A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook （ES- BGK） model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, t...A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook （ES- BGK） model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in the Burnett level, two kinds of discrete velocity model are introduced and the relations between nonequilibrium quantities and the viscous stress and heat flux in the Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, those based on the Navier-Stokes or the Burnett equations.展开更多
In [16] a visco-elastic relaxation system, called the relaxed Burnett system, was proposed by Jin and Slemrod as a moment approximation to the Boltzmann equation. The relaxed Burnett system is weakly parabolic, has a ...In [16] a visco-elastic relaxation system, called the relaxed Burnett system, was proposed by Jin and Slemrod as a moment approximation to the Boltzmann equation. The relaxed Burnett system is weakly parabolic, has a linearly hyperbolic convection part, and is endowed with a generalized entropy inequality. It agrees with the solution of the Boltzmann equation up to the Burnett order via the Chapman-Enskog expansion. We develop a one-dimensional non-oscillatory numerical scheme based on the relaxed Burnett system for the Boltzmann equation. We compare numerical results for stationary shocks based on this relaxation scheme, and those obtained by the DSMC (Direct Simulation Monte Carlo), by the Navier-Stokes equations and by the extended thermodynamics with thirteen moments (the Grad equations). Our numerical experiments show that the relaxed Burnett gives more accurate approximations to the shock profiles of the Boltzmann equation obtained by the DSMC, for a range of Mach numbers for hypersonic flows, than those obtained by the other hydrodynamic systems.展开更多
基金The authors would like to acknowledge the support of the National Natural Science Foundation of China （Grant Nos. 11475028, 11772064, 11502117, and U1530261）, and Science Challenge Project （Grant Nos. JCKY2016212A501 and TZ2016002）.
文摘A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook （ES- BGK） model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in the Burnett level, two kinds of discrete velocity model are introduced and the relations between nonequilibrium quantities and the viscous stress and heat flux in the Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, those based on the Navier-Stokes or the Burnett equations.
基金Supported by NSF grant DMS-0196106 Supported by NSF grant DMS-9803223 and DMS-00711463.
文摘In [16] a visco-elastic relaxation system, called the relaxed Burnett system, was proposed by Jin and Slemrod as a moment approximation to the Boltzmann equation. The relaxed Burnett system is weakly parabolic, has a linearly hyperbolic convection part, and is endowed with a generalized entropy inequality. It agrees with the solution of the Boltzmann equation up to the Burnett order via the Chapman-Enskog expansion. We develop a one-dimensional non-oscillatory numerical scheme based on the relaxed Burnett system for the Boltzmann equation. We compare numerical results for stationary shocks based on this relaxation scheme, and those obtained by the DSMC (Direct Simulation Monte Carlo), by the Navier-Stokes equations and by the extended thermodynamics with thirteen moments (the Grad equations). Our numerical experiments show that the relaxed Burnett gives more accurate approximations to the shock profiles of the Boltzmann equation obtained by the DSMC, for a range of Mach numbers for hypersonic flows, than those obtained by the other hydrodynamic systems.
