Abstract: A new difference scheme called GVC8 is developed, and thescheme are used in the direct numerical simulation of decaying compressibleturbulence. In the DNS we have successfully improved the turbulent Machnumber up to 0.95. The statistical quantities thus obtained at lowerturbulent Mach number agree well with those from previous authors start withsame initial conditions, but they are limited to simulate at lower turbulentMach numbers due to so-called start-up problem. Energy spectrum ofcompressible turbulent flow is analyzed.