Phase-field method based on discrete unified gas-kinetic scheme for large-density-ratio two-phase flows

Area of Science:

• Computational fluid dynamics
• Multiphase flow modeling
• Kinetic theory

Background:

• Accurate simulation of incompressible multiphase fluid flows is crucial for various engineering applications.
• Existing methods often face challenges in precisely capturing complex interface dynamics and large property ratios.
• The discrete unified gas-kinetic scheme (DUGKS) offers a promising kinetic approach for fluid flow simulations.

Purpose of the Study:

• To propose a novel phase-field method within the DUGKS framework for incompressible multiphase fluid flows.
• To develop kinetic models for solving the Allen-Cahn equation (interface behavior) and incompressible hydrodynamic equations (flow field).
• To validate the proposed method through a series of benchmark cases and comparisons with the lattice Boltzmann method (LBM).

Main Methods:

• Development of two kinetic models: one for the conservative Allen-Cahn equation and another for incompressible hydrodynamic equations.
• Utilizing a truncated equilibrium distribution function and a modified source term to recover macroscopic equations via Chapman-Enskog analysis.
• Simplification of source term calculations involving high-order derivatives in the quasi-incompressible model.

Main Results:

• The method achieved second-order convergence in interface diagonal translation tests.
• Demonstrated capability in tracking severely deformed interfaces and provided reliable solutions for stationary bubble and spinodal decomposition problems with high density ratios.
• Simulated layered Poiseuille flow with large viscosity ratios, showing good agreement with analytical solutions.
• Precisely predicted interface evolution in Rayleigh-Taylor instability, although detailed complex patterns were not fully captured due to numerical dissipation.

Conclusions:

• The proposed DUGKS-based phase-field method is effective for simulating incompressible multiphase flows, particularly in capturing overall interface behavior and flow dynamics.
• The method shows good accuracy and stability for various benchmark cases, including those with large density and viscosity ratios.
• Further improvements, such as developing a high-order DUGKS, are needed to resolve intricate interface details and reduce numerical dissipation for complex phenomena.