We present high resolution numerical simulations of incompressible two-dimensional flows in tube bundles, staggered or in-line, as encountered in heat exchangers or chemical reactors. We study the time evolution of several flows in arrays of cylinders, squares and double-cruciform shaped tubes at a Reynolds number of 200. The numerical scheme is either based on adaptive wavelet or Fourier pseudo-spectral space discretization with adaptive time stepping. A volume penalization method is used to impose no-slip boundary conditions on the tubes. Lift and drag coefficients for the different geometries of tube bundles are compared and perspectives for fluid–structure interaction are given.