高超声速化学反应源项雅可比矩阵的对角化

Diagonalization on Jacobian matrix of source term for hypersonic chemical reactive flows

基于Von Neumann稳定性理论,对高超声速化学反应流中源项雅可比(Jacobian)矩阵应用不同对角化方法的耦合隐式格式进行稳定性分析。详细推导出对角化方法情况下数值方法的增长因子,并分析不同对角化方法条件下的增长因子与CFL(Courant-Friedrichs-Lewy)数及波数之间的关系。理论分析与数值验证表明,Kim方法较Eberhardt和Ju方法更适合源项雅可比矩阵的对角化,保证数值求解在较大的CFL数条件下也能够实现稳定快速计算。另外,结合计算得到的刚性参数,稳定性分析结果还指出在高超声速化学反应外部流场中,激波与驻点之间的亚声速高温高压状态是导致数值格式计算不稳定的物理因素。

The stability of a coupled implicit scheme,in which the Jacobian matrix of chemical source term is diagonalized by different methods,is mainly studied based on Von Neumann stability theory.The amplification factor of the present schemes,which use different diagonalized methods,is deduced in detail in paper,and its relations with the courant-Friedrichs-Lewy（CFL）number and the wave number are analyzed.The theoretical analyses and numerical validations show that,the Kim method is more suitable for diagonalizing the Jacobian matrix than the Eberhardt and Ju methods,so that the steadier and more efficient computation can also be achieved for larger CFL number.In addition,with the stiffness parameters obtained,the analyses still show that the computational instability mainly results from the high temperature and pressure with subsonic state between the shock and stagnation point in the outer flow field of hypersonic reactive flows.