Computation of the three-dimensional flow in the intake ports and the cylinders of real engines, including moving valves and piston, has been carried out by solving the Navier-Stokes equations. No explicit turbulence models are used. An extended version of the SIMPLE and ICE method is employed to simulate density variations in engines, which are connected with compression rate, heat transfer, and compressibility. A third-order upwind scheme is combined with this method. Computational results show complex flow fields such as separated flows near the valve seat and small vortices of the order of the mesh size near the end of compression. These computational results are compared with the LDV measurements.