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Motivation: Can we efficiently simulate rarefied gas flows in regimes where CFD fails and DSMC becomes too expensive?
Computational Fluid Dynamics (CFD) loses physical accuracy in rarefied regimes due to the breakdown of continuum assumptions.
Direct Simulation Monte Carlo (DSMC) is accurate across all Knudsen regimes but becomes prohibitively expensive near the continuum regime.
A Stochastic Particle Fokker-Planck Method
The Fokker–Planck (FP) equation is a simplified form of the Boltzmann equation that models intermolecular collisions as a drift–diffusion process in velocity space. Unlike the Direct Simulation Monte Carlo (DSMC) method, which explicitly simulates binary collisions, the FP approach evolves particles along stochastic trajectories governed by drift and diffusion coefficients. This particle-based framework preserves the advantages of DSMC algorithms—such as boundary treatment and particle sampling—while significantly reducing computational cost in near-continuum regimes. By extending the FP method to monatomic, diatomic, and mixture gases, including internal energy exchanges, the approach enables efficient and accurate simulations of multiscale rarefied flows.
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