爆轰问题的一个高效二维离散玻尔兹曼模型

An Efficient Two-Dimensional Discrete Boltzmann Model of Detonation

摘要: 本文构建了多松弛时间离散玻尔兹曼模型，并使用该模型模拟爆轰现象。相对于我们之前的一个模型[Xu A., Lin C., Zhang G., Li Y., Phys. Rev. E 91 (2015) 043306]，本模型在模拟有化学反应或无化学反应流体系统时的计算效率更高。这是因为前者使用了24个离散速度，而本模型只使用16个。在模拟部分高马赫物理系统时，本模型表现出更高的数值稳定性。使用该模型，本文分四种情况模拟了爆轰波激发的Richtmyer-Meshkov不稳定性问题。当爆轰波由反应物传向另一种较轻的不反应的物质时，由于突然失去能量补充，温度急剧下降，在物质界附近将会出现一层高密区域。

Abstract: A modified multiple-relaxation-time discrete Boltzmann model is proposed to simulate detona-tion. Compared with our previous model [A. Xu, C. Lin, G. Zhang, Y. Li, Phys. Rev. E 91 (2015) 043306] adopting 24 discrete velocities, this model employs only 16 ones and consequently has smaller computational cost of simulating reactive or nonreactive fluid flows. Additionally, this model has a better stability than the previous one in our numerical tests. Using this model, we simulate the Richtmyer-Meshkov instability induced by detonation wave in four cases. It is in-teresting to find that, when a detonation wave travels from the chemical reactant to a lighter nonreactive medium, since the chemical energy does not release any more, the temperature re-duces suddenly, and consequently a region with higher density exists around the material in-terface.