A Well-Balanced Unified Gas-Kinetic Scheme for Multicomponent Flows under External Force Field

Area of Science:

• Multiphase flow dynamics
• Computational fluid dynamics
• Astrophysical fluid mechanics

Background:

• Atmospheric evolution and galaxy formation involve complex multicomponent gas flows under gravity.
• Gas dynamics under external forces exhibit multiscale behavior due to density variations, challenging numerical methods.
• Accurately capturing scale-dependent physics is vital for simulating these phenomena.

Purpose of the Study:

• To develop a well-balanced unified gas-kinetic scheme (UGKS) for simulating cross-scale multicomponent gas flows under external force fields.
• To ensure the numerical scheme can accurately evolve gravitational systems to hydrostatic equilibrium and maintain it.
• To provide a robust tool for studying long-term evolving systems like galaxy formation.

Main Methods:

• Development of a unified gas-kinetic scheme (UGKS) based on the Boltzmann model equation for gas mixtures.
• Leveraging space-time integral solutions to construct numerical flux functions.
• Formal theoretical analysis and numerical validations to prove the well-balanced property of the scheme.

Main Results:

• The developed UGKS accurately captures scale-dependent flow physics in multicomponent gases under gravity.
• The scheme demonstrates the capability to evolve systems to hydrostatic equilibrium and maintain it.
• New physical phenomena, such as decoupled transport of gas components in the transition regime, were identified and studied.

Conclusions:

• The well-balanced UGKS is effective for simulating cross-scale multicomponent flows under external force fields.
• The scheme provides a self-conditioned mechanism to recover flow dynamics across various regimes.
• This method is crucial for accurate long-term simulations in fields like atmospheric science and astrophysics.