SOLUTION OF THE STEADY EULER EQUATIONS IN A GENERALIZED LAGRANGIAN FORMULATION

A second-order Godunov-type shock-capturing scheme for solving the steady Euler equations in generalized Lagrangian coordinates has been developed and applied to compute steady supersonic and hypersonic now problems. Following Hui and Zhao, the Lagrangian distance and a stream function are used as the coordinate lines that not only simplify the Riemann solution procedure but also have an intrinsic flow adaptive property embedded. Numerical examples for various supersonic flows involving strong flow discontinuities are given. Good agreement is obtained between computed results and shock expansion theory or available experimental data. It was found that the resolution of the slip line is almost exactly without smearing, the resolution of shock is always crisp even at increasing Mach number, and the Prandtl-Meyer expansion is adequately resolved with the second-order-accurate scheme