Lattice BGK kinetic model for high-speed compressible flows: Hydrodynamic and nonequilibrium behaviors

Abstract

PACS 47.11.-j -Computational methods in fluid dynamics. PACS 51.10.+y -Kinetic and transport theory of gases. PACS 05.20.Dd -Kinetic theory.Abstract. -We present a simple and general approach to formulate the lattice BGK model for high speed compressible flows. The main point consists of two parts: an appropriate discrete equilibrium distribution function (DEDF) f eq and a discrete velocity model with flexible velocity size. The DEDF is obtained by f eq = C −1 M, where M is a set of moment of the Maxwellian distribution function, and C is the matrix connecting the DEDF and the moments. The numerical components of C are determined by the discrete velocity model. The calculation of C −1 is based on the analytic solution which is a function of the parameter controlling the sizes of discrete velocity. The choosing of discrete velocity model has a high flexibility. The specific heat ratio of the system can be flexible. The approach works for the one-, two-and three-dimensional model constructions. As an example, we compose a new lattice BGK kinetic model which works not only for recovering the Navier-Stokes equations in the continuum limit but also for measuring the departure of system from its thermodynamic equilibrium. Via adjusting the sizes of the discrete velocities the stably simulated Mach number can be significantly increased up to 30 or even higher. The model is verified and validated by well-known benchmark tests. Some macroscopic behaviors of the system due to deviating from thermodynamic equilibrium around the shock wave interfaces are shown.

Multiple-relaxation-time lattice Boltzmann kinetic model for combustion

“…In 2013 we proposed a uniform scheme for formulating LBKM [76]. In the current work we formulate the discrete velocity model according to the same idea.…”

“…The LB kinetic model inherits naturally the function of Boltzmann equation, describing non-equilibrium effects in the system [33,44,68,[76][77][78][79]. The departure of the system from local thermodynamic non-equilibrium can be measured by the difference between the high order kinetic moments of f i and f eq i which are just (f k −f eq k ) in the current MRT-LB kinetic equation, (1).…”

“…In recent years the development of LB models for high speed compressible flows [69][70][71][72][73][74][75][76][77] makes it possible to simulate systems with shock wave. Very recently we presented two LBKMs for high Mach combustion and detonation phenomena [78,79].…”

Lattice Boltzmann kinetic modeling and simulation of thermal liquid–vapor system

“…In the recent two decades the lattice Boltzmann (LB) method has been becoming a promising simulation tool for various complex systems, 1,2 ranging from the low Mach number nearly incompressible°ows 3 to high speed compressible°ows under shocks, 4,5 from simple°uids to multiphase and/or multi-component°uids, [6][7][8][9][10][11][12][13][14] from phase transition kinetics 6,[8][9][10][11][12][13][14] to hydrodynamic instabilities, [15][16][17][18] etc. The LB methods in literature can be roughly classi¯ed into two categories, new solvers of various partial di®erential equations and kinetic models of various complex systems.…”

“…This idea was further speci¯ed in following works and considerable new physical insights for various systems were obtained from a more fundamental level. 2,5,[16][17][18] Most early LB models for multiphase°ows were for isothermal system and have been successfully applied to a wide variety of°ow problems, such as drop collisions, 19 wetting, 20 phase separation and phase ordering, 6-10 etc. In recent years, some thermal LB (TLB) multiphase models [11][12][13][14][21][22][23] have appeared.…”