Large eddy simulations of the transition process in a supersonic flat-plate boundary layer at free-stream Mach number of 4.5 and Reynolds number of 10000 were carried out using high precision weighted essentially non-oscillation (WENO) schemes. The inviscid flux was discretized by fifth-order

seventh-order

ninth-order WENO schemes separately and the viscous flux was discretized by fourth-order center difference scheme. The temporal discretization was made by means of third-order Runge-Kutta with total variation diminishing(TVD). By imposing a pair of the most unstable oblique first-mode disturbances on the inflow boundary

the transition progress of the flow from laminar

transition process to full turbulence was compared using three WENO schemes. Results indicate that the fifth-order WENO scheme is more dissipative than the seventh-order and ninth-order schemes

so it's difficult to capture eddy and pulse in the flow field. The dissipation of ninth-order WENO scheme is small

enabling to capture smaller eddy and high frequency. To study a problem with high frequency fluctuation or capture fine eddy

it's advisable to use the scheme higher than seventh-order.