The computational domain used in flow simulation is usually based on piecewise-linear representations, yielding triangular/tetrahedral or quadrangular/hexahedral grids. However, it deals with a second-order approximation of the geometry only, although more accurate representations are often available, for instance when the geometry is defined using Computer-Aided Design (CAD) techniques. Despite the progress in mesh generation, this has not really changed for thirty years. At the same time, flow simulation has evolved significantly, using very high-order schemes, being embedded in multidisciplinary analyses or optimization loops, involving more and more complex models. In this context, is it reasonable to continue using low-order representations for the geometry ? How to move to higher-order, possibly exact with respect to CAD data, geometrical representations ?