基于附加Runge-Kutta方法的高精度气相爆轰数值模拟

Additive Runge-Kutta Methods for Accurate H_2-O_2-Ar Detonation Simulation

多组分反应欧拉方程是气相爆轰的控制方程,其源项存在刚性。应用显式格式求解,由于格式稳定性条件的限制,时间步长远小于CFL(Courant-Friedrichs-Lewy)条件得出的时间步长,给求解带来很大困难。引入一种IMEX(Implicit-Explicit)型附加Runge-Kutta算法,对非刚性对流项进行显式处理,源项用半隐式格式处理,整体具有高精度和L-稳定性,并进行算例考核。在此基础上,利用基元反应模型对气相爆轰问题进行了数值研究。结果表明,该算法能够很好地处理源项引起的刚性问题,准确地捕捉和描述爆轰波的复杂结构和典型特征,同时也能够很好地模拟爆轰波在楔面上的马赫反射问题。

We report here the additive Runge-Kutta methods for computing reactive Euler equations with a stiff source term, and in particular, 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 ther- mal-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 simulate the gaseous detonation in a stoichiometric H2-O2-Ar mixture based on a detailed el- ementary chemical reaction model comprised of 9 species and 19 elementary reactions. The results showed that the stiffly-accurate additive Runge-Kutta methods can well capture the discontinuity,and accurately describe the detonation complex wave configurations such as the triple wave structure and cellular pattern.