Amethod for simulating moving impermeable boundaries within a fixed Cartesian mesh is described. The scheme leverages the automated volume mesh generation process which has previously been demonstrated for static geometries. An implicit dual-time method is used for the time advance, which limits the number of times the geometry must be intersected with the Cartesian volume mesh over a complete simulation. A general motion is decomposed into a rigid-body motion of the entire computational domain, with a relative-body motion superimposed. The rigid-domain motion is treated using an ALE formulation, which confines the required geometry processing only to the regions of relative motion within the domain. A detailed space-time analysis is used to present and discuss the moving-boundary scheme, with particular attention given to complexities arising in multiple dimensions. A hierarchy of conservative approximations for the evolution of the moving geometry over a timestep is presented. Preliminary results are discussed in one, two and three dimensions using CFL numbers based upon the moving wall velocity of between 1 and 20.