L. Chopp, Peter W. Voorhees, "Phase Field Modeling with Large Driving Forces," npj Computational Materials, 9 (2023) 166. doi: 10.1038/s41524-023-01118-0
Here, a 1D KKS model is used for demonstration. Several assumptions are made for simplification so that we can focus on the problem of the large driving force and the driving force extension method.
The driving force extension method is used to solve the stability problem resulting from a large driving force in phase field modeling.
Phase field equation typically has the following form
where
To solve the problem of the large driving force but still use a large grid size, the driving force extension method introduces a simple modification of the phase field equation
where
Here,
The algorithm for the projection
You will need Python 3 installed.
If you don't have Python, you can use Colab (Google account is needed)
Also, you need numpy and matplotlib. Install them by
pip install numpy matplotlib
To use the jupyter notebook, you need to install jupyter by
pip install jupyterlab
To open the jupyter notebook, run in the terminal
jupyter-lab
A browser window should automatically open.
-
driving_force_extension.ipynb : tutorial notebook
-
driving_force_extension.py : python script in case you don't have jupyter
The python script is generated by
jupyter nbconvert --to script driving_force_extension.ipynb
- dg : derivative of the double well (times 0.5)
- laplacian_1d : Laplacian (cell-based)
- apply_bc : apply boundary condition
- velext_simple : a simple velocity extension in 1D
- velext_fim : a general velocity extension in 1D
- kks1d : the KKS model
If you use the driving force extension method in your work, please cite our paper
Zhang, J., Chadwick, A.F., Chopp, D.L. et al. Phase field modeling with large driving forces. npj Comput Mater 9, 166 (2023).
You can use the BibTeX
@article{Zhang2023,
title={Phase field modeling with large driving forces},
author={Zhang, Jin and Chadwick, Alexander F and Chopp, David L and Voorhees, Peter W},
journal={npj Computational Materials},
volume={9},
number={1},
pages={166},
year={2023},
publisher={Nature Publishing Group UK London}
}
For questions, comments, suggestions, or bug reports, email me at jzhang@northwestern.edu or visit github.