Time-developing turbulent boundary layers over an isothermal flat plate at free-stream Mach numbers of 0.3 and 0.7 are computed using an explicit finite-difference method on structured multi-block grids. The size of each block is adjusted depending on the dimension of the largest structures present locally in the flow. This alleviates the cost of calculations in which the wall layer is resolved, and may result in substantial savings of memory and CPU time, if several layers are used. In the calculations presented the near-wall region is computed using a domain with a spanwise length Lo+ = 820, which is sufficient to contain several streaks. This grid block is repeated periodically in the spanwise direction. The outer layer, which contains larger structures, is computed using a domain that is twice as wide (Lo+ = 1640). Although the flow at the interface between the blocks has a periodicity length determined by the inner-layer block, within a few grid points longer wavelengths are generated. The velocity statistics and rms intensities compare well with single-block calculations that use substantially more grid points.