Modified unified kinetic scheme for all flow regimes.

Area of Science:

• Computational fluid dynamics
• Kinetic theory
• Non-equilibrium thermodynamics

Background:

• Accurate prediction of fluid flow is crucial in many scientific and engineering fields.
• Existing models often struggle with complex flow regimes, particularly the transition regime.
• Kinetic schemes offer a promising approach but require refinement for broader applicability.

Purpose of the Study:

• To develop a modified unified kinetic scheme for predicting fluid flow behaviors across all flow regimes.
• To incorporate both free transport and collision mechanisms in macrovariable evolution.
• To enhance the physical realism and numerical accuracy of fluid flow simulations.

Main Methods:

• Calculating time evolution of macrovariables at cell interfaces by considering free transport and collision mechanisms.
• Obtaining macrovariable evolution through conservation constraints.
• Directly deriving the evolution of local Maxwellian distribution from macrovariable evolution via a one-to-one mapping.

Main Results:

• The modified scheme provides more physically realistic predictions of flow behaviors.
• Improved numerical accuracy is achieved across all flow regimes, especially in the complex transition flow regime.
• The enhancements introduce no additional computational complexity.

Conclusions:

• The developed unified kinetic scheme offers a significant advancement in fluid flow prediction.
• The method's ability to handle all flow regimes accurately, including the transition regime, makes it highly valuable.
• The computational efficiency of this improved scheme makes it practical for widespread application.