基于附加Runge-Kutta方法的高精度气相爆轰数值模拟

摘要

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 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 simulate the gaseous detonation in a stoichiometric H2-O2-Ar mixture 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 well capture the discontinuity,and accurately describe the detonation complex wave configurations such as the triple wave structure and cellular pattern.