The Direct numerical simulation (DNS) of decaying compressible MHD turbulence is examined in this p& per for the purpose of investigating fundamental aspects of the interaction between flow, magnetic, and electric fields in aerospace related applications. The current emphasis of MHD turbulence differs from the traditional emphasis on astrophysical problems. A few results are surveyed on the differences between MHD turbulence and non-MHD turbulence. The full formulation is used in the present work in the sense that the three conservation equations for the magnetic induction field are calculated, in addition to the standard flow equations. The initial conditions on the flow and magnetic fields are discussed critically because of the focus on decaying turbulence. Calculations for non-random initial conditions are carried out using the high-order Padetype compact finite difference schemes and preliminary results are reported for a turbulence Reynolds number Re = 250, magnetic Reynolds number R, = 20, and magnetic pressure Reynolds number Rb = 0.1. The Mach numbers are 0.2 and 0.6.