In this article a multiblock finite-volume technique with a second-order total variation diminishing spatial discretization and an efficient implicit time integration has been developed to simulate complex internal flows at high Mach numbers. This method employs a lower and upper approximate factorization of the implicit operator with symmetric successive over relaxation sweeps. In the presence of multiblocks, an asynchronousinterface treatment has been devised for an accurate coupling of the blocks. A detailed validation by comparison of the computed results with experiments has shown the capabilities of the method to resolve complex highspeed internal flows and to simulate the influence of bleed as a boundary-layer control system.