Simplified unified wave-particle method with quantified model-competition mechanism for numerical calculation of...

Area of Science:

• Computational fluid dynamics
• Multiscale flow modeling
• Kinetic theory

Background:

• Accurate simulation of fluid flows across various scales (from rarefied to continuum) remains a challenge.
• Existing methods often struggle to bridge the gap between kinetic and continuum regimes.
• The Boltzmann-BGK equation provides a foundation for understanding gas kinetic phenomena.

Purpose of the Study:

• To develop a novel numerical method for multiscale fluid flow simulation.
• To quantitatively determine the interplay between rarefied and continuum flow models.
• To validate the proposed method across diverse flow regimes.

Main Methods:

• Extraction of a quantified model-competition (QMC) mechanism from the Boltzmann-BGK equation.
• Construction of a simplified unified wave-particle (SUWP) method combining stochastic particle and Navier-Stokes solvers.
• Quantitative weighting of rarefied and continuum models within each computational cell based on the QMC mechanism.

Main Results:

• The SUWP method demonstrated validity and accuracy across multiple test cases.
• Successful simulation of high nonequilibrium shock waves and unsteady shock tubes (wide Kn range).
• Accurate modeling of hypersonic flow around a cylinder from free-molecular to near-continuum regimes, including viscous boundary layers.

Conclusions:

• The QMC mechanism provides a robust framework for unifying different flow models.
• The SUWP method offers a promising approach for accurate and efficient multiscale flow simulations.
• The study highlights the importance of quantitatively balancing kinetic and continuum descriptions.