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To probe both the Hydrodynamic Non-Equilibrium (HNE) and ThermodynamicNon-Equilibrium (TNE) in the combustion process, a two-dimensionalMultiple-Relaxation-Time (MRT) version of Lattice Boltzmann Kinetic Model(LBKM)for combustion phenomena is presented. The chemical energy released in theprogress of combustion is dynamically coupled into the system by adding achemical term to the LB kinetic equation. Beside describing the evolutions ofthe conserved quantities, the density, momentum and energy, which are what theNavier-Stokes model describes, the MRT-LBKM presents also a coarse-graineddescription on the evolutions of some non-conserved quantities. The currentmodel works for both subsonic and supersonic flows with or without chemicalreaction. In this model both the specific-heat ratio and the Prandtl number areflexible, the TNE effects are naturally presented in each simulation step. Themodel is verified and validated via well-known benchmark tests. As an initialapplication, various non-equilibrium behaviours, including the complexinterplays between various HNEs, between various TNEs and between the HNE andTNE, around the detonation wave in the unsteady and steady one-dimensionaldetonation processes are preliminarily probed. It is found that the systemviscosity (or heat conductivity) decreases the local TNE, but increase theglobal TNE around the detonation wave, that even locally, the system viscosity(or heat conductivity) results in two kinds of competing trends, to increaseand to decrease the TNE effects. The physical reason is that the viscosity (orheat conductivity) takes part in both the thermodynamic and hydrodynamicresponses.

Multiple-relaxation-time lattice Boltzmann kinetic model for combustion