Discrete Boltzmann model with split collision for nonequilibrium reactive flows*

Abstract

A multi-relaxation-time discrete Boltzmann model (DBM) with split collision is proposed for both subsonic and supersonic compressible reacting flows, where chemical reactions take place among various components. The physical model is based on a unified set of discrete Boltzmann equations that describes the evolution of each chemical species with adjustable acceleration, specific heat ratio, and Prandtl number. On the right-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, respectively. The source terms can be calculated in three ways, among which the matrix inversion method possesses the highest physical accuracy and computational efficiency. Through Chapman–Enskog analysis, it is proved that the DBM is consistent with the reactive Navier–Stokes equations, Fick's law and the Stefan–Maxwell diffusion equation in the hydrodynamic limit. Compared with the one-step-relaxation model, the split collision model offers a detailed and precise description of hydrodynamic, thermodynamic, and chemical nonequilibrium effects. Finally, the model is validated by six benchmarks, including multicomponent diffusion, mixture in the force field, Kelvin–Helmholtz instability, flame at constant pressure, opposing chemical reaction, and steady detonation.