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基于附加Runge-Kutta方法的高精度气相爆轰数值模拟

DOI: 10.11858/gywlxb.2013.02.010, PP. 230-238

Keywords: 源项,附加Runge-Kutta方法,刚性,气相爆轰

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Abstract:

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。

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