Burnett-level multi-relaxation-time central-moment discrete Boltzmann modeling of reactive flows

A multi-relaxation-time central-moment discrete Boltzmann method (CDBM) is developed for compressible reactive flows, incorporating the effects of chemical reactions. The Chapman–Enskog multiscale analysis demonstrates that the model recovers the Burnett equations in the hydrodynamic limit, with tunable specific heat ratios and Prandtl numbers. Within the CDBM framework, a unified Boltzmann equation governs the evolution of hydrodynamic variables, thermodynamic quantities, and higher-order central moments. The collision and reaction term are consistently computed via matrix inversion method. A two-dimensional twenty-five discrete velocities, exhibiting favorable spatial symmetry, is constructed and employed. The model is validated through simulations of the thermal Couette flow, homogeneous chemical reaction, steady detonation wave, and collision of two detonation waves. This work presents a versatile numerical simulation tool capable of addressing complex reactive flows characterized by hydrodynamic and thermodynamic nonequilibrium effects, applicable to both scientific research and engineering practice.

Novelty and Significance Statement

The present work contains three novel aspects: $•$ The first Burnett-level CDBM is proposed for compressible reactive flows with both hydrodynamic and thermodynamic nonequilibrium effects. $•$ The reaction term is designed to naturally couple chemical reactions with physical fields, including conservation variables and high-order kinetic moments. $•$ The discrete velocity set with high spatial symmetry is constructed to ensure computational accuracy and numerical robustness. These contributions are helpful for exploring complex reactive flows beyond the Navier–Stokes level, which is crucial for advancing the predictive capability of combustion modeling in high-speed and high-gradient regimes.