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Motivated by improving the performance of particle based Monte-Carlo simulations in the transitional regime, Fokker-Planck kinetic models have been devised and studied as approxi-* = post collision values Subscripts c = cell coll = collision

Bhatnagar-Gross-Krook (BGK) models are widely used to study rarefied gas dynamics. However, as simplified versions of the Boltzmann collision model, their performances are uncertain and need to be carefully investigated in highly nonequilibrium flows. In this study, several common BGK models, such as the Ellipsoidal Statistical BGK (ES-BGK) and Shakhov BGK (S-BGK) models, are theoretically analyzed using their moment equations. Then, numerical comparisons are performed between the Boltzmann collision model and BGK models based on various benchmarks, such as Fourier flow, Couette flow, and shock wave. The prediction performance of the ES-BGK model is better than that of the S-BGK model in Fourier flow, while prediction performance of the S-BGK model is better than that of the ES-BGK model in Couette flow and shock wave. However, with increasing Knudsen number or Mach number, the results of both ES-BGK and S-BGK deviate from the Boltzmann solutions. These phenomena are attributed to the incorrect governing equations of high-order moments of BGK models. To improve the performance of the current BGK models, the S-BGK model is extended by adding more high-order moments into the target distribution function of the original one. Our analytical and numerical results demonstrate that the extended S-BGK (S-BGK+) model provides the same relaxation coefficients as the Boltzmann collision model for the production terms of high-order moment equations. Compared to the other BGK models, the proposed S-BGK+ model exhibits better performance for various flow regimes.

This study examines a new hybrid particle scheme used as an alternative means of multiscale flow simulation. The hybrid particle scheme employs the direct simulation Monte Carlo (DSMC) method in rarefied flow regions and the low diffusion (LD) particle method in continuum flow regions. The numerical procedures of the low diffusion particle method are implemented within an existing DSMC algorithm. The performance of the LD-DSMC approach is assessed by studying Mach 10 nitrogen flow over a sphere with a global Knudsen number of 0.002. The hybrid scheme results show good overall agreement with results from standard DSMC and CFD computation. Subcell procedures are utilized to improve computational efficiency and reduce sensitivity to DSMC cell size in the hybrid scheme. This makes it possible to perform the LD-DSMC simulation on a much coarser mesh that leads to a significant reduction in computation time.

Hypersonic aerothermodynamics for a probe entering a planetary atmosphere is an important issue in space exploration. The probe experiences various Knudsen number regimes, ranging from rarefied to continuum, due to density variation in the planet's atmosphere. To simulate such multiscale flows, a novel hybrid particle scheme is employed in the present work. The hybrid particle scheme employs the direct simulation Monte Carlo (DSMC) method in rarefied flow regions and the low diffusion (LD) particle method in continuum flow regions. Numerical procedures in the low diffusion particle method are implemented within an existing DSMC algorithm. The hybrid scheme is assessed by studying Mach 10 nitrogen flow over a sphere with a global Knudsen number of 0.002. Standard DSMC and CFD results are compared with the LD-DSMC hybrid simulation results. The hybrid scheme results show good overall agreement with results from standard DSMC computation, while CFD is inaccurate especially in the wake where a highly rarefied region exists. The LD-DSMC hybrid solution is able to increase computational efficiency by 20% in comparison to DSMC. Also, a module initializing the LD-DSMC hybrid method with a Navier-Stokes solution is developed. The initialized solution agrees well with DSMC and requires only 45% of the resources.