A Lagrangian random vortex-boundary element method has been developed for the simulation of unsteady incompressible flow inside three-dimensional domains with time-dependent boundaries, similar to IC engines. The solution method is entirely grid-free in the fluid domain and eliminates the difficult task of volumetric meshing of the complex engine geometry. Furthermore, due to the Lagrangian evaluation of the convective processes, numerical viscosity is virtually removed; thus permitting the direct simulation of flow at high Reynolds numbers. In this paper, a brief description of the numerical methodology is given, followed by an example of induction flow in an off-centered port-cylinder assembly with a harmonically driven piston and a valve seat situated directly below the port. The predicted flow is shown to resemble the flow visualization results of a laboratory experiment, despite the crude approximation used to represent the geometry.