Relaxation schemes for inviscid transonic flows

A class of numerical schemes for inviscid transonic flows are studied in this thesis. They are based on second order accurate central difference approximations(box-scheme) to the viscous-transonic equation. A successive line relaxation method (SLR), an alternating direction implicit method (ADI) and a multigrid ADI method are developed for solving the non-linear difference equations. Inviscid transonic flows over a symmetric airfoil at zero-angle of attack in an infinite domain and in a wind-tunnel environment with wall suction are computed using the three relaxation schemes. Both subcritical and supercritical flows are calculated. Convergence histories of the approximate solutions show that the ADI method is about three times faster than the line relaxation method and multigrid ADI method is about twice as fast as the ADI method.