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

TL;DR

This paper introduces a second-order accurate stochastic particle Fokker-Planck model for diatomic gases, significantly improving computational efficiency and accuracy in simulating rarefied gas flows compared to previous models.

Contribution

The study develops a unified stochastic particle FPM model with second-order spatio-temporal accuracy, enhancing efficiency and accuracy over existing first-order models.

Findings

Good agreement with DSMC results

Reduced computational cost

Enables larger cell sizes and time steps

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.