Abstract: Limiting flux method is used to improve the compact schemes for discontinuous fluid problems. A limiter is contrived. A series of calculation with third-order to 8th-order schemes are given. It is shown that the limiting flux method provides solutions with high-order accuracy and high resolutions. And it restrains numerical oscillations as well. The limited flux compact scheme is robust in a large range of Mach numbers. It is able to capture discontinuities in fewer grids.

Key words: compact scheme, limit flux, high-order scheme, differential scheme, shock capture