The inner flow fields of scramjet intake model are simulated numerically by two dimensional Euler equations using an implicit finite difference scheme. For this simulations, the numerical scheme based on chakravarthy Osher's type TVD formulations is improved for both multi-grid and moving-grid application. To investigate the methods of recovery from unstart conditions in scramjet, at first, the dynamic and numerical simulations were conducted from steady condition to unstart condition using moving-grid.