An eighth-order filter method for a wide range of compressible flow speeds (H. C. Yee and B. Sjogreen, Proceedings of ICOSAHOM09, June 22–26, 2009, Trondheim, Norway) is employed for large eddy simulations (LES) of temporally evolving mixing layers (TML) for different convective Mach numbers (Mc) and Reynolds numbers. The high-order filter method is designed for accurate and efficient simulations of shock-free compressible turbulence, turbulence with shocklets, and turbulence with strong shocks with minimum tuning of scheme parameters. The value of the Mc considered is for the TML range from the quasi-incompressible regime to the highly compressible supersonic regime. The three main characteristics of compressible TML (the self-similarity property, compressibility effects, and the presence of large-scale structures with shocklets for high Mc) are considered for the LES study. The LES results that used the same scheme parameters for all studied cases agree well with experimental results and published direct numerical simulations (DNS). Published 2012. This article is a US Government work and is in the public domain in the USA.