High-order modified flux approach(MFA) type essentially non-oscillating (ENO) schemes with the artificial compression method(ACM) are developed to capture shocks and contact surfaces in unsteady compressible flows and to calculate acoustic wave propagation, the amplitude of which is generally small compared with flow quantities. In order to obtain high resolution near the discontinuities and to resolve the small amplitudes, in this paper the artificial compression method(ACM) is successfully applied to the high-order MFA-ENO schemes which are developed in this paper. To reduce the additional computational time for the ACM, we use the delta forms of the characteristic variables and apply the ACM to all the characteristic waves, including the acoustic wave. The results show that these schemes give high resolution in capturing shocks, contact surfaces, and small-amplitude acoustic waves. In one-dimensional case, the scalar waves and shock interaction problems are calculated to test the high-order schemes. In two-dimensional case, shock wave with a compression corner and acoustic radiation in a baffled plane are studied. Also, in an axisymmetric shock tube, the exhaust jet flow excited by a blast wave expelled are investigated. The ENO schemes are extended to the Navier-Stokes equation to simulate the steady viscous flow.
