Local volume-conserving lattice Boltzmann model for incompressible multiphase flows

Area of Science:

• Computational fluid dynamics
• Phase field modeling
• Numerical analysis

Background:

• The classical Cahn-Hilliard equation is widely used for two-phase fluid dynamics simulations.
• A key limitation is its inability to guarantee volume conservation for each phase.
• This deficiency hinders accurate simulation of fluid interfaces.

Purpose of the Study:

• To address the volume non-conservation issue in classical Cahn-Hilliard simulations.
• To develop an accurate interface-capturing lattice Boltzmann model for two-phase flow.
• To improve the simulation of droplet dynamics and interface morphology.

Main Methods:

• Introduced a modified Cahn-Hilliard equation combining profile correction and level-set approaches.
• Developed an interface-capturing lattice Boltzmann model based on the modified equation.
• Performed numerical simulations including stationary droplets, vortex, Rayleigh-Plateau instability, and shear flow deformation.

Main Results:

• The proposed lattice Boltzmann model effectively maintains local volume conservation.
• Accurate interface capturing was demonstrated across various simulation scenarios.
• The model showed superior volume conservation and interface morphology representation compared to classical Cahn-Hilliard-based models, especially for small droplets.

Conclusions:

• The modified Cahn-Hilliard equation and the proposed lattice Boltzmann model overcome the volume non-conservation limitations of classical methods.
• This approach provides a more accurate and reliable tool for simulating two-phase fluid dynamics.
• The enhanced model is particularly beneficial for problems involving small droplets and complex interface dynamics.