A study of compressible turbulent Couette flow in a plane channel with isothermal wall was performed using large eddy simulation. Mach numbers, based on the wall velocity and sound speed at the wall, of 0.3 and 1.5 are considered; Reynolds number, defined in terms of the wall velocity and the channel half-width, is 1300. This paper addresses an effect of artificial viscosity both in cases with subsonic and supersonic wall-bounded turbulent flow to develop a highly resolute scheme suitable for large eddy simulation.