Group velocity control scheme and two-dimensional Riemann solver

It is a challenging work to simulate flows with strong shock waves and contact discontinuities in the field of computational fluid dynamics, which are the basic elements of many practical flows. The 3rd order upwind compact scheme is of the character of high precision and high resolution, but numerical oscillation occurs when it is used to simulate shock waves. According to the characters of group velocity, a group velocity control (GVC) scheme was constructed based on the 3rd order upwind compact scheme, which can simulate the complex flows with strong shock waves and contact discontinuities correctly. Based on the GVC scheme, a numerical solver was constructed to simulate two-dimensional interface problems of high pressure ratio and high density ratio. Numerical results show that it is an effective method to identify shock waves and contact discontinuities.