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High-order lattice-Boltzmann model for the Cahn-Hilliard equation
Chunhua Zhang1, Zhaoli Guo1, Hong Liang2
1State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China.
Physical Review. E
|May 22, 2019
Summary
This study introduces a high-order lattice Boltzmann equation model for the Cahn-Hilliard equation (CHE) to accurately simulate two-phase fluid flows. The new model enhances interface tracking accuracy and stability compared to existing methods.
Area of Science:
- Computational fluid dynamics
- Phase-field modeling
Background:
- The Cahn-Hilliard equation (CHE) is crucial for modeling two-phase fluid flows.
- Accurate interface tracking is essential for predicting fluid behavior.
Purpose of the Study:
- Develop a high-order lattice Boltzmann equation (LBE) model for the CHE.
- Improve accuracy and stability in interface tracking for two-phase flows.
Main Methods:
- Utilized a fourth-order Chapman-Enskog expansion for LBE model development.
- Performed truncation error analysis to identify and correct leading error terms.
- Employed Maxwell iteration for result verification.
Main Results:
- Identified a leading truncation error proportional to the Peclet number.
- Incorporated a correction term to recover the CHE up to third order.
- Demonstrated improved accuracy and stability in benchmark simulations.
Conclusions:
- The proposed high-order LBE model offers superior performance for CHE simulations.
- This advancement is beneficial for accurate interface tracking in complex fluid systems.
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