Multi-dimensional code has been developed to simulate the effect of geometry on mass flow rate and flow pattern in the induction system of an internal combustion engine. The unsteady compressible Navier-Stokes equations in general curvilinear coordinates are solved by a new method of lines. In the method of lines, the governing equations are spatially discretized by a finite difference approximation and the resulting system of ordinary differential equations is integrated. As a time integration scheme, we newly propose to use the rational Runge-Kutta scheme in order to efficiently simulate the flows in the induction system. The domain-decomposition technique is introduced so that body-fitted structured grid can be easily generated for such complex geometry as a real intake port shape. The present code is applied to 2 and 3 dimensional steady flows in intake port/cylinder assembly with a valve. The results show that the present method can be adapted easily to complex geometry and efficiently produce reliable solution on a vector super-computer.