Discrete Boltzmann model with split collision for combustion with nonequilibrium effects

A multi-relaxation-time discrete Boltzmann model (DBM) with split collision is proposed for both subsonic and supersonic compressible combustion where the chemical reaction takes place among various components. The physical model is based on a unified set of discrete Boltzmann equations which describes the evolution of each chemical species with an adjustable acceleration, specific heat ratio and Prandtl number. On the righ-hand side of discrete Boltzmann equations, the collision, force, and reaction terms denote the change rates of distribution functions due to self- and cross-collisions, external forces, and chemical reactions. The source terms can be calculated in three ways among which the matrix inversion method possesses the highest physical accuracy and computational efficiency. Via the Chapman-Enskog analysis, it is proved that the DBM is consistent with the reactive Navier-Stokes equations with external forces, Fick's law and Stefan-Maxwell diffusion equation in the hydrodynamic limit. Compared with the one-step-relaxation model, the hydrodynamic, thermodynamic, and chemical nonequilibrium effects can be captured and measured more detailedly and precisely by the split collision model. Finally, the model is validated by six benchmarks, i.e., the multicomponent diffusion, Kelvin-Helmholtz instability, mixture in the force field, flame at constant pressure, opposing chemical reaction, and steady detonation.