| We present finite difference methods for two and three dimensional nonequilibrium hypersonic flow problems. The description of the flowfield is based on the Euler equations and a chemical reaction model accounting for the finite rate reactions. The Euler and chemical equations are strongly coupled. At high Mach number, very high temperature behind the main shock causes steep gradients immediately behind the shock and strong stiffness in the shock layer that make numerical computation difficult. The existance of an entropy layer near the body causes similar problem.; To obtain accurate numerical results for such problems efficiently, we adopt the following four techniques: a "shock-fitting method" to determine the exact boundary of the high temperature region; a smooth coordinate transformation of computational domain to avoid difficulties arising from the lack of resolution immediately behind the shock and near the body; combination of implicit and explicit schemes in order to make the computation efficient; implicit treatment of the right hand side terms to overcome the difficulties due to the stiffness. Here "shock-fitting" means that in the process of computation, we take all the strong and weak discontinuities as boundaries dividing the computational region into several zones.; Using our method with implicit finite difference schemes, we were able to compute the flow about a concave corner until a very large distance from the corner without encountering any numerical difficulties. We obtained the limit of shock angle easily. The flow properties converged to their equilibrium limits in the shock layer, except near the shock and near the body where the steep gradients exist.; 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 become singular at the interaction point. There exist a new main shock, a contact discontinuity and an expansion wave. Therefore, the problem is very complicated. Using proper combinations of implicit and explicit schemes according to the property of the equations and boundary conditions, we obtained accurate computational result for the flow behind the interaction point. |
