Abstract: Traditional computational fluid dynamics based on solving Navier-Stokes equations has achieved great success in many fields, but it has also encountered new bottlenecks and challenges in aerospace, microfluidic and other fields. The reasons can be divided into two aspects:(A) the problem of physical modeling; (B) the numerical accuracy and stability caused by discrete scheme. Reasonable and functional physical model is the premise of numerical simulation research. Problems at the level of physical modeling cannot be solved by improving numerical accuracy. A series of new concepts of combustion such as micro-scale combustion remind us that these more abundant but previously poorly understood characteristics of non-equilibrium behavior contains a large number of physical functions to be explored. In this paper we review the progress of Discrete Boltzmann Modeling method (DBM) for nonequilibrium combustion from the perspective of physical modeling and complex physical field analysis. DBM is one of the specific applications of coarse-grained modeling theory in non-equilibrium statistical physics in the field of fluid mechanics. It is a further development of phase space description method in the form of discrete Boltzmann equation. The methodology of DBM is to decompose a complex problem and select a perspective to study a set of kinetic properties of the system, so it is required that the kinetic moments describing this set of properties maintain their values in the model simplification. Based on the independent components of the kinetic moments, the phase space is constructed. The phase space and its subspaces are used to describe the non-equilibrium behavior of the system. The research perspective and modeling accuracy will be adjusted as the research progresses. With the help of DBM, kinetic processes such as the non-equilibrium and mutual conversion of internal energy in different degrees of freedom during the reaction process, which cannot be simulated by Navier-Stokes model, can be studied. In the process of internal and external explosions, the geometric convergent and divergent effects are equivalent to an "external field force", and the system is always in thermodynamic equilibrium state at the center of the sphere. At the von Neumann pressure peak, the system is not the furthest off equilibrium, but near equilibrium. The theoretical Chapmann-Jouguet values, the theoretical Zeldovich-Neumann-Doering (ZND) values and the DBM results are mutually verified outside the post-peak reaction region of von Neumann. The results of DBM in the reaction zone are consistent with those of ZND. In the compression stage before the von Neumann pressure peak, the DBM results are more physically reasonable. In the process of shock compression, compared with other degrees of freedom, the internal energy on the degree of freedom where the compression wave is located increases first, so the internal energy on this degree of freedom always deviates from its equilibrium state in the positive direction, while the internal energy on the transverse degree of freedom always deviates from its equilibrium state in the negative direction. From the perspective of the two-fluid model, the reactants and products deviate from thermodynamic equilibrium in opposite directions.

Key words: combustion, detonation, non-equilibrium, discrete effects, mesoscale modeling, kinetic theory