  In this paper we present a lattice Boltzmann model for combustion and
detonation. In this model the fluid behavior is described by a
finite-difference lattice Boltzmann model by Gan et al. [Physica A, 2008, 387:
1721]. The chemical reaction is described by the Lee-Tarver model [Phys.
Fluids, 1980, 23: 2362]. The reaction heat is naturally coupled with the flow
behavior. Due to the separation of time scales in the chemical and
thermodynamic processes, a key technique for a successful simulation is to use
the operator-splitting scheme. The new model is verified and validated by
well-known benchmark tests. As a specific application of the new model, we
studied the simple steady detonation phenomenon. To show the merit of LB model
over the traditional ones, we focus on the reaction zone to study the
non-equilibrium effects. It is interesting to find that, at the von Neumann
peak, the system is nearly in its thermodynamic equilibrium. At the two sides
of the von Neumann peak, the system deviates from its equilibrium in opposite
directions. In the front of von Neumann peak, due to the strong compression
from the reaction product behind the von Neumann peak, the system experiences a
sudden deviation from thermodynamic equilibrium. Behind the von Neumann peak,
the release of chemical energy results in thermal expansion of the matter
within the reaction zone, which drives the system to deviate the thermodynamic
equilibrium in the opposite direction. From the deviation from thermodynamic
equilibrium, defined in this paper, one can understand more on the macroscopic
effects of the system due to the deviation from its thermodynamic equilibrium.
