基于我们课题组以前提出的高速可压LBGK模型[Gan, Xu, Zhang, Yang, EPL 103 (2013) 24003]，发展了一个适用于模拟爆轰问题的离散Boltzmann模型。化学反应率模型采用只保留增长项的Lee模型。基于新构建的模型，模拟了不同反应速率的爆轰情形，找到了一个临界反应速率。当反应速率等于临界反应速率时，模拟的结果与CJ理论值符合较好。当反应速率低于临界反应速率时，爆轰波的波结构中会出现von-Neumann峰，之后从峰值点过渡到稳态，稳态为CJ爆轰状态。当反应速率高于临界反应速率时，爆轰波会以高于CJ爆轰波速的速度向前传播，稳态为弱爆轰状态。
Based on the high-speed compressible model proposed in our group [Gan, Xu, Zhang, Yang, EPL 103 (2013) 24003], a new discrete Boltzmann model for detonation is presented. A new reaction rate function is adopted which comes from Lee’s model but only the growth term is used. Based on the new model, several kinds of detonations with different reaction rates are simulated and a critical reaction rate is found. In the case where the value of reaction rate equals to the critical value, the simulation results coincide well with CJ theory. In the cases where the reaction rates are lower than the critical value, the von-Neumann peak will appear firstly and then steady state is reached behind the detonation wave. The steady states in those cases are in the CJ detonation states. In the cases where reaction rates are higher than the critical rate, the detonation wave propagates at a speed faster than that of CJ detonation and the steady states in those cases are in the weak detonation states.
Nikolaev, Yu.A., Vasil’ev, A.A. and Ul’yanitskii, B.Yu. (2003) Gas detonation and its application in engineering and technologies. Combustion, Explosion, and Shock Waves, 39, 382-410. http://dx.doi.org/10.1023/A:1024726619703