Multiple-relaxation-time lattice Boltzmann kinetic model for combustion
  To probe both the Hydrodynamic Non-Equilibrium (HNE) and Thermodynamic Non-Equilibrium (TNE) in the combustion process, a two-dimensional Multiple-Relaxation-Time (MRT) version of Lattice Boltzmann Kinetic Model(LBKM) for combustion phenomena is presented. The chemical energy released in the progress of combustion is dynamically coupled into the system by adding a chemical term to the LB kinetic equation. Beside describing the evolutions of the conserved quantities, the density, momentum and energy, which are what the Navier-Stokes model describes, the MRT-LBKM presents also a coarse-grained description on the evolutions of some non-conserved quantities. The current model works for both subsonic and supersonic flows with or without chemical reaction. In this model both the specific-heat ratio and the Prandtl number are flexible, the TNE effects are naturally presented in each simulation step. The model is verified and validated via well-known benchmark tests. As an initial application, various non-equilibrium behaviours, including the complex interplays between various HNEs, between various TNEs and between the HNE and TNE, around the detonation wave in the unsteady and steady one-dimensional detonation processes are preliminarily probed. It is found that the system viscosity (or heat conductivity) decreases the local TNE, but increase the global TNE around the detonation wave, that even locally, the system viscosity (or heat conductivity) results in two kinds of competing trends, to increase and to decrease the TNE effects. The physical reason is that the viscosity (or heat conductivity) takes part in both the thermodynamic and hydrodynamic responses. 
Aiguo Xu, Chuandong Lin, Guangcai Zhang, and Yingjun Li
cond-mat.soft physics.flu-dyn