Assessment of Various Fokker-Planck Methods for Hypersonic Rarefied Flows

The Boltzmann equation provides a statistical description of dilute gas, which is valid from the continuum to the free molecular regime. The Direct Simulation Monte Carlo (DSMC) method has been extensively used to obtain the numerical solution of the Boltzmann equation. However, the DSMC method becomes prohibitively expensive in the low Knudsen number regime due to a lot of collisions. The particle-based Fokker-Planck method has been studied to reduce the computational cost of the DSMC method. The Fokker-Planck operator approximates the discrete collision process as a convection-diffusion process in the velocity space. A few Fokker-Planck (FP) models have been proposed to achieve consistency with the Boltzmann equation in the hydrodynamic limit. However, comprehensive comparative study to assess their performance is still scarce. In this work, the Cubic-FP model, ES-FP FP model, and Quad-EFP model are numerically investigated to assess their accuracy and efficiency. The Lofthouse case of hypersonic cylinder flow is studied with the DSMC solution as the reference. The comparison results show that the ES-FP and Quad-EFP models, which satisfy the H-theorem, provide better predictions than the Cubic-FP model.