The turbulence-generation mechanism in the intake and compression processes of an engine with a square cylinder is investigated by performing a three-dimensional numerical simulation. Emphasis is placed on the influences of the intake turbulence and the compression effect on the TDC turbulence. The compressible Navier-Stokes equations are solved without any explicit turbulence models. The employed numerical algorithm is an extended version of the ICE method, and the third-order upwind scheme is employed for the convective terms. The obtained computational results agreed well with the experimental visualization using freon as the working fluid under the Mach-number condition over 0.5. It is shown that the drastic transition to turbulence near TDC is grasped by computations using this numerical method.