Research on the implicit Runge-Kutta Scheme for the unsteady reactive nonequilibrium flow

In this paper, the implicit Runge-Kutta Scheme is derived to solve the NS equations, and its characters of stability, precision and efficiency are studied respectively. Some benchmark cases are calculated to validate the capabilities of the numerical program.The results show that the implicit R-K method given in this paper has high stability, high precision and high efficiency, which make it suitable to compute the unsteady reactive nonequilibrium flow.