Double-distribution-function discrete Boltzmann model for combustion

A 2-dimensional discrete Boltzmann model for combustion is presented. Mathematically, the model is composed of two coupled discrete Boltzmann equations for two species and a phenomenological equation for chemical reaction process. Physically, apart from the macroscopic behaviors described by a reactive Navier-Stokes model, this model presents also more information on the thermodynamic nonequilibrium. This model adopts 16 discrete velocities. It works for both subsonic and supersonic combustion phenomena with flexible specific heat ratio. To discuss the physical accuracy of the coarse-grained model for nonequilibrium behaviors, three other discrete velocity models are used for comparisons. Numerical results are compared with analytical solutions based on both the first-order and second-order truncations of the distribution function. It is confirmed that the physical accuracy increases with the increasing moment relations needed by nonequlibrium manifestations. Furthermore, compared with the single distribution function model, this model can simulate more details of combustion.