Particle-based fluid dynamics: Comparison of different Bhatnagar-Gross-Krook models and the direct simulation Monte Carlo method for hypersonic flows

Abstract

The Bhatnagar-Gross-Krook (BGK) model as well as its extensions (ellipsoidal statistical BGK, Shakhov BGK, unified BGK) are used in particle-based fluid dynamics and compared with the Direct Simulation Monte Carlo (DSMC) method. To this

Particle-based hybrid and multiscale methods for nonequilibrium gas flows

“…The ESBGK model replaces the Maxwell distribution with an anisotropic Gaussian distribution, which is the same as that used in the ES-FP method. It was validated in detail for a variety of gas flows and showed a very good agreement with DSMC results [57]. Recently, the particle ESBGK method has been extended to diatomic molecules [58] and included quantized vibrational energies [59].…”

“…Another target distribution function that is frequently used to correct the Prandtl number is the Shakhov distribution function [56]. The particle SBGK method was described in the reference [57]. It was shown that the SBGK method performs slightly better in the reproduction of correct shock structures in hypersonic flows compared with the ESBGK method.…”

“…Nevertheless, it was also shown that the energy conservation scheme for the particle method becomes more complicated for the SBGK model and that the computational time increases compared to the ESBGK model. An overview and comparison of different sampling methods for each of the mentioned target distribution functions as well as the discussion of different energy and momentum conserving schemes are given in the reference [57].…”

An Efficient Algorithm of the Unified Stochastic Particle Bhatnagar-Gross-Krook Method for the Simulation of Multi-Scale Gas Flows

“…t f is a target distribution function for the relaxation process [19]. In the original BGK model, t f is assumed to be the Maxwellian distribution function, i.e.…”

“…As decoupling the particle motion and collision in most stochastic particle methods, they only asymptotically preserve the Euler limit. For example, considering the traditional stochastic particle BGK (SP-BGK) method [8,19], when the time step is much larger than the mean collision time, its numerical viscosity is of the first order of the time step, i.e. num BGK t …”