We present our numerical results for certain unsteady flows past oscillating cylinders and aerofoils. The computations are based on the stabilized space‐time finite element formulation. The implicit equation systems resulting from the space‐time finite element discretizations are solved using iterative solution techniques.

One of the problems studied is flow past a cylinder which is forced to oscillate in the horizontal direction. In this case we observe a change from an unsymmetric mode of vortex shedding to a symmetric one. An extensive study was carried out for the case in which a cylinder is mounted on lightly damped springs and allowed to oscillate in the vertical direction. In this case the motion of the cylinder needs to be determined as part of the solution, and under certain conditions this motion changes the vortex‐shedding pattern of the flow field significantly. This non‐linear fluid‐structure interaction exhibits certain interesting behaviour such as ‘lock‐in’ and ‘hysteresis’, which are in good agreement with the laboratory experiments carried out by other researchers in the past. Preliminary results for flow past a pitching aerofoil are also presented.