Exponential Bhatnagar-Gross-Krook integrator for multiscale particle-based kinetic simulations

Area of Science:

• Computational physics
• Fluid dynamics
• Numerical analysis

Background:

• Multiscale rarefied flow simulations face challenges due to disparate spatiotemporal scales.
• Existing particle-based simulators require improved methods for handling particle advection and collisions.

Purpose of the Study:

• To develop a novel, consistent numerical scheme for coupled particle advection and BGK collision evolution.
• To enhance the accuracy and efficiency of particle-based stochastic simulations for rarefied gas dynamics.

Main Methods:

• A novel BGK particle method integrating high-order time integration and modified particle distributions.
• The scheme is designed for compatibility with existing Direct Simulation Monte Carlo (DSMC) codes.
• Probabilistic interpretation of time integration ensures step-size independence.

Main Results:

• Demonstrated accuracy and performance across a wide range of rarefaction parameters for prototypic gas flows.
• The scheme honors positivity of the velocity distribution.
• The method shows robustness and flexibility for multiscale gas phenomena.

Conclusions:

• The developed exponential BGK integrator offers a robust and flexible approach for rarefied gas simulations.
• This scheme facilitates more affordable and accurate simulations of large-scale, multiscale rarefied gas phenomena.
• The method is readily implementable in existing particle-based simulation frameworks.