Free-Energy-Based Discrete Unified Gas Kinetic Scheme for van der Waals Fluid.

Area of Science:

• Computational Fluid Dynamics
• Multiphase Flow Modeling
• Free-Energy Theory

Background:

• The free-energy model is a robust approach for multiphase flow simulations.
• Discrete Unified Gas-Kinetic Scheme (DUGKS) offers efficient implementation.
• Integrating free-energy models into DUGKS presents challenges.

Purpose of the Study:

• Identify limitations of applying classical lattice Boltzmann free-energy models to DUGKS.
• Develop a well-balanced free-energy model for DUGKS to overcome identified hindrances.
• Validate the performance and stability of the improved DUGKS for multiphase flows.

Main Methods:

• Introduced classical lattice Boltzmann free-energy model into DUGKS with various flux reconstruction schemes.
• Developed and coupled a well-balanced free-energy model with DUGKS.
• Validated the model using coexisting density curves, Laplace's law, quiescent droplet tests, spinodal decomposition, and droplet coalescence.

Main Results:

• Force imbalance amplified by reconstruction errors hinders direct free-energy model application in DUGKS.
• The well-balanced free-energy model effectively removes amplified force imbalance influences.
• Consistent performance across different reconstruction schemes was observed for steady-state multiphase flows.
• Spurious currents were reduced to machine accuracy (10-15) in quiescent droplet tests.
• Stability issues were identified in transient flow simulations like spinodal decomposition and droplet coalescence.

Conclusions:

• The well-balanced free-energy model significantly enhances DUGKS for steady-state multiphase flow simulations.
• The improved DUGKS demonstrates high accuracy and minimal spurious currents.
• Further research is necessary to address the stability limitations of the current model in transient flow scenarios.