  A new lattice Boltzmann model (LBM) for chemically reactive mixtures is
presented. The approach capitalizes on the recently introduced
thermodynamically consistent LBM for multicomponent mixtures of ideal gases.
Similar to the non-reactive case, the present LBM features Stefan--Maxwell
diffusion of chemical species and a fully on-lattice mean-field realization of
the momentum and energy of the flow. Besides introducing the reaction mechanism
into the kinetic equations for the species, the proposed LBM also features a
new realization of the compressible flow by using a concept of extended
equilibrium on a standard lattice in three dimensions. The full thermodynamic
consistency of the original non-reactive multicomponent LBM enables to extend
the temperature dynamics to the reactive mixtures by merely including the
enthalpy of formation in addition to the previously considered sensible energy.
Furthermore, we describe in detail the boundary conditions to be used for
reactive flows of practical interest. The model is validated against a direct
numerical simulation of various burning regimes of a hydrogen/air mixture in a
microchannel, in two and three dimensions. Excellent comparison in these
demanding benchmarks indicates that the proposed LBM can be a valuable and
universal model for complex reactive flows.
