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Phase-field lattice Boltzmann model for interface tracking of a binary fluid system based on the Allen-Cahn equation
1Department of Aeronautics and Astronautics, Fudan University, 220 Handan Road, Shanghai, 200433, China.
Physical Review. E
|December 17, 2020
Summary
A new lattice Boltzmann (LB) model accurately tracks binary fluid interfaces using the Allen-Cahn equation. This phase field model demonstrates enhanced accuracy and stability in complex simulations.
Area of Science:
- Computational fluid dynamics
- Multiphase flow modeling
- Phase field methods
Background:
- Accurate simulation of binary fluid interfaces is crucial for understanding phenomena like droplet formation and instability.
- Existing models often face challenges with accuracy and stability in complex flow scenarios.
- The Allen-Cahn equation is a common phase field model, but its conservative form requires careful numerical implementation.
Purpose of the Study:
- To develop and validate a novel lattice Boltzmann (LB) model for tracking binary fluid interfaces.
- To ensure the model correctly recovers the conservative-form Allen-Cahn equation.
- To demonstrate the model's capability in simulating various complex two- and three-dimensional fluid systems.
Main Methods:
- A conservative-form lattice Boltzmann model was developed using a modified LB equation and an equilibrium distribution function.
- Chapman-Enskog analysis was employed to verify the recovery of the conservative Allen-Cahn equation.
- Extensive 2D and 3D benchmark tests were performed, including interface translation, rotation, and deformation in shear flows.
- Coupling with incompressible hydrodynamic equations allowed simulation of droplet dynamics, spinodal decomposition, and Rayleigh-Taylor instability.
Main Results:
- The proposed LB model accurately captures binary fluid interfaces.
- Benchmark tests demonstrated superior accuracy and stability compared to existing models.
- Simulations of stationary droplets, spinodal decomposition, and Rayleigh-Taylor instability showed the model's effectiveness.
- The model successfully recovered the conservative Allen-Cahn equation via Chapman-Enskog analysis.
Conclusions:
- The developed lattice Boltzmann model provides a robust and accurate method for simulating binary fluid systems.
- The model exhibits enhanced performance in handling complex interface dynamics.
- This approach offers a valuable tool for research in multiphase flow and complex fluid phenomena.
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