Improving Spatio-Temporal Accuracy of the Stochastic Particle Fokker-Planck Model

Abstract

Accurate prediction of rarefied gas flows is important for space vehicle design, particularly in rarefied regimes where the Navier-Stokes equations are no more valid. While the direct simulation Monte Carlo (DSMC) method acts as a numerical solver for rarefied gas flows, it becomes inefficient when dealing with near-continuum regimes. The Fokker-Planck (FP) model improves computational efficiency by approximating particle collisions as a drift-diffusion process. The FP model has been extended to handle diatomic gases, such as the Fokker-Planck-Master (FPM) model. The FPM model's first-order accuracy in both time and space limits computational efficiency gains. This study proposes a unified stochastic particle FPM (USP-FPM) model that achieves second-order spatio-temporal accuracy for diatomic gases. Temporal accuracy is improved by introducing second-order energy relaxation into the USP-FP method. Spatial accuracy is improved by employing a polynomial reconstruction method for macroscopic properties. The USP-FPM model is validated through two numerical simulations: relaxation to thermal equilibrium in a homogeneous flow and hypersonic flow over a vertical plate. The results demonstrate that the USP-FPM model shows good agreement with DSMC results and significantly reduces computational cost by enabling larger cell sizes and time steps.