Based on a high-order compact upwind scheme,a high-order shock-fitting finite difference scheme is studied for numerical simulation of the generation of boundary layer disturbance waves due to free-stream waves.Both steady and unsteady flow solutions of the receptivity problem are obtained by computing full Navier-Stokes equations.Numerical simulation of receptivity to free-stream disturbances for hypersonic boundary layers is performed.

Based on the Fourier analysis method, a fully-discretized dispersion relation is derived for a family of high accuracy upwind compact difference schemes by considering one dimensional linear convetion equation temporally discretized by the explicit multi-step Runge-Kutta algorithm. The effects of CFL numbers on the characteristics of these schemes, including dissipation and dispersion errors, phase velocity and group velocity, are analyzed. The two-dimensional anisotropy problem is discussed. Moreover, an eigenvalue analysis is performed. Two numerical examples are used to show the high accuracy and resolution of these schemes.

A high order accurate finite difference scheme is proposed in light of the upwind compact method^[1].The flux vectors in Euler equations are approximated by using upwind compact difference.In order to prevent the nonphysical oscillations in the vicinity of the shock the group velocity control(GVC)method is used.The reason of oscillation production in numerical solutions is nonuniformity of group velocity of wave packets.GVC is for improvement of the shock resolution.The present scheme has third order accruracy in smooth regions.

The stability of temporally evolving compressible plane mixing layers is investigated numerically by solving the three dimensional compressible linear disturbance equations.A high order finite difference method is used.The effects of key parameters such as convective Mach number and Reynolds number on the stability characteristics of compressible mixing layers are analyzed.The comparsions between two and three dimensional,viscous and inviscid disturbances are presented.Part of the numerical results obtained here are in agreement with those of relative literature.

Inorder to simulate multiscale physical problems constructing high order accurate difference schemes is needed. The fourth order accurate compact scheme is reconstructed using the method of diffusion analogy developed by authors in order to make the scheme dissipative. The modified compact scheme with fourth order accuracy in space and third order accuracy in time is used to compute the 2-D shock reflection problems. The computed results show the scheme developod to correctly simulate multiscaler physical problems also can be used to capture the shock well.

In this paper, we present a modified implicit ENO scheme and combine it with CSCM-like implicit supra-characteristic boundary treatment. Numencal experiment with this scheme for 2-D channel fupersonic flow aboat 4% circular arc has damenstrated the sharp shock-capturing capability of the scheme. The results are also compared with those of TVD scheme. The futher application to the viscid flow in simplified inlet is made. They show a good agreelment with the results of SIP/Beam-warming schemes except nearby the reflection point of shock. But our results seem to be more reasonable.

A upwind compact scheme with dispersion regulator is developed and discussed. The scheme developed is dissipative and the dispersion term in the truncation error can be controlled. According to the behaviour of the flow parameters near the shock the scheme with specially chosen control function gives high resolution. The scheme is simple, efficient and the shock can be captured well. The scheme is used to compute the shock reflection problem, and the computed results are satisfactory.