(untitled) (Journal of Computational Mathematics, 2021)
A shock interaction problem is solved with finite difference methods for a hypersonic flow of air with chemical reactions. If a body has two concave corners, a secondary shock is formed in the shock layer and it meets the main shock later. As the two shocks meet, the flow becomes singular at the interaction point, and a new main shock, a contact discontinuity and an expansion wave appear as a result of interaction between the two shocks. Therefore, the problem is very complicated. Using proper combinations of implicit and explicit finite difference schemes according to the property of the equations and the boundary conditions, we compute the flow behind the interaction point successfully.