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中文摘要：
我们这里为与一个生硬来源学期计算反应 Euler 方程报导添加剂 Runge-Kutta 方法，并且特别地，他们在气体的爆炸模拟的应用。在气体的爆炸的来源术语在这些时间规模的反应过程和一些多是的热化学药品的非平衡期间由于时间规模的宽范围的存在是生硬的比水动力学的小流动。高顺序， L 稳定，当非生硬的部分明确地被处理时，在这份报纸建议的添加剂 Runge-Kutta 方法变成了生硬来源术语生硬部分和非生硬的部分，生硬部分含蓄地在被解决。建议方法成功地被用于基于由 9 种类和 19 基本反应组成的一个详细基本化学反应模型在 stoichiometric H2/O2/Ar 混合物模仿气体的爆炸。结果证明僵硬地精确的添加剂 Runge-Kutta 方法能捕获断绝很好，并且精确地描述爆炸建筑群波浪配置例如三倍的波浪结构和细胞的模式。
英文摘要：
We report here the additive Runge-Kutta methods for computing reactive Euler equations with a stiff source term, and in particu- lar, their applications in gaseous detonation simulations. The source term in gaseous detonation is stiff due to the presence of wide range of time scales during thermal-chemical non-equilibrium reactive processes and some of these time scales are much smaller than that of hydrodynamic flow. The high order, L-stable, additive Runge-Kutta methods proposed in this paper resolved the stiff source term into the stiff part and non-stiff part, in which the stiff part was solved implicitly while the non-stiff part was handled explicitly. The proposed method was successfully applied to simulating the gaseous detonation in a stoichiometric HE/O2/Ar mix- ture based on a detailed elementary chemical reaction model comprised of 9 species and 19 elementary reactions. The results showed that the stiffly accurate additive Runge-Kutta methods can capture the discontinuity well, and describe the detonation complex wave configurations accurately such as the triple wave structure and cellular pattern.
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