An evaluation of the hybrid Fokker-Planck-DSMC approach for high-speed rarefied gas flows

Abstract

The Direct Simulation Monte Carlo (DSMC) method has been widely used for simulations of rarefied gas flows. It has been proven that the numerical solution of the DSMC method converges to the Boltzmann equation, providing a solid physical foundation for high Knudsen numbers. However, many aerospace engineering problems include both low and high-density regions in a single domain, making the DSMC method computationally expensive. Over the past decade, the particle Fokker-Planck (FP) method has been studied as a means to reduce computational costs near the continuum regime. While enhancing efficiency, the FP method loses physical accuracy at high Knudsen numbers. Aiming for universal accuracy and efficiency across the whole range of Knudsen numbers, the hybrid FP-DSMC method has been studied. Nevertheless, consistent comparisons among the DSMC, FP, and hybrid FP-DSMC methods have received limited attention so far. This paper presents a consistent comparative study of the DSMC, FP, and hybrid FP-DSMC methods to assess the accuracy and efficiency of the hybrid FP-DSMC method. The hybrid FP-DSMC solver is developed based on the open-source SPARTA framework. The benchmark problems include supersonic flow in a planar nozzle, hypersonic flow around a cylinder, and hypersonic flow around a THAAD-like missile. The results demonstrate that the hybrid FP-DSMC method can be more efficient than the DSMC method while being more accurate than the FP method. The speed-up achieved by the FP-DSMC method ranged from 1.5 to 14 times compared to the converged DSMC simulation.