Particle simulation of nonequilibrium gas flows based on ellipsoidal statistical Fokker-Planck model

In order to improve the efficiency of particle simulation method for gas flows spanning the rarefied and continuum regimes, one promising approach is to employ the Fokker-Planck-type gas kinetic model. The ellipsoidal statistical Fokker-Planck (ES-FP) model treats the evolution of individual molecular velocity as a continuous stochastic process, which can be equivalently described by the Langevin dynamics where the forces acting on each gas molecule are a linear drag force and an anisotropic fluctuating force. By utilizing the exact stochastic integral solution of the corresponding Langevin equation, the ES-FP model is numerically implemented in a particle Monte Carlo manner. In a validation of the particle scheme, excellent agreement is obtained between the simulation results and the analytical solution for the same initial-value problem of ES-FP equation. The ES-FP particle method is used to simulate the relaxation process in a nonequilibrium gas, and agrees well with the direct simulation Monte Carlo (DSMC) method in the predictions of viscous stress and heat flux. Furthermore, extensive ES-FP particle simulations are performed for Couette flows at different Knudsen numbers ranging from 0.001 to 10, as well as supersonic flat-plate flows at different Knudsen numbers ranging from 0.001 to 0.1. Both flow fields and surface quantities are investigated and compared with the DSMC or theoretical solutions. In the ES-FP simulations, the Prandtl number of gas can be corrected, and the physical behaviors in different flow regimes can be properly captured. With reasonable agreement between the ES-FP and DSMC results, the ES-FP simulation is found to be more efficient than DSMC and can significantly save memory cost and CPU time, especially for multi-dimensional flows in the low-Knudsen-number regime.