Multiscale methods in computational fluid and solid mechanics

First, an attempt is made towards gaining a more systematic understanding of recent progress in multiscale modelling in computational solid and fluid mechanics. Sub- sequently, the discussion is focused on variational multiscale methods for the compressible and incompressible Navier-Stokes equations. Examples are given of the application of this class of methods to a turbulent channel flow. Finally, multigrid methods, which can also be conceived as a subclass of multiscale methods, are applied to fluid-structure interaction problems. 1